|
Unit |
Functions
& Limits |
|
01 |
Multiple Choice Questions
q
Each question has four
possible answers. Select the correct answer and encircle it.
Q.1
The term
function was introduced by:
(a) Euler (b) Newton
(c) Lagrange (d) Leibniz
Q.2
The symbol y = f(x) i.e. y
is equal to f of x, invented by Swiss mathematician
---------. 12801002
(a) Euler (b) Cauchy
(c) Leibniz (d) Newton
Q.3
A function
P(x) = 6x + 7x + 5x + 1 is called a polynomial function of degree
---------- with leading coefficient ------------.
12801003
(a) 4 , 6 (b) 2 , 7
(c) 2 , 3 (d) 2 , 5
Q.4
If a
variable y depends on a variable x
in such a way that each value of x determines exactly one value of y, then y is a ------------ of x. 12801004
(a) Independent variable
(b) not function
(c) function (d) None of these
Q.5
A function, in which the
variables are
------------ numbers, then function is
called a real-valued function of real numbers.
12801005
(a) complex (b) rational
(c) real (d) None of these
Q.6
Let ¦(x) =
x + , then ¦ = 12801006
(a) ¦(x+ 1) (b) ¦(x)
(c) (d) ¦(x)
Q.7
If ¦(x) =
, then ¦(cos x)
equals:
12801007
(a) 2 tan (b) tan
(c) tanx (d) cot
Q.8
Domain of
the rational function
y = is: 12801008
(a) Q(x)
> 0 (b) Q(x)
< 0
(c) Q(x)
= 0 (d) Q(x)
¹ 0
Q.9
For the
function ¦(x) =
, f(1) is:
12801009
(a) x
+ 1 (b) undefined
(c) indeterminate
(d) zero
Q.10
If a
function f is from a set X to a set Y, then set X is called the ------------ of
f.
12801010
(a) domain (b) range
(c) co-domain (d) None of these
Q.11
Let ¦(x) =
then domain of ¦ is the set of all real numbers except: 12801011
(a) 0 (b) 1
(c) 2 (d) 3
Q.12
Let ¦(x) =
x, real valued function then domain of ¦ is the set of all: 12801012
(a) real numbers (b) integers
(c) complex numbers
(d) natural numbers
Q.13
Let ¦(x) = , then domain of ¦ is the set of all real numbers except: 12801013
(a) 4, - 4 (b) 0
(c) 2, - 2 (d) 0, 4
Q.14
If ¦(x)= , then domain of ¦(x)
is: 12801014
(a) [ 0,
¥) (b) [ – 1, ¥)
(c)
[ 1, ¥] (d) [ 1, ¥)
Q.15
If ¦(x) =
, then range of ¦(x)
is: (Board 2007) 12801015
(a) (– ¥, ¥) (b) [ – ¥, ¥ ]
(c) [
0, ¥) (d) [
– 1, ¥)
Q.16 The domain of the function
¦(x)= is: 12801016
(a) R (b) R – { 2}
(c) R
– {2 , –2} (d) R – {– 2}
Q.17
The range
of the function ¦(x) =
|x|
is:
(a) (– ¥ , ¥) (b) [0,
¥) 12801017
(c)
(– ¥, 0] (d) (0, ¥)
Q.18
Let ¦(x) =
x, then range of ¦ is the set of all: 12801018
(a) real numbers
(b) non-negative real numbers
(c) non-negative integers
(d) complex numbers
Q.19
Let ¦(x) =
x+ 3, then domain of ¦ is the: 12801019
(a) Set of all integers
(b) Set of natural numbers
(c) Set of real numbers
(d) Set of rational numbers
Q.20
Domain 
= Range f
and Range
=
------------. 12801020
(a)
Domain f
(b)
Range f
(c)
Domain 
(d)
None of these
Q.21
A function
P(x) = ax + ax
+ ax + … + ax + ax + a is called a polynomial function of degree n, with
leading coefficient a. 12801021
(a)
a = 0 (b) a = 0
(c)
a ¹ 0 (d) a ¹ 0
Q.22
A function,
in which the variable appears as exponent (power), is called a\an ------------
function. 12801022
(a)
constant (b) explicit
(c)
exponential (d) inverse
Q.23
Let ¦(x) =
, then range of ¦ is the set:
12801023
(a) ] - ¥, ¥ [
(b) [0, ¥)
(c) [3, ¥]
(d) [ -3, 3]
Q.24
Which of
the following functions is a polynomial function? 12801044
(a) 
,
x ¹
-
2
(b) x+ 6x+ 7x+ x+ + 4
(c)
(d) ax+ b + c
Q.25
If the
degree of a polynomial function is ----------, then it is called a linear
function.
(a)
0 (b) 1
12801025
(c)
2 (d) 3
Q.26
Let X and Y
be the set of real numbers, a function C : X ® Y defined by C(x) = a " x Î X , a Î Y and a is a constant number. Then C is called a\an
------------ function. 12801026
(a)
constant
(b) implicit
(c)
identity
(d) inverse
Q.27
Which of
the following is a rational function? 12801027
(a) , x ¹ - 2
(b) , x > 0
(c)
(d) , x ¹ 5
Q.28
Which one
is a constant function?
(a) f(x) = x (b) f(x) = x 12801028
(c) f (x) = x + 1 (d) f(x) =
14
Q.29
A function
I : X ® X for any set X, of the form I(x) = x " x Î X is called a\an
------------ function. 12801029
(a)
constant (b) implicit
(c)
identity (d) inverse
Q.30 If x and y are so mixed up and y cannot be expressed in terms of the
independent variable x, then y is called a\an ------------ function of x. 12801030
(a)
constant (b) explicit
(c)
implicit (d) inverse
Q.31 Which one is an identity function?
12801031
(a) f(x)
=
(b) f(x)
= g(x)
(c) f (x)
= x
(d) f(x)
= 1
Q.32
Which one
is not an exponential function? 12801032
(a) 3 (b) n
(c) e (d) x
Q.33
Which one
is an exponential function?
(a) 2 (b) x 12801033
(c) logx (d) x
Q.34
If ¦(x) = ax + b, where a ¹ 0 , a and b are real numbers, then ¦(x) is a: 12801034
(a) constant function
(b) absolute linear function
(c) linear
function
(d) quadratic function
Q.35
y = logx, where a > 0 and a ¹ 1 is called a
------------- function of x. 12801035
(a)
implicit (b) explicit
(c)
exponential (d) logarithmic
Q.36
y = logx is known as
the ----------- of x. 12801036
(a)
common logarithmic
(b)
natural logarithmic
(c)
exponential (d) None of these
Q.37
If f(x) = |x| , f(x) is a 12801037
(a) constant function
(b) absolute function
(c)
linear function
(d) quadratic function
Q.38
If x =
, Then y =
logx = ln x, is known as the ------------ of x. 12801038
(a)
common logarithmic
(b)
natural logarithmic
(c)
exponential
(d)
None of these
Q.39
sinh x =
12801039
(a) 
(b) 
(c) 
(d) 
Q.40
cosh x =
12801040
(a) (b)
(c) 
(d) 
Q.41
tanh x = 12801041
(a) 
(b)
(c) 
(d) 
Q.42
sech x = 12801042
(a) 
(b) 
(c) (d)
Q.43
csch x =
12801043
(a) 
(b)
(c) (d)
Q.44
coth x =
12801044
(a)
(b)
(c) 
(d)
Q.45
coshx - sinhx = 12801045
(a) 1 (b) - 1
(c) 2 (d) - 2
Q.46
coshx + sinhx = 12801046
(a) cosh x (b)
cosh 2x
(c) sinh 2x (d) tanh 2x
Q.47
sinh–1x = 12801047
(a) ln (x + ) x > 1
(b) ln (x + ) for all x
(c) 
(d) ln 0 <
x < 1
Q.48 cosh–1x = 12801048
(a) ln (1 + ) x > 1
(b) ln (x +
) 
(c) 
0 < x < 1
(d) 
Q.49
tanh–1x = 12801049
(a) ln |x| < 1
(b) ln |x| < 1
(c) ln 
0 < x < 1
(d) ln
x 
0
Q.50
sech–1x = 12801050
(a) ln |x| < 1
(b) ln x 0
(c) ln 0 < x <
1
(d) ln | x |
< 1
Q.51
csch–1x = 12801051
(a) ln x 0
(b) ln 0 < x <
1
(c) ln 
x
0
(d) ln |x| <
1
Q.52
coth–1x = 12801052
(a) ln |x| < 2
(b) ln |x| < 1
(c) ln |x| 0
(d) ln x > 1
Q.53
Inverse
hyperbolic functions are expressed in terms of natural: 12801053
(a) numbers (b) exponentials
(c) logarithms (d) sines
Q.54
Which one
is an explicit function?
(a) x+ 2xy + y + 7 = 0 12801054
(b) xy
+ xy + xy+ 1 = 0
(c) y =
x+ x+ + 10
(d) xy+ y+ xy = 4
Q.55
y = is a\an ------------ function of x. 12801055
(a)
constant
(b) implicit
(c)
explicit
(d) inverse
Q.56
Which one
is an implicit function?
(a) y =
¦(x) (b) ¦(x, y) = c 12801056
(c) x =
¦(u), y = g(u)
(d) y =
¦(u), u = g(x)
Q.57
Which one
is an implicit function?
(a) xy + xy+ x+ y = 2 12801057
(b) y =
x+ 1
(c) x+ x+ x + 1 = y
(d) y =
f(x)
Q.58
Which one
is an explicit function?
(a) y =
¦(x) 12801058
(b) ¦(x, y) = 0
(c) x =
¦(t), y = g(t)
(d) none of these
Q.59
Every
relation, which can be represented by a linear equation in two variables,
represents a: 12801059
(a) graph
(b) function
(c)
cartesian product
(d) relation
Q.60
A function
from set X to set Y is denoted by: 12801060
(a) ¦ : X ® X
(b) ¦ : Y ® Y
(c) ¦ : X ® Y
(d) ¦ : Y ® X
Q.61
If y is an image of x under the
function f, we denote it by: 12801061
(a) x =
¦(y) (b) x = y
(c) y =
¦(x) (d) ¦(x, y) = c
Q.62
The value
of the parameter a, for which the function ¦(x) = 1 + ax, a ¹ 0 is the inverse of itself is: 12801062
(a) 1 (b) - 1
(c) 2 (d) - 2
Q.63
The curves
y = |x|+ 2|x|+ 1 and
y = x3+ 2x2+
1 have the same graph for:
(a) x
> 0 (b) x
³ 0 12801063
(c) x ¹ 0 (d) all x
Q.64
Parametric
equations x = a cos t,
y = a sin t represent the equation of:
(a) line (b) circle 12801064
(c) parabola (d) ellipse
Q.65
Parametric
equations: x = a cos q,
y = b sin q represent the equation of: 12801065
(a) parabola (b) hyperbola (c)
ellipse (d) circle
Q.66 Parametric equations x = a sec q,
y = b tan q represent the equation of: 12801066
(a) line (b) parabola
(c) ellipse (d) hyperbola
Q.67
If f(x) = , x ¹1 then f–1 (x) equals
(a) (b) 12801067
(c)
(d)
Q.68
Inverse of
¦(x) = is: 12801068
(a) ¦–1 (x) = x- 1
(b) ¦–1 (x) =
(c) ¦–1 (x) = 1 - x
(d) ¦–1 (x) = x+ 1
Q.69
Let ¦(x) =
4 - x,
g(x) = 2x + 1, then
¦og (x)
is: 12801069
(a) 5 + 2x
(b) 3 - 2x
(c) 2 + 3x
(d) 2 - 3x
Q.70 The perimeter P of square as a function of its
area A is: 12801070
(a) (b) 2
(c)
4 (d)
Q.71 The area A of a circle as a function of its
circumference C is: 12801071
(a) (b)
(c)
(d)
Q.72
The volume
V of a cube as a function of the area A of its base is: 12801072
(a) (b) A
(c)
(d)
Q.73
If f(-x) = f(x) for all x in the domain
of f, then f is : 12801073
(a) constant function
(b) identity function
(c) even function
(d) odd function
Q.74 If f(- x) = - f(x)
for all x in the domain of f, then f
is: 12801074
(a) linear function
(b) identity function
(c) odd function
(d) even function
Q.75
If f (x) is odd
function. If and only if:
(a) f(– x)
= – f(x) 12801075
(b) f(– x)
= f(x)
(c)
f(x) = 3f( – x)
(d) f(x)=
– 3f( – x)
Q.76
f(x) is even function. If and
only if:
(a) f(– x) = – f(x) 12801076
(b) f(– x) = f(x)
(c)
f(x) = 3f(– x)
(d) f(x) = – 3f(– x)
Q.77 If f is any function, then is always: 12801077
(a) even (b)
odd
(c)
one-one (d) zero
Q.78
f(x) = sin
x + cos x is ------------ function. 12801078
(a)
even
(b)
odd
(c)
composite
(d)
neither even nor odd function
Q.79
Let f(x)
= cos x, then f(x) is an: 12801079
(a) even function
(b) odd function
(c) power function
(d) none of these
Q.80 Let f(x)
= x+ sin x, then f(x) is: 12801080
(a) even function
(b) odd function
(c) power function
(d) none of these
Q.81
Let f(x)= x+ cos x,
then f(x) is: 12801081
(a) an odd function
(b) an even function
(c) neither even nor odd
(d) a constant
function
Q.82
If f(x)
= x + 1, then the value of fof is equal to: 12801082
(a) x + 2x + 1
(b) x – 2x + 2
(c)
x + 2x + 2
(d) x + 2x – 2
Q.83
If a relation
is given by: 12801083
R = 
then Dom of
R is
(a)
{ 2, 4, 6 ,10 } (b) { 2, 4, 6 }
(c)
{ } (d) { 10 }
Q.84
is: (Board
2007) 12801084
(a) Function (b)
Not a Function
(c)
Ellipse (d)
Line
Q.85
then f(0)= (Board 2005) 12801085
(a) –1 (b) 0
(c)
1 (d) ¥
Q.86
The linear
function f(x) = ax+b is an identity function if: (Board 2007) 12801086
(a)
a = 0, b = 1 (b) a = 1, b = 0
(c)
a = 1, b = 1 (d) a = 0, b = 1
Q.87
Let f(x) =
4 - x, then 
= 12801087
(a) x (b) - x
(c) 4 + x (d) x - 4
Q.88
Let ¦(x) = , g(x) = 4 - x, then ¦og (x) = 12801088
(a) (b)
(c) (d) 2 + 1
Q.89
Let ¦(x) = - 2, g(x) = 2x + 1, then fog(x) = 12801089
(a) 2x + 1 (b) - 2x
(c) 4x + 3 (d) - 2
Q.90
Let f(x) =
4 - x, g(x) = - 2, then
fog (x) = 12801090
(a) 2 (b) 6
(c) 8 (d) 5
Q.91
The
function y = e = 2 is a\an
------------- function of x. 12801091
(a) constant (b) explicit
(c) exponential (d) logarithmic
Q.92 If y = f(x), then the variable x
is called ------------ variable of a function f. 12801092
(a) dependent (b) independent
(c) image of y (d) None of these
Q.93
[f(x) - g(x)] = ------------. 12801093
(a)
f(x) - g(x)
(b)
f(x) ´ g(x)
(c)
f(x) + g(x)
(d)
f(x) ± g(x)
Q.94
[f(x)] = ------------. 12801094
(a) f(x) (b) n ´ [ f(x)]
(c)
[ f(x)] (d) None of
these
Q.95 If k is any real number, then
[k.f(x)] = ------------. (Board 2012) 12801095
(a)
k f(x) (b) k x f(x)
(c)
f(x) (d) None
of these
Q.96
(Board 2005,
10) 12801096
(a) undefined (b) 3a2
(c) a2 (d) 0
Q.97 Limx(0x tan 12801097
(a) equals 0 (b) equals 1
(c) equals ¥ (d) does not exist.
Q.98 If Limx(0 exists, then: 12801098
(a) both Limx(0f(x) and Limx(0g(x) exist
(b) Limx(0f(x) exist but
Limx(0g(x) need not
exist
(c) Limx(0f(x) need not
exist but Limx(0g(x) exist
(d) neither Limx(0f(x) nor Limx(0g(x) may
exist.
Q.99
Limx(af(x) = l if and only if: 12801099
(a) Limh(0f(a + h) = l
(b) Limh(af(a + h) = l
(c) Limx(af(a + h) =
0
(d) Limh(0f(a + h) =
0
Q.100
is: 12801100
(a) x + 1 (b)
2
(c)
indeterminate (d) 0
Q.101
Limx(2 = 12801101
(a) 1 (b) 2
(c)
3 (d) 4
Q.102
Limx(
3 = 12801102
(a) (b)
(c) (d)
Q.103
Limx(
a = --------------12801103
(a) n a (b) n
a
(c)
0 (d) does not exist
Q.104
Limx( 4 = 12801104
(a) 8 (b) 3
(c) 10 (d) 0
Q.105
Limx(4 = 12801105
(a)
(b)
(c)
(d)
Q.106
Limx(16 = 12801106
(a)
2 (b) 5
(c) 8 (d) 7
Q.107
Limx(2 = 12801107
(a)
(b)
(c)
(d)
Q.108
Limx(0
12801108
(a) (b) 1
(c) (d)
Q.109
Limx(0 = 12801109
(a) 1 (b) 5
(c) 3 (d)
Q.110
Limx(3 = 12801110
(a) 1
(b) 3
(c)
(d) None of these.
Q.111
Limx(( = 12801111
(a) (b) 1
(c) 2 (d) 0
Q.112
f(x) = 
; x ¹ 3 is discontinuous because: (Board 2012) 12801112
(a)
(b)
does not exist
(c)
does not exist
(d)
None of these
Q.113
Let the
function ¦(x) be defined by
¦(x) = , x ¹ 0 and ¦(0) = 0. Then: 12801113
(a) Limx(0¦(x) exists and is equal to ¦(0)
(b) Limx(0¦(x) exists but is not equal to
¦(0)
(c) ¦(x) is continuous at x = 0
(d) None
of these.
Q.114
Let ¦(x) = sin x. Then 12801114
(a)
¦(x) is
continuous for all values of x
(b) ¦(x) is continuous for all values
except x =
(c) ¦(x) is discontinuous at x = 0
(d) None of these.
Q.115
The value
of f(0) so that
f(x) = (x+1) is continuous
at x = 0 is:
12801115
(a)
0 (b)
(c) e (d)
e
Q.116
represent:
(Board 2014) 12801116
(a)
Line (b) Circle
(c) Parabola (d)
Hyperbola
Q.117
equals:
(Board 2014) 12801117
(a)
0 (b)
(c) 
(d) 
Q.118
If 
then
(Board 2013) 12801118
(a)
(b)
(c) 
(d)
Q.119
If f (x) = x2 –x then f (–2) is
equal to:
(Board 2015) 12801119
(a)
2 (b) 6
(c)
0 (d) –6
Q.120
equals :
(Board 2015) 12801120
(a) e (b) e–1
(c) e–2 (d) 
Q.121
If 
then:
(Board 2015) 12801121
(a)
a–x
(b) ax
(c)
e–x
(d) ex
Short Answer Questions
Q.1
Define a function. (Board 2012) 12801122
Q.2
Define domain and range of a function. 12801123
Q.3
Let ¦(x) = x. Find the
domain and range of ¦. 12801124
Q.4
Define a linear function. 12801125
Q.5
Let ¦(x) = . Find the
domain and range of ¦. 12801126
Q.6
Let 
. Find the
domain and range of ¦. 12801127
Q.7
Find domain
of ¦(x) = 12801128
Q.8
Express the
perimeter P of square as a function of its area A. 12801129
Q.9
Express the area A of a circle as a function of its
circumference C. 12801130
Q.10
Express the
volume V of a cube as a function of the area A of its base. 12801131
Q.11 Define
Algebraic functions. 12801132
Q.12 Define a
polynomial function. 12801133
Q.13 Define a
linear function. 12801134
Q.14
Define an Identity function. 12801135
Q.15 Define a
quadratic function. 12801136
Q.16 Define a
constant function. 12801137
Q.17
Define a rational function. 12801138
Q.18
Define explicit
function. 12801139
Q.19
Define implicit
function. 12801140
Q.20
Define
exponential function. 12801141
Q.21
Define
logarithmic function. 12801142
(Board 2007)
Q.22
What do you
mean by real valued function of a real variable?
12801143
Q.23
Define sinh
x, cosh x, tanh x in terms of natural exponential function. 12801144
Q.24
Define csch
x, sech x, coth x in terms of natural exponential function. 12801145
Q.25 Define
inverse of a function. 12801146
(Board 2010)
Q.26 Define the
composition function.
12801147
Q.27 Is composite
function commutative?
12801148
Q.28 Show that the parametric equations
x = a cos t and y = a sin t represent equation of the circle x + y = a. 12801149
Q.29
If f(x) = , x ¹1 find f–1 (x) 12801150
Q.30
Write
the hyperbolic cotangent function in terms of exponential function.
12801151
Q.31
Define the
range of a function f from set X to set Y. 12801152
Q.32
Show that
the parametric equations
x = a sec q, y = b tan q represent the equation of hyperbola - = 1. 12801153
Q.33
Without
finding the inverse, state the domain and range of f. 12801154
given that f(x) = , x ¹ 4
Q.34
Without
finding the inverse, state the domain and range of f given that
f(x) = , x ¹ – 3 12801155
Q.35
Without
finding the inverse, state the domain and range of f-1 given that
f(x) = (x – 5) , x ³ 5 12801156
Q.36
What is the
domain and range of identity function?
12801157
Q.37
What is the
domain and range of polynomial function? 12801158
Q.38
Given f(x)
= x - 2x + 4x - 1 , find f(0) 12801159
Q.39
Given
that f(x) = x– x. Find f(– 2).
12801160
Q.40
Find where f(x)=6x–9.
Q.41
Determine
the function
f(x) = 3x - 2x + 7 is an even or odd function. 12801162
Q.42
Prove the
identity:
Sinh 2x = 2
sinhx – cosh x
(Board
2005, 12) 12801163
Q.43
Prove the
identity: sechx =1–tanhx.
12801164
Q.44
Let the
real valued functions f and g be defined by f(x) = 2x + 1 and g (x)=x-1. Then find the value of g(x). 12801165
Q.45
Without
finding the inverse, state the domain and range of f, where
f(x) = 2 + 12801166
Q.46 Define the even functions. (Board 2012)
12801167
Q.47 Prove the identity (Board 2011)
12801168
coshx + sinh x = cosh 2x
Q.48 If P(x) = ax + ax + ax
+ … + ax + ax + a is a polynomial function of degree n,
then show that P(x) = P(c) 12801169
Q.49
Prove the identity coshx-sinhx = 1
12801170
Q.50 Define the odd function. 12801171
Q.51
Let f:R ® R be the function defined by f(x) =
2x + 1. The find f–1 (x). 12801172
Q.52
Determine the function f(x) = is an even or odd function. 12801173
Q.53
Find where f(x)=sin x
(Board
2008) 12801174
Q.54
Find where f(x)=cos x
12801175
Q.55
Find the domain and the range of the function g(x) = 2x – 5. 12801176
Q.56
Let f(x) = . Find the domain and range of f. 12801177
Q.57
Given f(x) = x - 2x + 4x - 1 and x ¹ 0 , find f 12801178
Q.58
Find the domain and the range of the function g(x)= 
12801179
Q.59
Find the domain and the range of the function g(x) = . 12801180
Q.60 Given f(x) = x–
ax + bx + 1
If
f(2) = – 3 and f( – 1) = 0. Find the
values of a and b. 12801181
Q.61
Show that the parametric equations x = at, y = 2at represent the equation of
parabola y= 4ax. 12801182
Q.62
Find the domain and the range of the function g(x) = . 12801183
Q.63
Prove the identity:
cschx = cothx – 1. 12801184
Q.64
Determine whether the function
f(x) = x+ x is even or odd. 12801185
Q.65
Determine whether the function
f(x) = (x + 2) is even or odd. 12801186
Q.66
Determine whether the function
f(x) = x + 6 is even or odd. (Board 2007)
12801187
Q.67
Let the real valued functions f and g be defined by f(x) = 2x + 1 and
g(x) = x - 1. Then find the value of f(x). 12801188
Q.68 Define the parametric functions. 12801189
Q.69
Determine whether the function
f(x) = is even or odd. 12801190
Q.70
Given g(x)= , x¹1. Find gog (x).
12801191
Q.71
Given f(x) = ; g(x) =
,
x ¹ 0. Find fog (x) 12801192
Q.72
Given f(x)= ; g(x)= , x ¹ 0. Find gof (x). 12801193
Q.73 Given
f(x) = . Find fof(x).
12801194
Q.74
Given f(x) = , x ¹ 1;
g(x) = (x+1). Find fog (x). 12801195
Q.75 Given f(x) =
, x ¹ 1;
g(x) = (x+1). Find gof (x). 12801196
Q.76
For the real valued functions,
f(x) = – 2x + 8, find f–1 (x). 12801197
Q.77
Without finding the inverse, state the domain and range of f–1 given that
f(x) = . 12801198
Q.78
Find the domain and range of the function f(x) = x + 1. 12801199
Q.79
Find the domain and range of the function defined by
f(x) =
12801200
Q.80 Explain
meaning of the phrase
“x
approaches to zero”. 12801201
Q.81 Explain meaning
of the phrase “x approaches to infinity”. 12801202
Q.82 Explain meaning of the phrase
“x approaches to a”. 12801203
Q.83
What is the difference between
x = 1 and x ® 1? 12801204
Q.84 What is the difference between value and limit of a
function? 12801205
Q.85 State the
Sandwitch theorem. 12801206
Q.86 Express the
limit (1 + 2h) in terms
of the number ‘e’. 12801207
Q.87 Show that (3 - x) = e 12801208
Q.88 Evaluate: 12801209
Q.89 Evaluate:
12801210
Q.90 Evaluate 12801211
Q.91 Evaluate 12801212
(Board 2006, 09, 11)
Q.92 Express in terms of e. 12801213
Q.93 Express in terms of e.
12801214
Q.94 Express in terms of e.
(1 + 3x) 12801215
Q.95 Express in terms of e.
(1 – 2h) 12801216
Q.96 Express in terms of e.
12801217
Q.97 Evaluate: 12801218
Q.98 Evaluate: 12801219
Q.99 Evaluate:
(Board 2012) 12801220
Q.100 Evaluate 12801221
Q.101
Evaluate 12801222
Q.102 Evaluate
12801223
Q.103
Evaluate:
12801224
Q.104 Evaluate: 12801225
Q.105
Evaluate: 12801226
Q.106 Evaluate: 12801227
Q.107
Evaluate: (Board 2007)
12801228
Q.108
Evaluate: 12801229
(Board 2008, 12)
Q.109
Evaluate:
12801230
Q.110 Evaluate:
12801231
(Board
2009)
Q.111 Evaluate:
12801232
Q.112 Evaluate: 12801233
Q.113 Evaluate: 
, x < 0 12801234
Q.114 Evaluate: , x >0 12801235
Q.115
Define the
continuous and discontinuous functions. 12801236
Q.116
Discuss the continuity of the function ¦(x) at x =
3 if ¦(x)= if x ¹ 3 12801237
Q.117
Is the
absolute-value function
f(x) = |x| continuous at 0? 12801238
Q.118
Discuss the
continuity of the function f(x) at x =
3 if
f(x) = (Board 2008)
12801239
Q.119
Define the
discontinuous function.
(Board 2009) 12801240
Q.120 Discuss the continuity of f at x = 3,
when f(x) = 12801241
Q.121
For f(x) = 3x - 5x + 4, discuss continuity of f at x
= 1. 12801242
Q.122
Determine whether f(x) exist, when f(x) = 12801243
Q.123 Discuss the continuity of the function g(x) at x =
3 if g(x) = if x ¹ 3
12801244
Q.124
Determine
whether f(x) exist, when f(x) = 12801245
Q.125 For f(x) = , discuss continuity of f at x = 1. 12801246
Q.126 Determine the left hand limit and right
Q.127 hand limit and then find limit of the function
f(x) = 2x2 + x - 5 at x = 1. 12801247
Q.128 Determine the left hand limit and right hand limit
and then find limit of the function f(x) = |x - 5| at x =
5. 12801248
Q.129 Discuss the continuity of
f(x) = at x = 2. 12801249
Q.130
Discuss the
continuity of
f(x) = at x = 1. 12801250
Q.131
If f(x) = , find “c” so that f(x) exists. 12801251
Q.132 Find the values m and n, so that given function f
is continuous: x = 3 12801252
f(x) =
Q.133
Find the
value of m, so that given function f is continuous: x = 4
f(x) = 12801253
|
Unit |
Differentiation |
|
02 |
Multiple Choice Questions
q
Each question has four possible answers. Select the correct answer and
encircle it.
Q.1
Sir Isaac Newton was
a(an) --------- mathematician. 12802001
(a) German (b) French
(c) Swiss (d) English
Q.2
Gottfried Whilhelm
Leibniz was a(an) ---------- mathematician. 12802002
(a) German (b) English
(c) Swiss (d) French
Q.3
The small change in the
value of x, positive or negative is called the
---------- of x. 12802003
(a) increment (b) differential
(c) derivative (d) None of these
Q.4
The symbol is used for the derivative of: 12802004
(a) x with respect to y
(b) y with respect to y
(c) y with respect to x
(d) x with respect to x
Q.5
if exists, is denoted by: (Board 2007, 15) 12802005
(a) f (x) (b) f ¢(x)
(c) f ¢(a) (d) None of these
Q.6
is called the derivative of f at ----------.
(Board 2005, 09) 12802006
(a) x = a (b) for all x
(c) x ® a (d) None of these
Q.7
---- used symbol for the derivative of y = f(x) with respect to x. 12802007
(a) Lagrange (b) Newton
(c) Leibniz (d) Cauchy
Q.8
Notation Df(x) for
derivative used by: (Board
2012) 12802008
(a) Cauchy (b) Newton
(c) Leibniz (d) Lagrange
Q.9
The quantity is defined as: 12802009
(a) Lim(x(0 (b) Lim(x(0
(c) Lim(y(0 (d) Lim(y(0
Q.10
If y = f(x) then is defined as: 12802010
(a) Lim(x(0 = Lim(x(0
(b) Lim(x(0 = Lim(x(0
(c) Lim(x(0 = Lim(x(0
(d) Lim(x(0 = Lim(x(0
Q.11
The instantaneous rate of change of y
with respect to x is given by: 12802011
(a) (b)
(c) (d)
Q.12
The derivative of x with
respect to y is given by: 12802012
(a) (b)
(c) (d)
Q.13
If y = 5x , is given by: 12802013
(a) 0 × 6x (b) 6x
(c) 30 x (d) 30 x
Q.14
If y = x , then is given by:
(Board 2015) 12802014
(a) x n (b) n x
(c) nx (d) x
Q.15
If y = , then is given by: 12802015
(a) 2 (b)
(c) (d)
Q.16
If y = f(u)
and u = F(x), then: 12802016
(a) = ¸
(b) = +
(c) = ´
(d) = ´
Q.17
If s is the
distance traveled by a body at time t, the velocity is given by the expression: 12802017
(a) (b)
(c) (d)
Q.18
For a square
of side x units, the rate of change
of area with respect to the side is given by: 12802018
(a) x (b) x
(c) 2x (d) 2
Q.19
{c.f(x)} = (Board 2012) 12802019
(a) c (b) f(x)
(c) c (d) f(x)
Q.20
{f(x) - g(x)}¢ = 12802020
(a) f ¢(x) - g ¢(x) (b) f ¢(x) ´ g ¢(x)
(c) f ¢(x) + g ¢(x) (d) f ¢(x) ± g ¢(x)
Q.21
[fog(x)]¢ = 12802021
(a) f ¢{g(x)} (b) f {g¢ (x)}
(c) f ¢{g(x)}´g¢(x) (d) None of these
Q.22
{f(x) ´
g(x)} = (Board 2006) 12802022
(a) f(x) ´
(b) ´ g(x)
(c) ´ g(x) + f(x) ´
(d) ´ g(x) - f(x) ´
Q.23
= , provided
(Board 2010) 12802023
(a) g(x) ¹ f(x) (b) g(x) ¹ 0
(c) g(x) = f(x) (d) g(x) = 0
Q.24
(c) = -------------, where c is any constant. 12802024
(a) c (b) 0
(c) 1 (d) - c
Q.25
where: 12802025
(Board 2007, 10)
(a) 
(b) 
(c) 
(d) 
Q.26
(x)
= n x, where n is any rational number is called ---------- rule. 12802026
(Board 2007, 08, 09)
(a) power rule
(b) chain rule
(c) derivative rule
(d) product rule
Q.27
(Board 2012) 12802027
(a) 
(b) 
(c) 
(d) 
Q.28
If y = , 0 < x < 1, then is equal to: 12802028
(a)
(b)
(c) (d) –
Q.29
= 12802029
(a) n ´ f ¢(x)
(b) n ´ f ¢(y) ´
(c) n ´ f ¢(y)
(d) n ´ f ¢(y) ´
Q.30
If y = , then is equal to:
12802030
(a) –
(b)
(c) – (d) None of these.
Q.31
[g(x)] = n [g(x)] ´ where n is any rational number is called
---------- rule. 12802031
(a) Power rule (b) Chain rule
(c) Power and Chain rule
(d) None of these
Q.32
(sin x) = 12802032
(a) sin x (b) cos x
(c) - sin x (d) - cos x
Q.33
(cos x) = 12802033
(a) sin x (b) - cos x
(c) - sin x (d) cos x
Q.34
(tan x) = 12802034
(a) sec x tan x (b)
secx
(c) - sec x tan x (d) - secx
Q.35
(– cosec x) = (Board
2011) 12802035
(a) cosec x cotx (b) cosecx
(c) + cosec x cotx (d) - cosecx
Q.36
(sec x) = (Board
2007, 10)
12802036
(a) sec x tan x (b) - secx
(c) - sec x tan x (d) secx
Q.37
(– cot x) = (Board
2006) 12802037
(a) cosecx
(b) + cosecx
(c) - cosec x cot x
(d) cosec x cot x
Q.38
(Board 2012) 12802038
(a) 
(b) 
(c) 
(d) 
Q.39
(sinx) = (Board 2010) 12802039
(a) (b) -
(c) (d) -
Q.40
(cosx) = 12802040
(a) (b)
(c) - (d) -
Q.41
(cosecx) = 12802041
(a) - (b)
(c) - (d)
Q.42
(sinhx) = (Board 2015) 12802042
(a) (b) -
(c) (d) -
Q.43
If 
then 
12802043
(a) cosx (b) sec2x
(c) 
(d) sinx
Q.44
(secx) = (Board 2010) 12802044
(a) - (b)
(c) - (d)
Q.45
(tanx) = (Board 2012) 12802045
(a) (b) -
(c) (d)
Q.46
(cotx) = (Board 2005) 12802046
(a) (b) -
(c) (d)
Q.47
(Board 2010) 12802047
(a) 0 (b) 1
(c) –1 (d) 2
Q.48
(sinh x) = 12802048
(a) sinh x (b) cosh x
(c) - sinh x (d) - cosh x
Q.49
(cosh x) = (Board 2005) 12802049
(a) sinh x (b) cosh x
(c) - sinh x (d) - cosh x
Q.50
(tanh x) = 12802050
(a) sech x tanh x
(b) - sech x tanh x
(c) sechx (d) - sechx
Q.51
(cosech x) = 12802051
(a) cosech x coth x
(b) cosechx
(c) - cosech x coth x
(d) - cosechx
Q.52
(sech x) = 12802052
(a) sech x tanh x
(b) - sechx
(c) - sech x tanh x
(d) sechx
Q.53
(coth x) = 12802053
(a) cosech x coth x
(b) - cosechx
(c) - cosech x coth x
(d) cosechx
Q.54
(Board 2012) 12802054
(a) 
(b)
(c) 
(d) 
Q.55
(tanhx) = (Board 2011) 12802055
(a) , |x| < 1
(b) 
(c)
(d) 
Q.56
(coshx) = 12802056
(a) - (b)
(c) (d) -
Q.57
(cosechx) = 12802057
(a)
(b) - x > 0
(c) - (d)
Q.58
(sech x) = 12802058
(a) - 0 < x < 1
(b)
(c) (d) -
Q.59
If y = e2x
then y2 = (Board 2005) 12802059
(a) e2x (b) 2e2x
(c) 4e2x (d) 16e2x
Q.60
(a) = (Board 2011) 12802060
(a) a (b)
(c) ax . ln a (d) x
Q.61
(Board 2012) 12802061
(a)
(b) 
(c) 
(d) 
Q.62
(logx) = (Board 2007) 12802062
(a) (b)
(c) x . ln a (d) x ×
Q.63
then (Board 2009) 12802063
(a) 
(b) 
(c) 
(d) 
Q.64
(Board 2006) 12802064
(a) 
(b) 
(c) 
(d) 
Q.65
y = cos x then (Board
2012) 12802065
(a) y4 + y = 0 (b) y4 – y =0
(c) y2 - y = 0 (d) y3 - y = 0
Q.66
1 + x +
+
+ ××× = 12802066
(a) e (b) sin x
(c) ln x (d) cos x
Q.67
------------------ = 1
+ nx + x
+
x
+ ××× 12802067
(a) e (b) sin x
(c) (1 + x) (d) cos x
Q.68
x -
+
-
+ ××××× = 12802068
(a) e (b) sin x
(c) (1 + x) (d) cos x
Q.69
is Maclaurin’s series expansion of (Board 2012) 12802069
(a)
Cos x (b) sin x
(c) ln (1 - x) (d) ln (1 + x)
Q.70
f(x) = f(0) + x
(0) + 
(0) + … is called: (Board 2008) 12802070
(a) Taylor’s series
(b) Binomial series
(c) Machlaurin’s series
(d) Laurent series
Q.71
Sin x = (Board
2009) 12802071
(a) x – 
+ ….
(b) 1- 
+ …….
(c) - x - 
(d) x - 
+ ….
Q.72
The Maclaurin series
expansion is valid only if it is: 12802072
(a) convergent (b) divergent
(c) increasing (d) decreasing
Q.73
The slope of the
tangent line to the graph of f defined by the equation
y = f(x) at (x , f(x)) is: 12802073
(a) f (x) (b) f ¢(x)
(c) (d)
Q.74
Let f be defined on an
interval (a, b) and let x, x Î (a, b). Then f is an increasing on the
interval (a, b) if -------- whenever x > x 12802074
(a) f(x) = f(x) (b) f(x) > f(x)
(c) f(x) ¹ f(x) (d) f(x) < f(x)
Q.75
Let f be a
differentiable function on the interval (a, b). Then f is a decreasing on (a,
b) if --------- for each x Î
(a, b). 12802075
(a) f ¢(x) ¹ 0 (b) f ¢(x) > 0
(c) f ¢(x) = 0 (d) f ¢(x) < 0
Q.76
If f(c) £ f(x) for all x Î
(c-dx,c+ dx), then the function f is said to have
a\an
---------- at x = c. 12802076
(a) decreasing (b) increasing
(c) relative maxima
(d) relative minima
Q.77
Let f be differentiable
function in a neighborhood of c where f ¢(c)=0. Then f has relative minima at c if f ¢¢(c) ----.12802077
(a) = 0 (b) > 0
(c) ¹ 0 (d) < 0
Q.78
Let f be defined on an interval (a, b) and let x, x Î (a, b). Then f is a\an
-------- on the interval (a, b) if f(x) < f(x) whenever x > x 12802078
(a) increasing (b) decreasing
(c) maxima (d) minima
Q.79
If f ¢(c) = 0, then the number c is called a ---------- value of f. 12802079
(a) Critical (b) Stationary
(c) Extrema (d) None of these
Q.80
The function f(x)= –3x2 has mini-
mum value at: (Board 2006) 12802080
(a) x = 3 (b) x
= 2
(c) x = 1 (d) x =
0
Q.81
The minimum value of
the function f (x) = x2 – x – 2 is: (Board 2007) 12802081
(a) 
(b) 
(c) - 1 (d) 0
Q.82
(Board 2014) 12802082
(a) 
(b) 
(c)
(d)
Q.83
If 
then 
12802083
(Board
2014)
(a) 
(b) 
(c) 
(d)
3
Q.84
(Board 2014) 12802084
(a) 
(b) 
(c) 
(d) 
Q.85
If 
then 
is: 12802085
(Board
2014)
(a) 
(b) 
(c) 
(d)
Q.86
If 
then 
12802086
(Board
2014)
(a) 
(b) 
(c) 
(d) 
Q.87
If 
then 
equals:
(Board
2014) 12802087
(a) 
(b) 
(c) 
(d) 
Q.88
The differential co-efficient of 
equals: (Board 2014) 12802088
(a) 
(b) 
(c) 
(d)
Q.89
is equal to: 12802089
(Board 2014)
(a) 
(b) 
(c) 
(d) 
Q.90
If 
then 
equals:
(Board 2014) 12802090
(a) tan x (b) cot x
(c) – tan x (d) – cot x
Q.91
Notation
for derivative was used by Newton is:
(Board 2013)
12802091
(a) 
(b) 
(c) 
(d) 
Q.92
is: 12802092
(Board 2013)
(a) 
(b) 
(c) 
(d) 
Q.93
is: (Board 2013) 12802093
(a) 
(b) 
(c) 
(d)
Q.94
If f(x) = cos x then f
’(0) is equal
to :
(Board 2015) 12802094
(a) 0 (b) –1
(c)
1 (d)
Q.95
If f
(x) = eax then 
(x) is equal
to:
(Board 2015) 12802095
(a)
(b)
–
(c)
aeax (d) –aeax
Q.96
If 
then y1 equals:
(Board 2015) 12802096
(a) cosec x cot x (b) –cosec x cotx (c) sec x tan x (d) –sec x tan x
Q.97
[
n x] is equal to:
(Board 2015) 12802097
(a) 
(b)
(c) 
2
(d) 
Q.98
equals:
(Board 2015) 12802098
(a)
(b) 
(c)
(d) 
Q.99
If f
(x + h) = cos (x +h), then 
(x) equals: (Board 2015) 12802099
(a) cos x (b) –cos x
(c) sin x (d) –sin x
Short Answer Questions
Q.1
What is increment of x? 12802100
Q.2
Write down the
instantaneous rate of change of distance ‘S’ at time ‘t’. 12802101
Q.3
What is the derivative
of f(x) with respect to x at x? (Board 2012) 12802102
Q.4
What is the derivative
of f(x) with respect to x at a? (Board 2012) 12802103
Q.5
Find by definition the derivative of f(x) = xm, 
. (Board 2012) 12802104
Q.6
Let
Find dy.
(Board 2011,
12) 12802105
Q.7
If 
. Find dy.
(Board 2012) 12802106
Q.8
Find the derivative of
f(x) = c by definition. (Board 2010) 12802107
Q.9
Find the derivative of
f(x) = x
by ab-initio method. 12802108
Q.10
Find the derivative of
f(x) = at x = a from first principles. (Board 2011) 12802109
Q.11
Define product rule of differentiation. 12802110
Q.12
Define quotient rule of differentiation. 12802111
Q.13
Find the derivative (x + 1) with respect to ‘x’. (Board 2011) 12802112
Q.14
Find the derivative of
y = x + x + x + 2x + 5 with respect to ‘x’. 12802113
Q.15
Differentiate w. r. t.
‘x’ :
12802114
Q.16
Deduce the differential coefficient of sec x from that of cos x. 12802115
Q.17
Differentiate x w.r.t x.
12802116
Q.18
If y =
prove that = secx. 12802117
Q.19
Differentiate w. r. t. ‘x’:
x+ 2x+ 3 12802118
Q.20
Differentiate w.r.t.‘x’:x+2x+ x
(Board
2005) 12802119
Q.21
Differentiate w. r. t. ‘x’ :
(Board 2008, 10, 11, 12) 12802120
Q.22
Differentiate w. r. t. ‘x’ :
(Board 2008) 12802121
Q.23
Find 
if 
.
(Board 2012) 12802122
Q.24
Differentiate w.r.t. ‘x’:
(Board 2006, 10) 12802123
Q.25
Differentiate w.r.t. ‘x’: 12802124
Q.26
Differentiate w. r. t. ‘x’:
(Board 2009) 12802125
Q.27
If y = – , show that
2x + y = 2 (Board 2010) 12802126
Q.28
If y = x + 2x + 2, prove that
= 4x (Board 2007) 12802127
Q.29
If tan y (1 + tan x) = 1 - tan x, show that = - 1. 12802128
Q.30
Find by making suitable substitution in the function defined as
y = (3x - 2x + 7) 12802129
Q.31
Find if y + x - 4x = 5. 12802130
Q.32
Find if x + y = 4.
(Board
2007,09)
12802131
Q.33
If x and y are the
functions of t, then what is by chain rule. 12802132
Q.34
Differentiate (1 + x) w. r. t x.
12802133
Q.35
Find if x = at and y = 2at.
(Board 2005) 12802134
Q.36
Differentiate x–
w.r.t x
(Board 2012) 12802135
Q.37
Find if 
(Board 2012) 12802136
Q.38
Find if 3x + 4y + 7 = 0 12802137
Q.39
Find if
xy + y = 2 12802138
Q.40
Find if
y = x cos y
(Board 2009) 12802139
Q.41
Find if
x = y sin y 12802140
Q.42
If
. Find y2.
(Board 2012) 12802141
Q.43
Find if y = sinh 2x 12802142
Q.44
Deduce the differential coefficient of cosec x from that of sin x. 12802143
Q.45
Find if y = tanhx
(Board
2010, 2011) 12802144
Q.46
Differentiate tanx
with respect to ‘x’. 12802145
Q.47
Differentiate cosx
with respect to ‘x’. 12802146
Q.48
Differentiate w. r. t. ‘x’ : cos
12802147
Q.49
If y = cot . Find .
(Board 2012) 12802148
Q.50
Differentiate w. r. t. ‘x’ : sin
Q.51
Differentiate sinx
with respect to ‘x’. 12802150
Q.52
If y = Tan (þ Tan x), show that y – þ = 0. (Board 2012)
12802151
Q.53
Differentiate y = a with respect to ‘x’. 12802152
Q.54
Differentiate ln (x + 2x) with respect to ‘x’. 12802153
Q.55
Differentiating y=e with respect to ‘x’. (Board 2009) 12802154
Q.56
Find if y = a 12802155
Q.57
Find if y = log(ax + bx + c)
12802156
Q.58
Find 
if f(x)
= e
(Board 2009) 12802157
Q.59
Find if
f(x) = e
(Board 2012) 12802158
Q.60
Find f¢(x)
if
f(x) = x e ; (x ¹ 0)
12802159
Q.61
Find if f(x)= e (1 + ln x) 12802160
Q.62
Differentiate a by ab-initio with respect to x. 12802161
Q.63
Differentiate y = a with respect to ‘x’. 12802162
Q.64
Find if y = e 12802163
Q.65
Find f¢ (x) if f(x) = 12802164
Q.66
Find f¢(x) if f(x) = ln
12802165
Q.67
Find if
y = x 12802166
Q.68
Find if
y = 12802167
Q.69
Find if
y = x ln 12802168
Q.70
Find if y = ln (9 - x)
(Board
2009) 12802169
Q.71
Find if y = e sin 2x 12802170
Q.72
Find if y = e
(Board 2009)12802171
Q.73
Find if y = x e 12802172
Q.74
Find if y = 5 e 12802173
Q.75
Differentiate (ln x) with respect to ‘x’. (Board 2009) 12802174
Q.76
Find if y =(ln x) (Board 2009)
12802175
Q.77
Find if y = cosh 2x (Board
2008)
12802176
Q.78
Find if y = sinh 3x 12802177
Q.79
Find if y = sinh 2x 12802178
Q.80
Find if y = ln (tanh x) 12802179
Q.81
Differentiate sinh
x with respect to ‘x’. 12802180
Q.82
Find if y = sinh (ax + b) 12802181
Q.83
Differentiate cosh
x with respect to ‘x’. 12802182
Q.84
Find if y = tanh
(sin x),
–
< x < 12802183
Q.85
Find if y = sinh(x) 12802184
Q.86
Find if y = sinh 12802185
Q.87
Differentiate tanh
x with respect to ‘x’. (Board 2009) 12802186
Q.88
Find y if x = at , y = bt 12802187
Q.89
Find y if y=2x-3x + 4x + x - 2
(Board
2012) 12802188
Q.90
Find y if y = (2x + 5) 12802189
Q.91
Find y if y = x × e
(Board 2008, 09, 10, 11) 12802190
Q.92
Find y if x + y = a 12802191
Q.93
Find y2 if y
= sin 3x 12802192
(Board
2008, 10, 12)
Q.94
Define a power series
expansion of a function. 12802193
Q.95
Define the Maclaurin
series expansion. 12802194
Q.96
State Taylor’s Theorem.
12802195
(Board
2012)
Q.97
Apply the Maclaurin
expansion to prove that: 12802196
ln (1 + x) = x - + - + ……………..
Q.98
Apply the Maclaurin
expansion to prove that: (Board
2011) 12802197
cos x = 1 - + – + …...........
Q.99
Apply the Maclaurin
expansion to prove that: 12802198
= 1 + - + +
…...........
Q.100
Apply the Maclaurin
expansion to prove that: (Board
2011) 12802199
e = 1 + x + + + ……….
Q.101
Apply the Maclaurin
expansion to prove that: e = 1 + 2x + +
+ …
(Board 2012) 12802200
Q.102
Show that: cos (x + h)
= cos x - h sin x - cos x +
sin x + … 12802201
Q.103
Expand f(x) = in the Maclaurin series. 12802202
Q.104
Prove that e
= e 12802203
Q.105
Show that 2 = 2 {1 + (ln 2)
h + (ln 2) h + (ln2) h + …} 12802204
Q.106
What is geometrical
meaning of the derivative? 12802205
Q.107
Define an increasing
function. 12802186
Q.108
What is critical value? 12802207
Q.109
What is relative maxima
of a function. 12802208
Q.110
State first derivative
rule. 12802209
Q.111
State second derivative
rule. 12802210
Q.112
What is relative
extrema of a function? 12802211
Q.113
What is Stationary
point? 12802212
Q.114
What is critical point? 12802213
Q.115
Define the turning
point. 12802214
Q.116
Determine the values of
x for which f defined as
f(x)
= x
+ 2x - 3 is increasing. 12802215
Q.117
Determine the values of
x for which f defined as f(x) = x + 2x - 3 is decreasing.
12802216
Q.118
Determine the intervals
in which
f is a decreasing if f(x) = x - 6x + 9x.
12802217
Q.119
Determine the intervals
in which f is increasing and decreasing if f(x ) = x.
12802218
Q.120
Determine the intervals
in which f is increasing or decreasing for the domain mentioned. f(x) = 4 -
x , x Î
(- 2 , 2)
(Board
2008) 12802219
Q.121
Determine the intervals
in which f is increasing or decreasing for the domain mentioned. f(x) = x + 3x + 2, x Î (- 4, 1)
(Board
2008) 12802220
Q.122
Examine the function
defined as
f(x) = 1 + x for extreme values. 12802221
(Board 2008,
09, 10)
Q.123
Find the extreme values for the following function defined as:
f(x) = x - x - 2 12802222
Q.124
Find the extreme values
for the following function defined as: (Board
2009)
f(x)
= 3x - 4x + 5 12802223
Q.125
Find two positive
integers whose sum is 30 and their product will be maximum. 12802224
Q.126
Divide 20 into two
parts so that sum of their squares will be minimum. 12802225
(Board 2012)
|
Unit |
Integration |
|
03 |
Multiple Choice Questions
q Each question has
four possible answers. Select the correct answer and encircle it.
Q.127
The term dy (or df) = f
¢(x) dx is called the -------------------------- of the dependent
variable y. 12803001
(a)
differentiation
(b)
integration
(c)
differential
(d)
None of these
Q.128
The technique or method to find such a function whose derivative is
given involves the inverse process of differentiation called: 12803002
(a)
differentiation
(b)
integration
(c)
differential
(d)
None of these
Q.129
f (x) dx = f(x) if: 12803003
(a)
f (x) = f(x)
(b)
[f (x)] = f(x)
(c)
[f (x)] = f (x)
(d)
[f (x)] = f(x) + c
Q.130
If f (x) is the integral of f(x), then
f(x) dx is given by: 12803004
(a)
f (a) + f (b)
(b)
f (a) ¸ f (b)
(c)
f (a) – f (b)
(d)
f (b) – f (a)
Q.131
Iff1(x)
and f2 (x) are any two antiderivatives of a function f (x), then
f(x) – f(x) = 12803005
(a) f (x) (b) a variable
(c) 0 (d) a constant
Q.132
An integral
of 3x is: 12803006
(a) x+c (b) 3
(c) 6x (d) x+c
Q.133
If = f(x) + c, then f(x) is called : 12803007
(a) integration
(b) integrand
(c) constant of integration
(d) None of these
Q.134 = -------- + c , (n ¹ - 1)
(a) n(ax + b)´ a 12803008
(b) ´
(c)
(d) None of these
Q.135
= --------- + c, (l ¹ 0)
1. 12803009
(a) e (b) l e
(c) m e (d) e
Q.136
= ---------------, where a is any constant. 12803010
(a)
(b) f(x)
(c)
a ´ (d)
a +
Q.137
= ------------ + c, f(x) > 0
(Board
2015) 12803011
(a)
f(x) (b) ln
|f(x)|
(c)
f ¢(x) (d) ln |f ¢(x)|
Q.138
If f¢(x) = f(x),
then f(x) is called a\an
--------------------- of f(x). 12803012
(a)
derivative (b) differential
(c)
integral (d) None of these
Q.139
The is symbol for: 12803013
(a)
integration
(b)
integration w.r.t.x
(c)
differentiation (d) None of these
Q.140
= ------------------ + c 12803014
(a)
nx (b) (n + 1)x
(c)
(d) None of these
Q.141
= --------- + c, (a ¹ 0).
(a)
cos (ax + b) 12803015
(b)
- cos (ax + b)
(c)
sin (ax + b)
(d)
- sin (ax + b)
Q.142
= -------------------- ln|sec
(ax + b)| + c, (a ¹ 0) 12803016
(a)
(b) b
(c)
- (d) ax + b
Q.143
= ---------------- + c. 12803017
(a) ln |sin x| (b) - ln |sin x|
(c) ln |cos x| (d) - ln |cos x|
Q.144
= -------------------- tan (ax + b) + c, (a ¹ 0) 12803018
(a) a (b)
(c) b (d) ax + b
Q.145
= -------------- + c. 12803019
(a) cot x (b) - cot x
(c) cosec x cot x
(d) -cosec x cot x
Q.146
= (Board 2015) 12803020
(a) tan x + c (b) - tan x + c
(c) sec x + c (d) - sec x + c
Q.147
= (Board 2012) 12803021
(a) ln |cos
x| + c
(b)
ln
|sec x| + c
(c)
ln
|sin x| + c
(d) None of these
Q.148
= -------
+ c, (a ¹ 0)
(a) cos (ax + b) 12803022
(b) - cos (ax+b)
(c) sin (ax + b) (d) - sin (ax+b)
Q.149
= ---------- cot
(ax + b) + c, (a ¹ 0) 12803023
(a) (b) b
(c) - (d) ax + b
Q.150
= ------, (a ¹ 0) 12803024
(a) tan (ax + b) + c
(b) - tan (ax + b) + c
(c) sec (ax +
b) + c
(d) - sec (ax + b) + c
Q.151
= ----- + c, (a
¹ 0)
(Board
2012) 12803025
(a)
ln |cos (ax + b)|
(b)
- ln |sin (ax + b)|
(c)
ln |sin (ax + b)|
(d)
- ln |cos (ax + b)|
Q.152
= 12803026
(a)
+
(b)
-
(c)
´
(d)
±
Q.153
is the method of: 12803027
(a)
integration (b)
differentiation
(c)
integration by parts
(d)
None of these
Q.154
= ---------. (Board 2015) 12803028
(a)
cos x + c (b) - cos x + c
(c)
sin x + c (d) - sin x + c
Q.155
= -----------. 12803029
(a)
tan x + c (b) - tan x + c
(c)
sec x tan x + c
(d)
- sec x tan
x+c
Q.156
= ---- cosec (ax + b) + c, (a¹0) where c is
the constant of integration. 12803030
(a)
a (b) - a
(c)
- (d) -
Q.157
= --------------------- + c, (ax + b ¹ 0, a ¹ 0) 12803031
(a)
ln |ax + b| (b) ln |bx + a|
(c)
a ln |ax + b|
(d)
ln |ax + b|
Q.158
dx = 12803032
(a) – + c
(b)
– + c
(c)
+ + c
(d)
Q.159 = 12803033
(a) ln |sec x + tan x| + c
(b) ln |cosec x - cot x| + c
(c) ln |sec x - tan x| + c
(d) ln |cosec x + cot x| + c
Q.160
= --------------- + c, (n ¹ - 1) 12803034
(a)
(n + 1) f(x)]
(b)
f(x)
(c)
n f(x)] (d)
Q.161
If , then ‘a’ is known as the
---------------------- of integration. 12803035
(a)
domain (b) range
(c)
lower limit (d) upper limit
Q.162
If = f(x) + c, as c is not definite, so f(x) + c is
called the
--------------------- of f(x). 12803036
(a)
integral (b) indefinite integral
(c)
differential (d) None of these
Q.163
If = f(x) + c, then c is called:
(a) integration (b) integrand
12803037
(c) constant of integration
(d) None of these
Q.164
= -------------- + c. 12803038
(a) cos x (b) - cos x
(c) sin x (d) - sin x
Q.165
= 12803039
(a) cosec x + c (b) - cosec x + c
(c) cot x + c (d) - cot x + c
Q.166
= --------- + c, (a > 0, a ¹ 1)
(a)
a (b) 12803040
(c) (d)
Q.167
To integrate dx we will make
substitution: 12803041
(a) x = 3 sec q (b) x = 3 tan q
(c) x = 3 sin q (d) x = 3 sinh q
Q.168
To integrate
dx we will make substitution: 12803042
(a) x = 2 tan q (b) x = 2 sec q
(c) x = 2 cos q (d) None of these.
Q.169
To integrate
dx we will make substitution: 12803043
(a) x = 3 tan q (b) x = 3 sec q
(c) x = 3 sin q (d) x = 9 tan q
Q.170
To integrate
dx we will make substitution: 12803044
(a) 5x = 3 sec q
(b) x = 3 sec q
(c) x = 3 sin q (d) 5x = 3 sin q
Q.171
To integrate dx we will make substitution: 12803045
(a) x = 3 tan q (b) 2 x = 3 tan q
(c) x = tan q (d) x = 9 tan q
Q.172
To integrate dx we will make substitution: 12803046
(a) x = 100 sin q
(b) x = 10 sin q
(c) x = 10 tan q
(d) x = 10 sin q
Q.173
= 12803047
(a)
f(x) × g(x) + + c
(b)
f(x) × g(x) - + c
(c)
f(x) × g(x) ´ + c
(d)
f(x) × g(x) + c
Q.174
lnx dx = (Board 2012,15) 12803048
(a) x lnx + x + c
(b) x lnx - x +
c
(c) x lnx + c (d) None of these.
Q.175
(Board 2012)
2.
12803049
(a) 
(b) 
(c) 
(d) 
Q.176
If f¢(x) = f(x) and
has a definite value f(b) - f(a), then it
is called the ---------------------- of f from a to
b. 12803050
(a)
integration by parts
(b)
definite integral
(c)
differentiation
(d)
None of these
Q.177
If the upper limit is a constant and the lower limit is a variable,
then the integral is a function of: 12803051
(a)
x (b) y
(c)
lower limit (d) upper limit
Q.178
If , then the interval [a, b] is called
the --------------------- of integration.
(a)
domain (b) range 12803052
(c)
lower limit (d) upper limit
Q.179
If , then ‘b’ is known as the
---------------------- of integration. 12803053
(a)
domain (b) range
(c)
lower limit (d) upper limit
Q.180
The area of the region, above the
x-axis and under the curve y = f(x) from a to b is given by ------------ . 12803054
(a)
(b) -
(c)
(d) None of these
Q.181
If the graph of f is entirely above the x-axis, then the definite
integral is
-----------------. 12803055
(a)
positive
(b)
positive or negative
(c)
negative
(d)
positive and negative
Q.182
If 
3.
then
(Board 2012) 12803056
(a)
8 (b) 5
(c)
3 (d) 5–3
Q.183
If the lower limit is a constant and the upper limit is a variable,
then the integral is a function of: 12803057
(a)
x
(b)
y
(c)
lower limit
(d)
upper limit
Q.184
as the area under the curve y = f(x)
from x = a to x = b and the x-axis is called : 12803058
(a)
integration by parts
(b)
definite integral
(c)
differentiation
(d)
None of these
Q.185
= ------- + c
(a)
e (b) f(x) 12803059
(c)
e f(x) (d) e + f(x)
Q.186
= 12803060
(a)
(b) -
(c)
(d) ±
Q.187
+ = ------------- ; where a < b < c. 12803061
(a) (b)
(c) (d)
Q.188
(Board 2012) 12803062
(a) 0 (b) 
(c) –1 (d)
1
Q.189 If the graph of f is entirely below the x-axis,
then the definite integral is:
12803063
(a) positive
(b) positive or negative
(c) negative
(d) positive and negative
Q.190
The area of the region, below the
x-axis and under the curve y = f(x) from a to b is given by: 12803064
(a)
(b)
-
(c)
-
(d)
None of these
Q.191
The order of a differential equation
y + 2x = 0 is: 12803065
(a)
0
(b)
1
(c)
2
(d)
None of these
Q.192
The general solution of differential equation of order n contains n
arbitrary constants, which can be determined by
--------------- initial value conditions. 12803066
(a)
0 (b) 1
(c)
2 (d) n
Q.193
The order of a differential equation
x + - 2x = 0 is : 12803067
(a)
0 (b) 1
(c)
2 (d) None of these
Q.194
The arbitrary constants involving in the solution of differential
equations can be determined by the given conditions. Such conditions are called
---------- condition.
(a)
initial values 12803068
(b)
general
(c)
boundary values
(d)
None of these
Q.195 For 
12803069
(Board 2014)
(a)
(b) 
(c)
(d) 
Q.196
12803070
(Board 2014)
(a)
(b) 
(c)
(d) 
Q.197
12803071
(Board 2014)
(a)
(b) 
(c)
(d) 
Q.198
12803072
(Board 2014)
(a)
(b) 
(c)
(d) 
Q.199
is equal to: 12803073
(Board 2014)
(a)
(b) 
(c)
(d) 
Q.200
Anti derivative of cot x is equal to:
(Board 2014) 12803074
(a)
(b) 
(c)
(d) 
Q.201
equals: 12803075
(Board 2013, 14)
(a)
(b) 
(c)
(d) 
Q.202
equals: 12803076
4.
(Board 2014,15)
(a)
(b) 
(c)
(d)
Q.203
Solution of 
is equal to: (Board
2014) 12803077
(a)
x.y = Constant
(b) 
Constant
(c)
constant
(d) 
constant
Q.204
12803078
(a)
(b) 
(c)
(d) 
Q.205
Solution of differential equation, 
is (Board 2015) 12803079
(a)
cex
(b) ce–x
(c)
ex (d) e–x
Q.206
The integration is the reverse
process of : (Board
2015) 12803080
(a) Induction
(b) Differentiation
(c) Tabulation
(d) Sublimation
Q.207
is equal to:
(Board
2015) 12803081
(a) 4 (b) –4
(c) 
(d)
Q.208
12803082
(a) 36 (b) 42
(c) 48 (d) 12
Q.209
(Board
2015) 12803083
(a)
(b) 
(c) 
(d) 
Q.210
is equal to:
(Board
2015) 12803084
(a) tan–1x (b) tan–1 x2
(c) cot–1 x (d) cot–1 x2
Q.211
equals:
(Board
2015) 12803085
(a) e2x sin x (b) e2x cos x
(c) –e2x sin x (d) –e2x cos x
Q.212
is equal to:
(Board
2015) 12803086
(a) 1 (b) 4
(c) 14 (d) 41
Short Answer Questions
5.
Q.1
Using differentials
find when
- ln
x = ln c 12803087
Q.2
Use differentials, find
the approximate the value of sin 46°. 12803088
(Board 2012)
Q.3
Use differentials to
approximate the value of . 12803089
Q.4
Define differential
coefficient.
12803090
Q.5
Find dy and dy of the function defined as f(x) = x, when x = 2 and
dx = 0.01 (Board 2005) 12803091
Q.6
The side of a cube is
measured to 20 cm with a maximum error of 0.12 cm in its measurement. Find the
maximum error in the calculated volume of the cube. 12803092
Q.7
Use differentials to approximate the
value of 12803093
Q.8
Find dy
and dy : y = when x changes
from 4 to 4.41. (Board 2005)
6. 12803094
Q.9
Find dy and dy in y = x2 -1 when x changes from 3 to 3.02. (Board 2011) 12803095
Q.10
Use differentials to
approximate the values of 12803096
Q.11
Use differentials to
approximate the value of cos 29° 12803097
Q.12
Use differentials to
approximate the value of sin 61° 12803098
Q.13
Find the approximate
increase in the volume of a cube if the length of its each edge changes from 5
to 5.02. 12803099
(Board 2011)
Q.14
Find the approximate
increase in the area of a circular disc if its diameter is increased from 44 cm
to 44.4. (Board 2005)
12803100
Q.15
What do you mean by
integration?
12803101
Q.16
Define indefinite
integral. 12803102
Q.17
Why we add the constant
of integration in indefinite integrals? 12803103
Q.18
Find 12803104
Q.19
Find . 12803105
Q.20
Find . 12803106
Q.21
Find .
12803107
Q.22
Find , l ¹ 0 12803108
Q.23
Find ,(ax
+ b ¹ 0, a ¹ 0)
12803109
Q.24
Find ,
(a ¹ 0) 12803110
Q.25
Find ,
(a ¹ 0)
12803111
Q.26
Evaluate 12803112
Q.27
Evaluate 12803113
Ans. = + c.
Q.28
Find . 12803114
Q.29
Find ,(a > 0, a ¹ 1,l¹ 0)
12803115
Q.30
Evaluate 12803116
Q.31
Evaluate 12803117
Q.32
Evaluate 12803118
Q.33
Evaluate 12803119
Q.34
Evaluate ;(at + b > 0)
Q.35
Evaluate
; (x > 0) 12803121
Q.36
Evaluate ; (x > 0) 12803122
Q.37
Evaluate ;(-a<x< a)
12803123
Q.38
Find . 12803124
Q.39
Find ,
(a ¹ 0) 12803125
Q.40
Evaluate 12803126
Q.41
Evaluate 12803127
Q.42
Evaluate (Board
2011)
12803128
Q.43
Evaluate 12803129
Q.44
Evaluate ; 12803130
Q.45
Evaluate 12803131
Q.46
Evaluate , x > 0
12803132
Q.47
Evaluate 12803133
Q.48
Find . 12803134
Q.49
Find .
12803135
Q.50
Find , (a ¹ 0)
12803136
Q.51
Evaluate 12803137
Q.52
Evaluate
7.
(Board 2012) 12803138
Q.53
Evaluate
8.
(Board 2011) 12803139
Q.54
Evaluate ;(a > 0 , a ¹ 1)
12803140
Q.55
Evaluate ;
9. (x > a or x < - a) 12803141
Q.56
Evaluate: (3x - 2x + 1) dx 12803142
Q.57
Evaluate:
dx (x
> 0)
12803143
Q.58
Evaluate: x dx (x > 0)
12803144
Q.59
Evaluate: (2x + 3) dx 12803145
Q.60
Evaluate: 
dx (x >
0)
12803146
Q.61
Evaluate: dx (x > 0)
12803147
Q.62
Evaluate: dx (x > 0)
12803148
Q.63
Evaluate: dy (y > 0)
(Board
2010) 12803149
Q.64
Evaluate: dq (q > 0)
12803150
Q.65
Evaluate: dx
10. (Board
2009)
12803151
Q.66
Evaluate: dx 12803152
Q.67
Evaluate: 
12803153
Q.68
Evaluate: 
dx 12803154
Q.69
Evaluate: 
sin (a+b) x dx 12803155
Q.70
Evaluate: 
dx 12803156
11. (1 - cos 2 x > 0)
Q.71
Evaluate: 
dx
(Board 2010) 12803157
Q.72
Evaluate: 
sinx dx
12. (Board
2011) 12803158
Q.73
Evaluate: 
dx
12803159
Q.74
Evaluate: 
dx 12803160
Q.75
Evaluate: cos 3x sin 2x dx
(Board 2012) 12803161
Sol: Let
I = cos 3x sin 2x dx
Q.76
Evaluate: dx 12803162
13. (1 + cos 2x ¹
0)
Q.77
Evaluate: 
tanx dx 12803163
14. (Board 2008, 09, 11)
Q.78
Evaluate 
12803164
Evaluate
x dx 12803165
Q.79
Evaluate dx 12803166
15. (Board 2011,
12)
Q.80
Evaluate 
dx
Q.81
Evaluate 
dx 12803168
Q.82
Evaluate 12803169
Q.83
Evaluate dx 12803170
16. (Board 2008, 10
Q.84
Evaluate 
dx 12803171
Q.85
Evaluate 
12803172
Q.86
Evaluate 
dx
17. (Board 2009) 12803173
Q.87
Evaluate 
dq 12803174
Q.88
Evaluate 
dx 12803175
(Board 2012)
Q.89
Evaluate cos x dx 12803176
Q.90
dx
12803177
Q.91
Evaluate 
dx 12803178
18. (Board 2010, 11)
Q.92
Evaluate 
dx 12803179
(Board 2009)
Q.93
Evaluate 
(Board 2012) 12803180
Q.94
Evaluate 
x 12803181
Q.95
Evaluate: tan4
x dx 12803182
Q.96
Evaluate: sec x dx 12803183
Q.97
Evaluate: tan3
x sec x dx 12803184
Q.98
Evaluate: 
dx 12803185
Q.99
Evaluate 
x5
ln x dx 12803186
Q.100 Show that
= e
f(x) + c 12803187
Q.101 Find 12803188
Q.102 Find (Board 2011)
12803189
Q.103
Evaluate 12803190
Q.104 Evaluate sin x dx 12803191
Q.105
Evaluate: 
x sinx dx (Board 2012) 12803192
Q.106
Evaluate: 
n x dx 12803193
Q.107
Evaluate: x. n x dx 12803194
Q.108
Evaluate: x3 ln x dx 12803195
Q.109 Evaluate: tan–1 x dx (Board
2011)
12803196
Q.110
Evaluate: x2
sin x dx 12803197
Q.111
Evaluate: x tan-1 x dx 12803198
Q.112
Evaluate: sin–1 x dx 12803199
Q.113 Evaluate: (ln x) dx
(Board 2010)
12803200
Q.114
Evaluate: ln (tan x) . secx dx
12803201
Q.115
Evaluate: 
dx 12803202
Q.116
Evaluate: 
dx
19.
(Board 2012) 12803203
Q.117
Evaluate: ex (cos x + sin x) dx
20.
12803204
Q.118
Evaluate: 
dx
12803205
Q.119
Evaluate: e2x [-sin x + 2 cos x] dx
(Board 2009,
12) 12803206
Q.120
Evaluate ; (x > a)
(Board 2008) 12803207
Q.121
Evaluate 
(Board 2011)
12803208
Q.122
Why we omit the
constant of integration in definite integrals. 12803209
Q.123 Find . 12803210
Q.124
In , what is
range, lower limit and upper limit of integration. 12803211
Q.125 Evaluate 12803212
Q.126
Evaluate
12803213
Q.127
Evaluate 12803214
Q.128
Evaluate (Board
2012)
12803215
Q.129
Evaluate (Board 2012)
12803216
Q.130 If = 5 and = 4, then
evaluate the definite integral 12803217
Q.131
Write down any two properties of
definite integral. (Board 2010) 12803218
Q.132
Evaluate
21. (Board
2015) 12803219
Q.133 Evaluate 12803220
Q.134 Find . 12803221
Q.135 Evaluate (Board 2011,15)
12803222
Q.136
If = 5 and = 4 , then evaluate the definite integral - 12803223
Q.137 Evaluate:
12803224
Q.138
Evaluate: 12803225
Q.139
Evaluate: 12803226
Q.140 Evaluate:
(Board 2009) 12803227
Q.141
Evaluate: 12803228
Q.142
Evaluate:
12803229
Q.143
Evaluate:
(Board 2011)
12803230
Q.144
Evaluate: 
12803231
Q.145
Evaluate:
12803232
Q.146
Evaluate: 12803233
22. (Board 2009)
Q.147
Evaluate: 12803234
Q.148
Evaluate:
(Board 2011) 12803235
Q.149 Evaluate: 12803236
23.
(Board 2008, 12)
Q.150
Evaluate: 12803237
(Board 2012)
Q.151 Evaluate: 12803238
24.
(Board 2012)
Q.152
Evaluate: 12803239
Q.153
Evaluate: 12803240
Q.154
Evaluate: 12803241
(Board 2007)
Q.155 Evaluate: 12803242
Q.156
Evaluate: 12803243
Q.157
Evaluate: 12803244
(Board 2010)
Q.158 Find the area bounded by the curve y=4 - x and the x-axis. (Board 2012) 12803245
Q.159 Find the area between the x-axis and the curve y = 4 - x in the first quadrant from x = 0 to x =
3. 12803246
Q.160 Find the area bounded by the curve
y = x + 3x and the x-axis. 12803247
(Board 2009)
Q.161 Find the area between the x-axis and the curve y = x+ 1 from x = 1 to
x = 2. (Board 2008) 12803248
Q.162 Find the area above the x-axis and under the curve y = 5 - x from x = -1 to x = 2. (Board 2009) 12803249
= 15 - 3 = 12 square units
Q.163 Find the area below the curve y = 3 and above the x-axis between
x = 1 and x = 4. 12803250
Q.164 Find the area bounded by cos function from x = - to x =
. 12803251
Q.165 A find the area above the x-axis bounded by the curve y2
= 3 - x from
x = –1 to x = 2. 12803252
Q.166 Find the area between the x-axis and the curve y = 4x - x (Board 2010) 12803253
Q.167 Find the area between the x - axis and the curve g(x) = cos x from x = – p to p (Board
2011) 12803254
Q.168 Find the area between the x-axis and the curve y = sin 2x from x =
0 to x =
12803255
Q.169
Solve the differential
equation
x (2y + 1) - 1 = 0 12803256
Q.170 Solve = 12803257
Q.171 Solve (sin y + y cos y) dy
25.
= [x (2 ln
x + 1)] dx
12803258
Q.172
State fundamental
theorem of calculus. (Board
2010) 12803259
Q.173 Solve the differential equation
(x - 1) dx + y dy = 0 12803260
Q.174
Solve 2e tan y dx+(1-e) secy dy=0; 12803261
Q.175 Solve = x + x - 3 , if y = 0
when x = 2. 12803262
Q.176 What are
initial value conditions?
26. 12803263
Q.177 Solve the differential equation
- 2y = 0 ,
x ¹0 , y > 0(Board 2008) 12803264
Q.178 The slope of the tangent at any point of the curve is given by = 2x - 2 , find the equation of the curve if y =
0 when x = -1.
12803265
Q.179
A particle is moving in
a straight line and its velocity is given by
v = t
- 7t + 10, find s (distance) in terms of t
if s = 0 when t = 0 12803266
Q.180 Cheek that the equation written against the differential equation
is its solution. x = 1 + y, y = cx -1 12803267
Q.181 Solve the following differential
equation: = - y 12803268
Q.182
Solve the following differential equation: y dx + x dy = 0 12803269
Q.183
Solve the following differential equation: = 12803270
Q.184
Solve the following differential equation: =
, (y > 0) 12803271
Q.185 Solve the following differential equation: sin y cosec x =1 12803272
Q.186 Solve the following differential equation: x dy + y (x - 1) dx = 0 12803273
Q.187 Solve the following differential equation: × = 12803274
Q.188 Solve the following differential equation: 2 x y = x - 1 (Board 2012)
12803275
Q.189
Solve the following differential equation: + = x 12803276
Q.190
Solve the following differential
equation:
sec x tan ydx+ sec y tan x dy = 0
27. 12803277
Q.191
Solve the following differential equation: 1
+ cos x tan y = 0 12803278
Q.192 Solve the following differential
equation: sec x + tan y = 0 12803279
Q.193 Solve the following differential
equation:
=
28. (Board
2011, 12) 12803280
|
Unit |
Introduction to Analytic Geometry |
|
04 |
Multiple Choice Questions
q Each question has
four possible answers. Select the correct answer and encircle it.
Q.1
The distance between two
points
P(x, y) and P(x, y) on the
co-ordinate plane is given by: 12804001
(a) +
(b)
(c)
(d)
Q.2
The distance of any point P (x, y) from the origin
O(0, 0) is given by: 12804002
(a) x+ y (b) x– y
(c) (d)
Q.3
The mid-point of the line
joining
A(x1, y1) and B(x2, y2) is: (Board
2008) 12804003
(a)
(b)
(c)
(d)
Q.4
The co-ordinates of a point dividing the line
segment joining the points
P(x, y) and P(x, y) internally in the ratio k: k has
co-ordinates: 12804004
(a)
(b)
(c)
(d)
Q.5
The co-ordinates of the
point which divides the join of P(x, y) and Q(x, y) externally in the
ratio m : n are given by:
12804005
(a)
(b)
(c)
(d)
Q.6
If A(x, y), B(x, y) and C(x,y) are the vertices
of a triangle ABC, then
co-ordinates of its centroid are given by:
12804006
(a)
(b)
(c)
(d)
Q.7
If A (x, y), B(x, y) and C(x,y) are the
vertices of a triangle ABC, then
co-ordinates of incentre are given by: 12804007
(a)
(b)
(c)
(d)
Q.8
If a pair of opposite sides
of a quadrilateral are equal and parallel then it is a: 12804008
(a) rectangle
(b) rhombus
(c) parallelogram
(d) None of these.
Q.9
x-coordinate of any point on Y-axis
is:
12804009
(a) 0 (b) x
(c) 1 (d) y
Q.10
y-coordinate of any point on X-axis
is:
12804010
(a) 0 (b) x
(c) 1 (d) y
Q.11
In a plane
two mutually perpendicular number lines x¢ox and y¢oy, one
horizontal and the other vertical are called : 12804011
(a) x-axis
(b) coordinate
axes
(c) y-axis
(d) None
of these
Q.12
If (x, y)
are the coordinate of a point P, then the second component of the ordered pair
is called: 12804012
(a) abscissa (b) ordinate
(c) coordinate
(d) ordered pair
Q.13
If the
distance between points (a, 5) and (1, 3) is 
, then a
= (Board 2009)
(a) 4 (b) 2 12804013
(c) 
(d) 1
Q.14
A
parallelogram is a rhombus if and only if its diagonals are: 12804014
(a) parallel
(b) perpendicular
(c) equal
(d) None of these.
Q.15
The
vertical line y¢oy is called:
12804015
(a) x-axis (b) y-axis
(c) abscissa (d) ordinate
Q.16
The
distance between the points
(1, 2), (2, 1), then: (Board 2009) 12804016
(a) 1 (b) 
(c) 2 (d) 
Q.17
If the
directed distances AP and PB have the same signs, then their ratio is positive
and P is said to divide AB: 12804017
(a) internally (b) may be divide
(c) externally (d) None of these
Q.18
The
centroid of a triangle is a point that divides each median in the ratio: 12804018
(a) 2
: 1 (b) 2
: 3
(c) 1
: 3 (d) 4 : 3
Q.19
The
intersection of any two sides of a triangle gives: 12804019
(a) median
(b)
altitude
(c) vertex
(d) None
of these
Q.20
If (x, y)
are the coordinates of a point, then the first component of the ordered pair is
called: 12804020
(a) abscissa
(b) ordinate
(c) coordinate
axes
(d) None
of these
Q.21
The
coordinate axes divide the plane into ------------ equal parts. 12804021
(a) 1 (b) 2
(c) 3 (d) 4
Q.22
If the
directed distances AP and PB have the opposite signs, i.e; p is beyond AB, then
their ratio is negative and P is said to divide AB: 12804022
(a) internally (b) may be divide
(c) externally (d) None of these
Q.23
The ratio
in which the line segments joining (2, 3) and (4, 1) is divided by the line
joining (1, 3) and (4, 3) is: 12804023
(a) 2 : 1 (b) 3 : 1
(c) 1 : 2 (d) None of these.
Q.24 Inclination of X-axis or of any line parallel to
X-axis is: 12804024
(a) zero (b) p
(c) (d)
undefined.
Q.25
Inclination
of Y-axis or of any line parallel to Y-axis is: 12804025
(a) p (b) zero
(c) (d) undefined.
Q.26 What is the nature of the line whose
equation is A x + B y + C = 0 when A = 0, B and C ¹
0: 12804026
(a) line parallel to x-axis
(b) line parallel to y-axis
(c) line passing through the origin
(d) both (a) and (b)
Q.27 What is the nature of the line whose
equation is A x + B y + C = 0 when B = 0, A and C ¹
0: 12804027
(a) line parallel to x-axis
(b) line parallel to y-axis
(c) line passing through the origin
(d) both (a) and (b)
Q.28 What is the nature of the line whose
equation is A x + B y + C = 0 when C = 0, A and B ¹
0 : 12804028
(a) line parallel to x-axis
(b) line parallel to y-axis
(c) line passing through the origin
(d) both (a) and (b)
Q.29 What is the nature of the line whose
equation is A x + B y + C = 0, when A ¹ 0, B ¹
0, C ¹ 0 : 12804029
(a) line parallel to x-axis
(b) line parallel to y-axis
(c) inclined
(d) both (a) and (b)
Q.30
If the points (a, 0), (0, b) and (x,
y) are collinear, then: 12804030
(a) + = 0 (b)
+ = 1
(c) + = 1
(d) None of these.
Q.31
Equation of
a line parallel to x-axis is: (Board 2007) 12804031
(a) x
= 0 (b) x = y
(c) y
= a (d) x = a
Q.32
The angle a Î [0° , 180°[ measured counter clock wise from positive x-axis to a non horizontal
straight line l is: 12804032
(a) slope
of l
(b) inclination of l
(c) gradient
of l
(d) None of these
Q.33
If the line
l is parallel to x-axis, then the
slope of l is: 12804033
(a) 0 (b) 1
(c) 2 (d) undefined
Q.34
The line l is horizontal if and only if slope is
equal to: 12804034
(a) 0 (b)
1
(c) 2 (d)
undefined
Q.35
The symbol ^ is used for: 12804035
(a) parallel lines
(b) perpendicular lines
(c) non-parallel lines
(d) None of these
Q.36
The symbol | | is used for: 12804036
(a) parallel lines
(b) perpendicular lines
(c) non-parallel lines
(d) None of these
Q.37
The symbol is used for: 12804037
(a) parallel lines
(b) non-parallel lines
(c) perpendicular lines
(d) coplanar lines
Q.38
The lines lying on the same
plane are called : (Board 2005) 12804038
(a) collinear
lines
(b) coplanar
lines
(c) concurrent (d) parallel
lines
Q.39
The two lines l and l with respective slopes m and m are parallel if and only if:
12804039
(a) m ¹ m (b) m´ m = - 1
(c) m = m (d) m´ m ¹ - 1
Q.40
The line x = a is on the
right of
y-axis, if: 12804040
(a) a
> 0 (b) a < 0
(c) a
= 0 (d) a ¹ 0
Q.41
y = mx + c is the equation
of straight line in: 12804041
(a) slope-intercept form
(b) two points form
(c) point slope form
(d) intercepts form
Q.42
x = x + r cos q , y = y + r sin q is called the equation of straight line in: 12804042
(a) point-slope
form
(b) two
points form
(c) normal
form
(d) sysmmetric
form
Q.43
The
perpendicular distance of the line 3x +
4y + 10 = 0 from the origin is: 12804043
(Board 2005)
(a) 0 (b) 1
(c) 2 (d) 3
Q.44
Intercepts form of equation
of line is: (Board 2005, 09) 12804044
(a) 
(b) 
(c) 
(d) 
Q.45
y - y = m (x - x) is the equation of straight line in: 12804045
(a) slope-intercept form
(b) point-slope form
(c) normal form
(d) intercepts form
Q.46
If a is the inclination of a non-vertical line l, then it
slope or gradient is: 12804046
(Board 2005)
(a) sin
a (b) cos a
(c) tan
a (d) cot a
Q.47
If the
inclination of a line lies between ]90° , 180°[ , then the slope of line is: 12804047
(a) positive (b) negative
(c) zero (d)
undefined
Q.48
y = - 2 is a line: 12804048
(a) parallel
to x-axis
(b) parallel
to y-axis
(c) perpendicular
to x-axis
(d) None
of these
Q.49
The line y
= a is above the x-axis, if:
12804049
(a) a
> 0 (b) a < 0
(c) a
¹ 0 (d) a = 0
Q.50
If the
lines 
and 
are
perpendicular, then:
12804050
(a) a a – b b = 0
(b) a a + b b = 0
(c) a b - a2 b1
= 0
(d) a b + a2 b1
= 0
Q.51 Two lines and are parallel
if:(Board 2005)
12804051
(a) 
(b) 
(c) 
(d) 
Q.52
If the
inclination of the line l lies
between ]0°,90°[, then the slope of l is: 12804052
(a) positive (b) undefined
(c) negative (d) None of these
Q.53
The points
A , B and C are collinear, then slope of
and slope of are: 12804053
(a) equal (b) opposite in sign
(c)
different (d) None
of these
Q.54
x = 4 is a
line: 12804054
(a) parallel
to x-axis
(b) parallel
to y-axis
(c) ^ to y-axis
(d) None
of these
Q.55
If a = 0,
then the line ax + by + c = 0 is parallel to: (Board 2008) 12804055
(a) y-axis (b) x-axis
(c) along
y-axis (d) none of these
Q.56
y - y = (x - x) is the equation of straight line in: 12804056
(a) slope-intercept
form
(b) two
points form
(c) symmetric
form
(d) two
intercepts form
Q.57
The distance d from the point P(x , y) to the
line ax + by + c = 0 is given by: 12804057
(a) d
=
(b) d
=
(c) d
=
(d) d
=
Q.58
If the line
l is parallel to y-axis, then the
slope of l is ------------. 12804058
(a) 0° (b) 90°
(c) 180° (d) undefined
Q.59
The two
lines l and l with respective slopes m and m are perpendicular if and only if: (Board 2006) 12804059
(a) m = m (b) m´m = - 1
(c) m ¹ m (d) m´m ¹ - 1
Q.60
The line y
= a is below the x-axis, if:
12804060
(a) a
> 0 (b) a < 0
(c) a
¹ 0 (d) a = 0
Q.61
The slope
of line y = x + is equal to: 12804061
(a) - (b)
(c) - (d)
Q.62
If a
straight line is perpendicular to
y-axis, then its slope is: (Board 2011)
12804062
(a) 1 (b)
–1
(c) 0 (d)
undefined
Q.63
The line l is vertical if and only if slope is: 12804063
(a) 0 (b) 1
(c) 2 (d)
undefined
Q.64
x = c is a
line: 12804064
(a)
perpendicular to x-axis
(b)
parallel to x-axis
(c)
perpendicular to y-axis
(d) None of these
Q.65
y = 2x + 3
is the: 12804065
(a) slope-intercept
form
(b) two
points form
(c) point
slope form
(d) intercepts
form
Q.66
The
equation of a line which passes the point (3, 4) and whose intercepts on the
axes are equal in magnitude but opposite in sign is: 12804066
(a) x
+ y - 1 = 0 (b) x - y - 1 = 0
(c) y - x + 1 = 0 (d) None of these.
Q.67
The
equation of a straight line passing through the origin and parallel to the line
3x - 2y + 1 = 0 is: 12804067
(a) y = x (b) y = x
(c) x = y (d) x = – y
Q.68
The equation to the straight
line which passes through the point (2, 9) and makes an angle of 45° with x- axis is: 12804068
(a) x + y + 7 = 0 (b) x - y + 7 = 0
(c) y - x + 7 = 0 (d) None of these
Q.69
The
equation of a straight line which parallel
to the line 3x - 2y + 5 = 0 and passes through (2,- 1) is: 12804069
(a) 3x + 2y - 8 = 0
(b) 3x - 2y + 8 = 0
(c) 3x - 2y - 8 =
0
(d) 3x + 2y + 8 = 0
Q.70 Infinite number of lines can pass through: 12804070
(a) one
point
(b) two
points
(c) three points
(d) four
points.
Q.71
Distance of the point (-3, 7) from
x-axis is: 12804071
(a)
3 (b) –3
(c) 7 (d) 10
Q.72
Distance of the point (-2, 3) from
y-axis is: 12804072
(a)
–2 (b) 2
(c) 3 (d) 1
Q.73
If matrix of the coefficients of the lines ax+by+c=0, ax + by+c2
= 0 and
ax + by + c= 0 is
singular, then lines are:
12804073
(a) collinear
(b) coplanar
(c) concurrent
(d) None
of these
Q.74
General
form of equation of line is:
(Board
2006) 12804074
(a) ax - by + c = 0
(b) ax + by - c = 0
(c) ax + by + c = 0
(d) ax - by - c =
0
Q.75
A quadrilateral
having two parallels and two non-parallel sides is called: 12804075
(a)
trapezium (b) rectangle
(c)
rhombus (d) None of these
Q.76
Two non-parallel lines in a
plane intersect each other at : 12804076
(a) one and only one point
(b) more than one point
(c) (0,
0)
(d) (1,
1)
Q.77
If the points A, B and C are
collinear, then area of the DABC will be: 12804077
(a) 0 (b) 2
(c) 1 (d) None
of these
Q.78
The angle between the lines 
and 
is:(Board 2009) 12804078
(a) 90o (b) 60o
(c) 45o (d) 30o
Q.79
The angle between the lines 
and 
is:
(Board 2009) 12804079
(a) 
(b) 
(c) 
(d)
Q.80
If P(x , y) , Q(x , y) and
R(x , y) are the vertices of the triangle, then area of the triangle is: 12804080
(a) (b)
(c) (d) None of these
Q.81
The area of
the triangle with vertices at the points (a, b + c), (b, c + a), (c, a + b) is: 12804081
(a) 0 (b) a + b + c
(c) ab + bc + ca (d) None of these
Q.82
has matrix form as:
(Board
2007) 12804082
(a) 
(b) 
(c) 
(d) 
Q.83
Three
nonparallel lines l: ax + by
+ c = 0, l: ax + by + c= 0 and l: ax + by + c= 0 are concurrent if and only if:
12804083
(a) ¹ 0
(b) =0
(c) = 1
(d) =0
Q.84 The pair of lines of homogeneous
second-degree equation ax+2hxy+by = 0 are real and coincident, if: 12804084
(a) h < ab (b) h > ab
(c) h = ab (d) None of these
Q.85
Two lines
of homogeneous second degree equation ax+2hxy + by = 0 are parallel if: 12804085
(a) h = ab
(b) h > ab
(c) h < ab
(d) None
of these
Q.86
A pair of
lines of homogeneous second degree equation ax + 2hxy + by2 = 0 are orthogonal, if:
(Board 2005, 11) 12804086
(a) a
- b = 0 (b) a + b = 0
(c) a
+ b > 0 (d) a - b < 0
Q.87
The pair of
lines of homogeneous second-degree equation ax +2hxy+by =0 are imaginary, if: 12804087
(a) h = ab (b) h > ab
(c) h < ab (d) None of these
Q.88
The pair of lines of
homogeneous second-degree equation ax+2hxy+by = 0 are real and
distinct, if: (Board 2007, 11)
12804088
(a) h < ab (b) h > ab
(c) h = ab (d) None of
these
Q.89
If q is measure of the angle between the pair of lines of homogeneous
second degree equation ax + 2hxy + by = 0 then: (Board 2009) 12804089
(a)
(b) 
(c)
(d) 
Q.90
Joint equation of y + 2x = 0,
y - 3x = 0 is: (Board 2007) 12804090
(a) 
(b)
(c)
(d)
Q.91
For any point (x, y) on
x-axis:
(Board 2014)12804091
(a) y
= 0
(b)
y = – 1
(c) y
= 1
(d)
y = 2
Q.92
The point
of concurrency of medians of triangle is called: (Board 2014)12804092
(a) In-centre (b) Centroid
(c) Circumcentre (d) Orthocentre
Q.93
Slope of
line perpendicular to line 2x– 3y + 1 = 0 is equal to: (Board 2014)12804093
(a) 
(b) 
(c) 
(d) 
Q.94
X-co-ordinate
of centroid of triangle ABC with A(–2, 3); B(–4, 1) ; C(3,5) equals:
(Board 2014)12804094
(a) – 1 (b) 1
(c) 3 (d) – 3
Q.95
The ratio
in which y-axis divides the line joining (2, –3) and (–5, 6) is:
(Board 2013)12804095
(a) 2 : 3 (b) 2 : 5
(c) 1 : 2 (d) 3 : 5
Q.96
Let 
and
then
is homogenous equation of degree:
(Board 2015)12804096
(a) 1 (b) 2
(c) 0 (d) n
Q.97
The slope
of tangent line to 
at 
is:
(Board 2015)12804097
(a) m (b) 
(c) 
(d) 
Q.98
The distance of point P (6 , –1) from the line 6x – 4y
+ 9 =0 is:
(Board 2015)12804097
(a)
49 (b) 
(c) 
(d) 
Q.99
The point of intersection of medians of a triangle is called: (Board 2015)12804097
(a) Centroid (b)
Orthocenter
(c) Circumcentre (d)
Incentre
Q.100 Slop
intercept form of line equals:
(Board 2015)12804097
(a) y – y1 = m(x–x1) (b)
(c)
x cosq + y sin q = p (d)
y = mx + c
Q.101 Point of intersection of lines x – 2y + 1
= 0 and 2x – y + 2 = 0 equals:
(Board 2015)12804097
(a) (1,0) (b) (0,
1)
(c) (–1, 0) (d) (0, –1)
Short Answer Questions
Q.1
What is analytic geometry? 12804098
Q.2
Define coordinate axes. 12804099
Q.3
Define centroid of a triangle. 12804100
Q.4
Define ortho-centre of a triangle. 12804101
Q.5
Define circum-centre of a triangle.
12804102
Q.6
Define in-centre of a triangle. 12804103
Q.7
What do you mean by the locus of a point? 12804104
Q.8
What is abscissa? 12804105
Q.9
What is ordinate? 12804106
Q.10
What are the coordinates of the
in-centre of a triangle whose vertices are A(x1, y1), B(x2,
y2), C(x3, y3). (Board 2009)
12804107
Q.11
Define the
external division of the line segment joining the two points in plane. (Board 2010) 12804108
Q.12
Show that the points A(-1,2),
B(7, 5) and C(2 , -6) are
vertices of a right triangle. 12804109
Q.13
Find the coordinates of the point that divides the
join of A(-6 , 3)
and B(5 , -2)
internally in the ratio 2 : 3. 12804110
Q.14
Show that the points A(-3,6),
B(3, 2) and C(6,0) are collinear. 12804111
(Board
2007)
Q.15
Find the coordinates of the point that divides the
join of A(-6 , 3) and
B(5, -2)
externally in the ratio 2 : 3. 12804112
Q.16
The point C(-5 , 3) is the centre of a circle and P(7 , -2) lies on
the circle. What is the radius of the circle? 12804113
Q.17
Find the coordinates of a point that divides the join
of A (-6, 3) and
B(5,-2) in the
ratio 2 : 3. (Board 2008) 12804114
Q.18
Find the distance between the two given points and
mid-point of the line segment joining the two points A, B (Board 2006) 12804115
Q.19
Show that the points 
and 
are vertices of a right triangle. 12804116
Q.20
Show that the points 
and 
are vertices of an isosceles triangle. 12804117
Q.21
Find h such that the points 
and are vertices of a right triangle with right angle at
the vertex A. 12804118
Q.22
Find h such that 
and 
are collinear.(Board 2008) 12804119
Q.23
The points 
and B(5, – 4) are ends of a diameter of a circle. Find
the centre and radius of the circle.
(Board
2009) 12804120
Q.24
Find h such that the points A(h,1) , B(2, 7) and C (–
6, – 7) are vertices of a right triangle
with right angle at the vertex A. 12804121
Q.25
Find the points trisecting join of
A(–1, 4) and B(6, 2). 12804122
Q.26
Find the point three-fifths of the way along the line
segment from
A(– 5, 8) to B(5, 3). (Board 2008) 12804123
Q.27
Define translation of axes.
(Board
2009, 10) 12804124
Q.28
The xy-coordinate axes are translated through the
point O¢ (4, 6).
The coordinates of the point P are
(2, -3) referred
to new axes. Find the coordinates of P referred to the original axes. 12804125
Q.29
The
coordinates of a point P are (-6 , 9). The axes are translated through the point O¢ (-3 , 2). Find the coordinates of P referred to the new axes. 12804126
Q.30
The two points P(3, 2) and O¢ (1, 3) are
given in xy-coordinate system. Find the XY-coordinates of P referred to the
translated axes O¢X and O¢Y. 12804127
Q.31
The xy-coordinate axes are translated through the point O¢(3, 4). The coordinates of P(8, 10) are given in the
XY-coordinate system. Find the coordinates of P in xy-coordinate. 12804128
Q.32
The xy-coordinates axes are rotated about the origin
through the indicated angle. The new axes are OX and OY. Find the
XY-coordinates of the point P with the given xy-coordinates. 12804129
P(5,
3) ; q = 45o
Q.33
The xy-coordinates axes are rotated about the origin
through the indicated angle. The new axes are OX and OY. Find the
XY-coordinates of the point P with the given xy-coordinates.
P(3, - 7) ; q = 30° (Board 2011)
12804130
Q.34
What is slope or gradient of a line?
12804131
Q.35
Define two point form of a line.
12804132
Q.36
Find the slope and inclination of the x-axis. 12804133
Q.37
Find the slope and inclination of the y-axis 12804134
Q.38
Find the slope and inclination of the line bisecting
the first and third quadrant.
12804135
Q.39
Find the slope and inclination of the line bisecting
the 2nd and fourth quadrant.
12804136
Q.40
Find slope of
line through the points (- 2, 1) and
(6, - 4). 12804137
Q.41
Define slope-intercept form of a line.
12804138
Q.42
Define point slope form of a line.
12804139
Q.43
What is inclination of a line? 12804140
(Board
2008)
Q.44
What are conditions for two lines to be coincident,
parallel, perpendicular or intersecting? 12804141
Q.45
What are the conditions for the collinearity of three
points. 12804142
Q.46
Find the slope and inclination of the line through the
points(3, – 4),(– 2, 5) 12804143
Q.47
By means of slopes, show that the following points lie
on a line:
(–
1, – 3) ; (1, 5) ; (2, 9) 12804144
Q.48
Show that the triangle with vertices A(1,1), B(4,5)
and C(12,-1) is a
right triangle. 12804145
Q.49
Find the equation of the straight line if its slope is
2 and y intercept is 5. 12804146
(Board
2006)
Q.50
Prove that equation of a non-vertical straight line l with slope m and passing through a
point Q(x , y) is given
by y - y = m(x - x) 12804147
Q.51
Equation of a line whose non-zero x and y intercepts
are a and b respectively, is given by + = 1 (Board 2011) 12804148
Q.52
Prove that equation of a non-vertical straight line
with slope m and
y-intercept c is given by y = mx + c 12804149
Q.53
Write down an equation of the line which cuts x-axis
at (2, 0) and y-axis at 0, - 4). 12804150
Q.54
Find the distance between the parallel
lines 2x+y+2=0 and 6x+3y - 8=0. 12804151
(Board
2005)
Q.55
Find the distance between the parallel lines l: 2x - 5y + 13 =
0 and
29. l: - 2x +
5y - 6 = 0 12804152
Q.56
Find the
distance from the point
P(6, -1) to the line 6x - 4y + 9 = 0 12804153
Q.57
Find the slope
of the line through the points (-2, 4) and (5, -11). (Board 2009)
12804154
Q.58
Find an equation of the line through the points P(2,
3) which forms an isosceles triangle with the coordinate axes in the first
quadrant 12804155
Q.59
Find the slope and angle of inclination of the line
joining the points.
( – 2, 4), (5, 11) 12804156
Q.60
Find the slope and angle of inclination of the line
joining the points.
(4, 6), (4, 8) 12804157
Q.61
Find k so that the line joining A(7, 3) ; B(k, – 6) and the line joining
C( – 4, 5); D ( – 6, 4) are parallel. 12804158
(Board
2009)
Q.62
Find k so
that 
is perpendicular to 
, where
A(7, 3) B(k,-6), C(–4,5),
D(–6,4) are given vertices.(Board 2008)
12804159
|
|
|
Q.63
Find k so that the line joining A(7, 3);
B(k, – 6) and the line joining
C( – 4, 5) ;
D ( – 6, 4) are perpendicular. 12804160
Q.64
Using slope, show that the triangle with vertices at
A(6, 1), B(2, 7) and C( – 6,
– 7) is a right triangle. 12804161
Q.65
Show that the points A(-3, 6), B(3 , 2) and C(6 , 0) are
collinear. 12804162
Q.66
Find the equation of the straight line if it is
perpendicular to line with slope
-6 and y
intercept is 12804163
Q.67
Define intercept form of a line.
12804164
Q.68
Find an
equation of the horizontal line through 
. 12804165
Q.69
Find an
equation of the vertical line through 
12804166
Q.70
Find an
equation of the line bisecting the first and third quadrants. 12804167
Q.71
Find an
equation of the line bisecting the second and fourth quadrants. 12804168
Q.72
Find an
equation of the line through
A(– 6, 5) having slope 7 12804169
Q.73
Find an equation
of the line through (8, – 3) having slope 0 12804170
Q.74
Find an
equation of the line through (– 8, 5) having slope undefined. 12804171
Q.75
Find the
equation of the horizontal line through (7, -9). (Board 2007, 10) 12804172
Q.76
Find an
equation of the line
y - intercept – 7 and slope – 5. 12804173
Q.77
Find an
equation of the line having x-intercept – 9 and slope 4. 12804174
Q.78
Find an
equation of the line having
x-intercept – 3 and y-intercept 4. 12804175
Q.79
Find an
equation of the perpendicular bisector joining the points
A(3, 5) and B(9, 8). (Board 2010) 12804176
Q.80
Find an
equation of the line through (–4, –6) and perpendicular to a line having slope
– . (Board
2015) 12804177
Q.81
The length of perpendicular from the origin to the
line is 5 units and the angle of inclination of the perpendicular is 120°. Find the
slope and y-intercept of the line.
(Board 2015) 12804178
Q.82
Find an
equation of the line through (11, –5) and parallel to a line with
slope – 24. 12804179
Q.83
Convert the
equation 15y–8x+3=0 into: (Board 2009)
12804180
(i) slope
intercept form.
(ii) two intercepts form.
(iii) normal form.
Q.84
Transform the equation:
5x - 12y+39 = 0
into two-intercept form.
12804181
Q.85
Transform the equation
5x-12y + 39 =
0 into Point-slope form.
12804182
Q.86
Transform the equation:
2x - 4y + 11 =
0 into Slope-intercept form.
(Board 2009) 12804183
Q.87
Find whether two lines joining
A(1, -2), B(2, 4)
and C(4, 1), D(-8, 2) are:
(i) Parallel 12804184
(ii) Perpendicular
(iii) None. (Board 2006)
Q.88
Two pairs of points are given. Find whether the two
lines determined by these points are (i) parallel, (ii) perpendicular (iii)
none. 12804185
(1,
– 2) , (2, 4) and (4, 1), ( – 8, 2)
Q.89
Check whether
the two lines are (i) parallel (ii)
perpendicular
3 y = 2x + 5 ; 3x + 2y – 8 =
0 12804186
Q.90
Check
whether the two lines are (i) parallel
(ii) perpendicular 12804187
4 y + 2x – 1 = 0, x – 2y – 7 =
0
Q.91
Check
whether the two lines are (i) parallel
(ii) perpendicular 12804188
4
x – y + 2 = 0, 12x – 3y + 1 = 0
Q.92
Check whether the two lines are
(i) parallel (ii) perpendicular 12804189
12x + 35 y – 7 = 0, 105x – 36y + 11 = 0
Q.93
Find an equation of the line through (–4, 7) and
parallel to the 2x – 7y + 4 = 0
12804190
Q.94
Find an
equation of the line through (5, – 8) and perpendicular to the join of
A (– 15, – 8), B(10, 7) 12804191
Q.95
Find whether
the given point lies above or below the given line. 12804192
(5, 8); 2x – 3y + 6 = 0
Q.96
Check
whether the given points are on the same or opposite sides of the given line.
(0, 0) and (– 4, 7); 5x–7y+70= 0 12804193
Q.97 Check whether the point (- 2, 4) lies above or below
the line 4x+ 5y - 3 = 0
(Board
2015) 12804194
Q.98
Check
whether the given points are on the same or opposite sides of the given line.
(2, 3) and (– 2, 3) ; 3x–5y+8 = 0 12804195
Q.99
Check whether the origin and the point P (5, - 8) lie on
the same side or on the opposite sides of the line 3x+7y+15= 0.
12804196
Q.100
Find the
area of the triangular region whose vertices are A(5, 3),
B(-2, 2), C(4, 2). (Board 2008) 12804197
Q.101
Find the area of the region bounded by the triangle
with vertices
(a, b + c), (a, b - c) and (- a, c). 12804198
(Board 2009)
Q.102
By considering the area of the region bounded by the
triangle with vertices
A(1, 4), B(2, - 3) and C
(3, - 10). Check
whether the three points are collinear or not. 12804199
Q.103
Define an angle from one line to other line. 12804200
Q.104
Find the angle from the line with slope to the
line with slope . 12804201
(Board
2010)
Q.105
Check whether the following lines are concurrent or not.
If concurrent, find the point of concurrency. 12804202
30. 3x - 4y - 3 = 0 5x
+ 12y + 1 = 0
31. 32x + 4y - 17 = 0
Q.106
What is family of lines? 12804203
Q.107
Write the equation of the line through the point of
intersection of the lines 3x – 4y – 10 = 0 and x + 2y – 10 = 0 in general form. (Board 2006) 12804204
Q.108
Check
whether the lines
4x -3y - 8 = 0, 3x -4y-6= 0 and x-y-2 = 0 are concurrent. (Board
2011) 12804205
Q.109
Find the
point of intersection of the lines. 12804206
3x
+ y + 12 = 0 and x + 2y – 1 = 0
Q.110
Find the
point of intersection of the lines. (Board
2007, 09) 12804207
x
+ 4y – 12 = 0 and x – 3y + 3 = 0
Q.111
Find the point of intersection of the lines 5x + 7y =
35 and x - 7y =
21 12804208
Q.112
Determine
the value of p such that the lines 2x - 3y - 1 = 0, 3x - y - 5 = 0 and
3x + py + 8 = 0 meet a point. 12804209
Q.113
Check
whether the lines
4x–3y–8 = 0, 3x – 4y – 6 = 0, x – y – 2 = 0 are concurrent. If so, find the
point where they meet. (Board 2008) 12804210
Q.114
Find the
angle measured from the line L to the line L where L : joining
(2, 7) and (7, 10) L : joining (1, 1) and
( – 5, 3) 12804211
Q.115
Find the
angle measured from the line L to the line L where:
(Board 2010)
L : joining (1, – 7) and (6, – 4)
L : joining ( – 1, 2) and ( – 6, – 1) 12804212
Q.116
Find the interior angle A of the triangle with
vertices A(-2,11), B(-6-3), C(4, -9). (Board 2008, 09) 12804213
Q.117
Express the
given system of equations in matrix form. Find whether the lines are
concurrent. 12804214
3x - 4 y -2 = 0, x+2y
- 4= 0, 3x -2y+5 = 0
Q.118
What is the area of trapezoidal region? 12804215
Q.119
Define an angle between the pair of lines of
homogeneous second degree equation. 12804216
Q.120
Define Trapezium.(Board 2009)
12804217
Q.121
Find a joint equation of the straight lines through
the origin perpendicular to the lines represented by x+ xy - 6y = 0
(Board 2015) 12804218
Q.122
Define normal form of a line. 12804219
Q.123
Find measure of the angle between the lines
represented by x - xy - 6y = 0
12804220
Q.124
In the triangle A(8, 6), B( – 4, 2), C(–2, – 6), find the slope of each
side of the triangle. 12804221
Q.125
Find the
condition that the lines
y = m1x + c1 ; y = m2 x+c2 and y =
m3 x+ c3 are concurrent. (Board
2011, 15) 12804222
Q.126
Find an equation
of each of the lines represented by
12804223
Q.127
Find
measure of the angle between the lines represented by 
12804224
Q.128
Find a
joint equation of the straight lines through the origin perpendicular to the
lines represented by: 12804225
(1)
Q.129
Find an equation of each of the lines represented by
20x+ 17xy - 24y = 0 12804226
Q.130
Find the
lines represented by:
Also find the angle between the lines. (Board 2010) 12804227
|
Unit |
Linear
Inequalities & Linear |
|
05 |
Multiple Choice Questions
q Each question has four possible
answers. Select the correct answer and encircle it.
Q.213
In-equalities
are expressed by the symbols: 12805001
(a) =, <, >, £, ³
(b) ¹, <, >, £, ³
(c) <, >, £, ³
(d) None of these
Q.214
ax £ b is an inequality of: 12805002
(a) one variable
(b) three variable
(c) two variable
(d) None of these
Q.215
ax + by
³ c is an inequality of: 12805003
(a) one variable
(b) three variable
(c) two variable
(d) None of these
Q.216
Non-vertical
lines divide the plane into ------------ half plane. 12805004
(a) upper and lower
(b) many
(c) left and right
(d) None of these
Q.217
There
are -------------- ordered pairs that satisfy the inequality ax + by > c. 12805005
(a) finitely many
(b) two
(c) infinitely many
(d) None of these
Q.218
The
order (or sense) of an inequality is changed by -------------, it each side by
a negative constant. 12805006
(a) adding (b)
subtracting
(c) dividing (d)
None of these
Q.219
The
graph of linear equation of the form ax + by = c is a ------------, where a, b
and c are constants and a, b are not both zero. 12805007
(a) curve (b) circle
(c) straight line
(d) None of these
Q.220
The
graph of linear equation of the form ax + by = c is dividing the plane into two
disjoint regions as ----------------------, where a, b and c are constants and
a, b are not both zero. 12805008
(a) ax + by £ c and ax + by ³ c
(b) ax + by < c and ax + by > c
(c) ax + by < c and ax + by ³ c
(d)
ax + by £ c and ax + by > c
Q.221
The
region of the graph ax+by > c is called ------- half plane. 12805009
(a) open (b) closed
(c) open as well as closed
(d) None of these
Q.222
The
graph of ax + by = c is called the ------------------ half planes ax + by >
c and ax + by < c. 12805010
(a) open (b)
boundary of
(c) closed
(d) None of these
Q.223
ax + b
< c is an inequality of: 12805011
(a) one variable
(b) three variable
(c) two variable
(d) None of these
Q.224
ax + by
< c is an inequality of: 12805012
(a) one variable
(b) three variable
(c) two variable
(d) None of these
Q.225
The
operation -------------- by a positive constant to each side of inequality will
affect the order (or sense) of inequality.
(a) adding 12805013
(b) subtracting
(c) multiplying
(d) None of these
Q.226
- ¥ < x < is the solution set of the inequality: 12805014
(a) x = (b) x
>
(c) x ¹ (d) x <
Q.227
A
solution of a linear inequality in x and y is an ordered pair of numbers, which
------------- the inequality. 12805015
(a) does not satisfies
(b) may be satisfies
(c) satisfies
(d) None of this
Q.228
The
region of the graph ax + by ³ c is called -------- half plane. 12805016
(a) open (b) closed
(c) open as well as closed
(d) None of these
Q.229
The linear equation -------------- is called the
associated or corresponding equation of the inequality ax+ by < c. 12805017
(a) ax + by ³ c (b) ax + by = c
(c) ax + by £ c (d) ax + by
> c
Q.230
x = c
is a vertical line parallel to
-------. 12805018
(a) x-axis
(b) y-axis may be
(c) y-axis
(d) None of these
Q.231
The inequality x < a is the open half plane to the
--------- of the boundary line
x = a. 12805019
(a) above (b) left
(c) below (d) right
Q.232
A point
of a solution region where two of its boundary lines intersects is called a
-------- point of the solution region. 12805020
(a) maximum (b) corner
(c) minimum
(d) None of these
Q.233
A
region, which is restricted to the
-------------- quadrant, is referred to as a feasible region for the set of
given constraints. 12805021
(a) first
(b) third
(c) second
(d) fourth
Q.234
The
graph of 2x + y < 2 is the open half plane which is ---------- the origin
side of 2x + y = 2. 12805022
(a) at
(b) not on
(c) on
(d) None of these
Q.235
The inequality ax + by < c where
a = 0 represents .… half plane. (Board
2012)
12805023
(a) left or right (b) upper or lower
(c) open (d) none of these
Q.236
The
feasible region is ------------- if it can easily be enclosed within a circle. 12805024
(a) bounded
(b) exist
(c) unbounded
(d) None of these
Q.237
ax + b
> c is an inequality of: 12805025
(a) one variable
(b) three variable
(c) two variable
(d) None of these
Q.238
The
inequality y > b is the open half plane to the --------- of the boundary
line
y = b. 12805026
(a) above (b) left
(c) below (d) right
Q.239
A
vertical line divides the plane into -------------- half planes. 12805027
(a) upper and lower
(b) many
(c) left and right
(d) None of these
Q.240
x=a is
a vertical line perpendicular to ----------. 12805028
(a) x-axis
(b) x-axis may be
(c) y-axis
(d) None of these
Q.241
The
inequality x ³ a is the closed half plane to the -------- of the boundary line
x = a. 12805029
(a) above (b) left
(c) below (d) right
Q.242
The
system of ------------------ involved in the problem concerned is called
problem constraints. 12805030
(a) linear equalities
(b) equations
(c) linear inequalities
(d) None of these
Q.243
The
graph of 2x + y £ 2 is the closed half plane which is ---------- the origin side of 2x +
y = 2. 12805031
(a) at (b) not on
(c) on
(d) None of these
Q.244
y = b
is a horizontal line parallel to
------. 12805032
(a) x-axis
(b) x-axis may be
(c) y-axis
(d) None of these
Q.245
The
inequality y £ b is the closed half plane to the -------- of the boundary line y = b. 12805033
(a) above (b) left
(c) below (d) right
Q.246
Solution of inequality x+2y <6
is:
(Board 2012) 12805034
(a) (1 , 1) (b)
(1 , 3)
(c) (1 , 4) (d) (1 ,
5)
Q.247
For
different values of k, the equation 4x + 5y = k represents lines
----------- to the line 4x + 5y = 0. 12805035
(a) perpendicular
(b) parallel
(c) equal
(d) None of these
Q.248
The
ordered pair ------- is a solution of the inequality x + 2y < 6. 12805036
(a) (3 , 3)
(b) (1 , 1)
(c) (4 , 4)
(d) None of these
Q.249
The
graph of linear equation of the form ax + by = c is a line, which divides the
plane into ------------ disjoint regions, where a, b and c are constants and a,
b are not both zero. 12805037
(a) one
(b) three
(c) two
(d) None of these
Q.250
y = b
is a horizontal line perpendicular to -----------. 12805038
(a) x-axis
(b) y-axis may be
(c) y-axis
(d) None of these
Q.251
If the
line segment obtained by joining any two points of a region lies entirely
within the region, then the region is called ---------. 12805039
(a) maximum (b)
vertex
(c) minimum (d) convex
Q.252
There are ------------ feasible solutions in the
feasible region. 12805040
(a) finitely
(b) two
(c) infinitely many
(d) None of these
Q.253
The
feasible solution, which maximizes or minimizes the objective function, is
called the -------------. 12805041
(a) maximum solution
(b) optimal solution
(c) minimum solution
(d) None of these
Q.254
A
function, which is to be maximized or minimized is called an
----------------------. 12805042
(a) maximum function
(b) objective function
(c) minimum function
(d) None of these
Q.255
A point
of a solution region where two of its boundary lines intersects is called a
---------- of the solution region. 12805043
(a) maximum
(b) vertex
(c) minimum (d)
None of these
Q.256
If a
function f(x,y) has same maximum value at any two points, then it is
-------------- at all the points of the line segment between these points. 12805044
(a) maximum (b)
minimum
(c) may be maximum
(d) may be minimum
Q.257
A point
does not lie in the feasible region is --------- corner point of the feasible
region. 12805045
(a) a
(b) may be a
(c) not a
(d) None of these
Q.258
In linear programming equations or
in-equations should not contain the terms like: 12805046
(a) x, y (b) ax, by
(c) bx, ay (d)
x, y, xy
Q.259
x = 4 is the solution of
inequality: (Board 2014) 12805047
(a) 
(b) 
(c) 
(d) 
Q.260
The non-negative inequalities are
called: (Board 2013) 12805048
(a) Parameters
(b) Constants
(c) Decision variables
(d) Vertices
Q.261
(1, 0) is the solution of
inequality:
(Board 2015) 12805049
(a) 7x + 2y < 8 (b)
x – 3y < 0
(c) 3x + 5y
< 6 (d) –3x + 5y > 2
Q.262
A
function which is to be maximized or minimized is called:
(Board 2015) 12805050
(a) Exponential
function
(b) Linear
function
(c) Quadratic
function
(d) Objective
function
Short Answer Questions
Q.263
In how many ways the
In-equalities are expressed. 12805051
Q.264
What is linear programming? 12805052
(Board 2008)
Q.265
If a function f(x, y) have same minimum value at any
two points, then what is value at the line segment between these points. 12805053
Q.266
What are the linear inequalities in one variable? 12805054
Q.267
Define an associated or corresp-onding equation of
the inequality
ax + by > c. (Board 2008) 12805055
Q.268
What are the linear inequalities in two variables? 12805056
Q.269
If a function f(x, y) have same maximum value at any
two points, then what is value at the line segment between these points. 12805057
Q.270
What is the open half plane in Linear inequalities
in two variable? 12805058
Q.271
What is the closed half plane in Linear inequalities
in one variable? 12805059
Q.272
What is the open half plane in linear inequalities
in one variable? 12805060
Q.273
What is the boundary of the half plane ax + by >
c. 12805061
Q.274
The graph of 2x + y < 2 lies on the origin side
or not. 12805062
Q.275
What are the open half planes in linear inequalities
in two variables? 12805063
Q.276
What is the boundary of the half plane ax + by > c. 12805064
Q.277
If (3, 2) is the solution of inequality x – y > 1 (Board 2007) 12805065
Q.278
Define problem constraints. 12805066
Q.279
Define decision variables. 12805067
Q.280
Define a corner point (vertex). 12805068
(Board 2010)
Q.281
Define an objective function. 12805069
(Board 2008,
12)
Q.282
Define a feasible solution set. 12805070
(Board 2008,
10, 12)
Q.283
Define convex region. 12805071
(Board
2008, 12)
Q.284
Define optimal solution. 12805072
Q.285
Define the solution region. 12805073
Q.286
Define feasible solution. (Board 2008)
12805074
Q.287
What are the linear inequalities in one variable? 12805075
Q.288
Define non-negative constraints and decision
variables. 12805076
Q.289
In how many ways the graph of linear equation of the
form ax + by = c divides the
plane. 12805077
Q.290
The region of graph 2x + y £ 2 lies on the origin side
or not. 12805078
Q.291
The region of graph 2x + y > 2 lies on the origin
side or not. 12805079
Q.292
What is a feasible solution of the system of linear
inequalities? 12805080
Q.293
State fundamental extreme point theorem. 12805081
Q.294
Check whether the region of graph
2x + 3y > 1 lies on the origin side or not.
12805082
Q.295
What is the closed half plane in linear inequalities
in one variable? 12805083
Q.296
What are constraints in
linear programming? 12805084
Q.297
What is the procedure for determ-ining optimal
solution? 12805085
Q.298
Indicate the solution set of linear inequality by
shading 3x + 7y > 21, y < 4.
(Board 2012) 12805086
Q.299
Graph solution region x – 2y < 6
(Board 2012) 12805087
Q.300
Graph the solution set of linear
in-equality 
in xy - plane. 12805088
(Board 2011)
|
Unit |
Conic
Section |
|
06 |
Multiple Choice Questions
q Each question has
four possible answers. Select the correct answer and encircle it.
Q.1
The curves obtained by cutting a double right circular
cone by a
--------- are called conics. 12806001
(a) straight line
(b) plane (c) curve
(d) None of these
Q.2
The two parts of a right circular cones are called: 12806002
(a) nappes
(b) apex of the cone
(c) generator
(d) vertex
Q.3
The fixed point of the conic is called:
12806003
(a) directrix (b) vertex
(c) focus
(d) None of these
Q.4
If the cone is cut by a plane perpendicular to the
axis of the cone, then the section is a\an: 12806004
(a) parabola (b) circular
cone
(c) ellipse (d) circle
Q.5
If the cutting plane is slightly tillted and cuts only
one nappe of the cone, then the section is a\an: 12806005
(a) ellipse (b) circular
cone
(c) circle (d) point
circle
Q.6
If the cutting plane is parallel to the axis of the
cone and intersects both of its nappes, then the section is a\an: 12806006
(a) parabola
(b) hyperbola
(c) ellipse
(d) None of these
Q.7
If equation of circle is (x - h) + (y - k) = r, then centre of a circle is:
12806007
(a) (- h, - k) (b) (h, k)
(c) (- h, k) (d) (h,
- k)
Q.8
The centre of circle x + y + 2gx
+ 2fy + c = 0 is: 12806008
(a) (- g, - f) (b) (- f, - g)
(c) (0 , 0)
(d) None of these
Q.9
If r is the radius of the circle and its centre is at
origin, then equation of circle is: 12806009
(a) x + y = a
(b) x + y = r
(c) x - y = a
(d) x - y = r
Q.10
If (h, k) and r is the centre and radius of the circle
respectively, then equation of a circle in standard form is:
12806010
(a) (x + h) + (y + k) = r
(b) (x - h) + (y - k)= r
(c) (x - h) - (y - k) = r
(d) x + y = r
Q.11
In equation of circle, coefficient of each of x and y are: 12806011
(a) not equal
(b) opposite in signs
(c) equal
(d) None of these
Q.12
The point (x , y) lies on the circle x + y + 2gx + 2fy + c = 0 only
if: 12806012
(a) x+y +2g x+2f y + c = 0
(b) x+y+2g x + 2f y + c > 0
(c) x+y+2g x + 2f y + c < 0
(d) None of these
Q.13
If r is the radius of any circle and c its centre,
then any point P(x , y) lies outside the circle
only if: 12806013
(a) |CP| < r (b) |CP| = r
(c) |CP| > r
(d) None of these
Q.14
The point (x, y) lies outside
the circle x + y + 2gx + 2fy + c = 0 only
if: 12806014
(a) x + y+2g x+2f y + c < 0
(b) x + y+2g x+2f y + c > 0
(c) x+y+2g x + 2f y + c = 0
(d) None of these
Q.15
If r is the radius of any circle and c its centre,
then any point P(x , y) lies on the circle only
if: 12806015
(a) |CP| < r (b) |CP| > r
(c) |CP| = r (d) None of these
Q.16
Two coincident tangents can be drawn to a circle from
any point P(x , y)
------------ the circle. 12806016
(a) inside (b) on
(c) outside
(d) None of these
Q.17
A line perpendicular to a radial chord of a circle at
the end-point
(which lies on the circle) is a: 12806017
(a) Secant (b) Diameter
(c) Chord (d) Tangent
Q.18
A circle is of radius 5 cm, the distance of a chord 8
cm long from its centre is: 12806018
(a) 4 cm (b) 3 cm
(c) 2.5 cm (d) 3.5
cm
Q.19
One of the angles of a triangle inscribed in a circle
is of 40. If one of it’s the diameter, the other
angles have the measures: 12806019
(a) 30, 110 (b) 40, 100
(c) 50, 90 (d) 20, 120
Q.20
Two circles of radius 3 cm and 4 cm touch each other
externally. The distance between their centres is: 12806020
(a) 1 cm (b) 4 cm
(c) 5 cm (d) 7 cm
Q.21
Two arcs of two different circles are congruent if: 12806021
(a) The circles are congruent
(b) The corresponding central
angle
are congruent
(c) Both a and b
(d) None of the above
Q.22
If a circle and a line intersect in two points, then
the line is called: 12806022
(a) A chord (b) A secant
(c) A diameter
(d) None of the above
Ans. (b)
Q.23
The distance between the centre of a circle and any
point of the circle is called:
12806023
(a) Tangents (b) secant
(c) Diameter (d) Radius
Q.24
Perpendicular dropped from the centre of a circle on a
chord ------------ the chord. 12806024
(a) normal (b) bisects
(c) equal to
(d) None of these
Q.25
A line segment having both the end-points on a circle
and passing through the centre of a
circle is known as: 12806025
(a) Diameter (b) Secant
(c) Radial chord (d) Chord
Q.26
A fixed line say l is called a --------- of the
conic. 12806026
(a) vertex (b) directrix
(c) focus (d) None of these
Q.27
A line touching a circle is called:
12806027
(a) Tangent (b) Secant
(c) Chord (d) Radial
chord
Q.28
A line segment having both the end-points on a circle
and not passing through the
centre is called a: 12806028
(a) A chord (b)
A secant
(c) A diameter
(d) None of the above
Q.29
The centre of the circle
is: 12806029
(a) 
(b) 
(c) 
(d) None
Q.30
The radius of the circle
is: 12806030
(a) 
(b) 
(c) 
(d) None
Q.31
The radius of circle x + y + 2gx
+ 2fy + c = 0 is: 12806031
(a) 
(b) 
(c) 
(d) None of these
Q.32
A line through a point say P perpendicular to the tangent to the curve
at P is called: 12806032
(a) straight line
(b) tangent line
(c) normal line
(d) None of these
Q.33
The point (x, y) lies inside the circle x + y+ 2gx + 2fy + c = 0 only if:
12806033
(a) x+y+2g x + 2f y + c = 0
(b) x + y + 2g x+2f y+c > 0
(c) x + y+2g x+2f y + c < 0
(d) None of these
Q.34
Any line y = mx + c intersects any circle x + y = r in: 12806034
(a) at least two points
(b) two points
(c) at most two points
(d) one point
Q.35
Length of a diameter of the circle x + y = a is: 12806034
(a) a (b) 4a
(c) 2a
(d) None of these
Q.36
The set of all points in the plane that are equally
distant from a fixed point is called a\an: 12806036
(a) circle (b) circular
cone
(c) ellipse (d) point
circle
Q.37
If the radius of a circle is zero, then the circle is
called a\an: 12806037
(a) circle (b) circular
cone
(c) ellipse (d) point
circle
Q.38
A line that touches the curve without cutting through
it is called: 12806038
(a) straight line
(b) tangent line
(c) normal line
(d) None of these
Q.39
If r is the radius of any circle and c its centre,
then any point P(x , y) lies inside the circle
only if: 12806039
(a) |CP| < r (b) |CP| = r
(c) |CP| > r (d) None
of these
Q.40
Two imaginary tangents can be drawn to a circle from
any point P(x, y)
--------------- the circle. 12806040
(a) inside (b) on
(c) outside
(d) None of these
Q.41
An angle in a semi-circle is: 12806041
(a) 0° (b) 90°
(c) 180°
(d) None of these
Q.42
All lines through a fixed point A and points on the
circle generates a right: 12806042
(a) parabola (b) circular
cone
(c) ellipse (d) circle
Q.43
Two real and distinct tangents can be drawn to a
circle from any point
P(x, y) ---------- the circle. 12806043
(a) inside (b) on
(c) outside
(d) None of these
Q.44
The parametric equations of the circle x + y = r are: 12806044
(a) x = r sin q, y = r sin q
(b) x = r cos q, y = r sin q
(c) x = r cos q, y = r cos q
(d) None of these
Q.45
The general equation of second degree Ax + By + Gx + Fy + c
= 0 is a\an
---------- if A ¹ B and both
are of the same signs. 12806045
(a) parabola (b) ellipse
(c) hyperbola (d) circle
Q.46
The equation of circle with points (x1, y1)
and (x2, y2) as the ends of the diameter is: 12806046
(a) 
(b) 
(c) 
(d) None
Q.47
A chord containing the centre of the circle is called
--------- of the circle. 12806047
(a) diameter (b) chord
(c) radius
(d) None of these
Q.48
If a point lies inside a circle, then its distance
from the centre is: 12806048
(a) Equal to the radius
(b) Less than the radius
(c) Greater than the radius
(d) Equal to or greater than the
radius
Q.49
The
equation x+ y+ 2x+3y = 10 represents a: 12806049
(a) a pair of lines
(b) circle
(c) ellipse (d) hyperbola
Q.50
The condition for the line y = mx + c to be a tangent
to the circle x + y = a is c = ------------. 12806050
(a) ± a
(b) ± a
(c) ± a
(d) ± a
Q.51
A line segment whose end points lie on the circle is
called a
-------- of the circle. 12806051
(a) radius (b) chord
(c) diameter
(d) None of these
Q.52
Measure of the central angle of a minor arc is
---------- the measure of the angle subtended in the corresponding major arc. 12806052
(a) equal (b) double
(c) not equal to
(d) None of these
Q.53
The radius of point circle is: 12806053
(a) 0 (b) 
(c) r (d) None
Q.54
If the focus lies on the y-axis with coordinates F(0, a) and directrix
of the parabola is y = - a, then the equation of
parabola is: 12806054
(a) x = 4ay (b) y = 4ax
(c) y = - 4ax (d) x = - 4ay
Q.55
The ratio between the measure of the radial segment
and the diameter of a circle is: 12806055
(a) 2 : 1 (b) 4 : 3
(c) 1 : 2 (d) 1 :
Q.56
A chord passing through the focus of a parabola is
called a --------- of the parabola. 12806056
(a) directrix (b) latus
rectum
(c) focus (d) focal chord
Q.57
If the equation of the parabola is to y = 4ax, then opening of the
parabola is to the right of the: 12806057
(a) x-axis (b) y
= x
(c) y-axis
(d) None of these
Q.58
If the equation of the parabola is to x = 4ay, then opening of the
parabola is to ----------- of the x-axis. 12806058
(a) left (b) upward
(c) right (d) downward
Q.59
The axis of the parabola x = 4ay is:
12806059
(a) x = 0 (b) x = - a
(c) y = 0 (d) y = - a
Q.60
The vertex of the parabola
x = - 4ay is: 12806060
(a) (- a, 0) (b) (0,
0)
(c) (0, - a) (d) (0, a)
Q.61
The graph of the parabola
y = - 4ax is symmetric about: 12806061
(a) x-axis (b) y
= x
(c) y-axis
(d) None of these
Q.62
The focus of the parabola y= 4ax is:
12806062
(a) (- a, 0) (b) (0,
a)
(c) (0, - a) (d) (a, 0)
Q.63
If the focus lies on the y-axis with coordinates F(0 ,
- a) and
directrix of the parabola is y = a, then the equation of the parabola is: 12806063
(a) x = 4ay (b) y = 4ax
(c) x = - 4ay (d) y = - 4ax
Q.64
The equ. of latus-rectum of the parabola y = - 4ax is: 12806064
(a) x = a (b) x = - a
(c) y = a (d) y = - a
Q.65
The graph of the parabola
y = - 4ax lies in quadrants: 12806065
(a) I and II (b) III
and IV
(c) II and III (d) I
and IV
Q.66
The eqn. of
directrix of the parabola y=-4ax is: 12806066
(a) x = a (b) x = - a
(c) y = a (d) y = - a
Q.67
The coordinates of the end points of the latus-rectum
of the parabola y = 4ax are (a, 2a) and ---------. 12806067
(a) (- a, - 2a) (b) (a, 2a)
(c) (a, - 2a) (d) (- a, 2a)
Q.68
The opening of the parabola y = 4ax is to the -------- of
the y-axis. 12806068
(a) left
(b) upward
(c) right
(d) downward
Q.69
The opening of the parabola x = 4ay is upward of the: 12806069
(a) x-axis
(b) y = c
(c) y-axis
(d) None of these
Q.70
The graph of the parabola x = 4ay lies in quadrants: 12806070
(a) I and II (b) III
and IV
(c) II and III (d) I
and III
Q.71
The vertex of the parabola
y = 4ax is: 12806071
(a) (- a, 0) (b) (a,
0)
(c) (0, - a) (d) (0, 0)
Q.72
The focus of the parabola y= - 4ax is: 12806072
(a) (- a, 0) (b) (a,
0)
(c) (0, - a) (d) (0, 0)
Q.73
The directrix of the parabola
x = 4ay is: 12806073
(a) x = a (b) x = - a
(c) y = a (d) y = - a
Q.74
A line joining two distinct points on a parabola is
called a ----------- of the parabola. 12806074
(a) chord (b) vertex
(c) focus (d) directrix
Q.75
The focus of the parabola x = - 4ay is: 12806075
(a) (- a, 0) (b) (0,
0)
(c) (0, - a) (d) (0, a)
Q.76
The conic is a parabola, if: 12806076
(a) e = 1 (b) e > 1
(c) 0 < e < 1 (d) e
= 0
Q.77
The opening of the parabola
y = – 4ax is to the left of the: 12806077
(a) x-axis (b) x
= 1
(c) y-axis (d) x
= 0
Q.78
The point where the axis meets the parabola is called
------------ of the parabola.
12806078
(a) directrix (b) vertex
(c) focus (d) eccentricity
Q.79
The length of the latus rectum of the parabola y = 4ax is: 12806079
(a) a (b) 4a
(c) 2a (d) None of these
Q.80
If the focus lies on the x-axis with coordinates F(- a, 0) and
directrix of the parabola is x = a, then the equation of the parabola is: 12806080
(a) x = 4ay (b) y = 4ax
(c) x = - 4ay (d) y = - 4ax
Q.81
The opening of the parabola
x = 4ay is to ------------ of the x-axis. 12806081
(a) left (b) upward
(c) right (d) downward
Q.82
The parabola y = 4ax lies in quadrants: 12806082
(a) I and II (b) III
and IV
(c) II and III (d) I
and IV
Q.83
The graph of the parabola
x = - 4ay symmetric about: 12806083
(a) x-axis (b) major
axis
(c) y-axis (d) minor
axis
Q.84
The equation of the latus-rectum of the parabola y = 4ax is: 12806084
(a) x = a (b) x = - a
(c) y = a (d) y = - a
Q.85
The axis of the parabola y=- 4ax is:
12806085
(a) x = a (b) x = 0
(c) y = a (d) y = 0
Q.86
The equ of latus-rectum of the parabola x = - 4ay is: 12806086
(a) x = a (b) x = - a
(c) y = a (d) y = - a
Q.87
y = 4ax, is the standard
equation of the: 12806087
(a) ellipse (b) parabola
(c) hyperbola
(d) None of these
Q.88
The focal chord perpendicular to the axis of the
parabola is called
-------------- of the parabola. 12806088
(a) directrix (b) latus
rectum
(c) focus (d) focal chord
Q.89
The graph of the parabola
x = - 4ay lies in quadrants: 12806089
(a) I and II (b) III
and IV
(c) II and III (d) I
and IV
Q.90
The axis of the parabola y = 4ax is:
12806090
(a) x = 0 (b) x = a
(c) y = 0 (d) y = a
Q.91
The directrix of the parabola x = - 4ay is: 12806091
(a) x = a (b) x = - a
(c) y = a (d) y = - a
Q.92
The vertex of the parabola
x = 4ay is: 12806092
(a) (- a, 0) (b) (0,
a)
(c) (0, - a) (d) (0, 0)
Q.93
The axis of the parabola x = - 4ay is: 12806093
(a) x = a (b) x = 0
(c) y = a (d) y = 0
Q.94
If the focus lies on the x-axis with coordinates F(a,
0) and directrix of the parabola is x = - a, then
the equation of parabola is: 12806094
(a) x = 4ay (b) y = 4ax
(c) x = - 4ay (d) y = - 4ax
Q.95
If the equation of the parabola is to y = - 4ax, then
opening of the parabola is to the -------- of the y-axis. 12806095
(a) left (b) upward
(c) right (d) downward
Q.96
If the equation of the parabola is to x = 4ay, then opening of the
parabola is to upward of the: 12806096
(a) x-axis (b) major
axis
(c) y-axis (d) minor
axis
Q.97
The graph of the parabola y = 4ax symmetric about: 12806097
(a) x-axis (b) major
axis
(c) y-axis (d) minor
axis
Q.98
The graph of the parabola x = 4ay symmetric about: 12806098
(a) x-axis (b) y
= x
(c) y-axis
(d) None of these
Q.99
The directrix of the parabola
y = 4ax is: 12806099
(a) x = a (b) x = - a
(c) y = a (d) y = - a
Q.100
The vertex of the parabola
y = - 4ax is: 12806100
(a) (- a, 0) (b) (a,
0)
(c) (0, - a) (d) (0, 0)
Q.101
The focus of the parabola x = 4ay is: 12806101
(a) (- a, 0) (b) (a,
0)
(c) (0, - a) (d) (0, a)
Q.102
The equation of the latus-rectum of the parabola x = 4ay is: 12806102
(a) y = a (b) y = - a
(c) x = a (d) x = - a
Q.103
The point of a parabola which is closest to the focus
is the: 12806103
(a) directrix (b) vertex
(c) focus (d) chord
Q.104
The number e denotes the ------------- of the conic. 12806104
(a) directrix (b) vertex
(c) focus (d) eccentricity
Q.105
The
equation 2x+ 3y= 36 represents: 12806105
(a) a circle (b) a
parabola
(c) an ellipse (d) a
hyperbola.
Q.106
The line y = x + touches
the ellipse + = 1, then: 12806106
(a) c = ± 10 (b) c = ± 12
(c) c = ± 13 (d) None of these.
Q.107
In equation of ellipse + = 1, if
a > b, then c = ----------. 12806107
(a) a - b (b) b - a
(c) a + b (d) b - a
Q.108 The
directrics of the ellipse
+ = 1, a > b is: 12806108
(a) x = ± (b) x = ±
(c) y = ± (d) y = ±
Q.109 The centre
of the ellipse + = 1, a
> b is: 12806109
(a) (a, 0) (b) (± b, 0)
(c) (0, 0) (d) (0,
± a)
Q.110
The eccentricity of the ellipse
+ = 1, a
> b is: 12806110
(a) e = > 1
(b) e = < 1
(c) e = ±
(d) None of these
Q.111
+ = 1 is an
equation of the
------------ in standard form. 12806111
(a) ellipse
(b) parabola
(c) hyperbola
(d) None of these
Q.112 The foci of
the ellipse
+ = 1, a
> b are: 12806112
(a) (0, ± c) (b) (± c, 0)
(c) (± a, 0) (d) (0,
± a)
Q.113 Eccentricity
of the ellipse
+ = 1, a
> b is: 12806113
(a) e > 1
(b) e < 1
(c) e = 0
(d) None of these
Q.114 The foci of
the ellipse
+ = 1, a
> b is: 12806114
(a) (0, ± c) (b) (± c, 0)
(c) (± a, 0) (d) (0,
± a)
Q.115
The vertices of the ellipse
+ = 1, a
> b is: 12806115
(a) (0, ± a) (b) (± c, 0)
(c) (± a, 0) (d) (0,
± c)
Q.116
The length of major axis of the ellipse + = 1, a
> b is: 12806116
(a) 4a (b) 2a
(c) 4b (d) 2b
Q.117
The major axis of the ellipse
+ = 1, a
> b is: 12806117
(a) x = 0 (b) x = - a
(c) y = 0 (d) y = - a
Q.118
The length of minor axis of the ellipse + = 1, a
> b is: 12806118
(a) a (b) 2a
(c) b (d) 2b
Q.119
The covertices of the ellipse
+ = 1, a
> b is: 12806119
(a) (± b, 0)
(b) (0, ± b)
(c) (± a, 0)
(d) (0, ± a)
Q.120
The centre of the ellipse
+ = 1, a
> b is: 12806120
(a) (0, 0) (b) (± c, 0)
(c) (a, 0) (d) (0,
a)
Q.121
Foci of ellipse 
lie
on the:
12806121
(a) x-axis
(b) major axis
(c) y-axis
(d) minor axis
Q.122
The major axis of the ellipse
+ = 1, a
> b is: 12806122
(a) x = a (b) x = 0
(c) y = a (d) y = 0
Q.123
Equation of
tangent to the ellipse
+ = 1 at the point (x1, y1) is given by:
12806123
(a) + = 1
(b) + = 1
(c) + = 0
(d) None of these.
Q.124 The line segment between the covertices of an ellipse
is called: 12806124
(a) minor axis
(b) major axis
(c) transverse axis
(d) principal axis
Q.125
In case of
ellipse + = 1: 12806125
(a) ae < (b) ae >
(c) ae = (d) 1 - e< 0
Q.126
The
equation of the ellipse whose foci are (0, ± 4) and the length of minor axis 6 units is: 12806126
(a) + = 1
(b) + = 1
(c) + = 1
(d) None of these.
Q.127
The
equation of an ellipse whose foci are (±2,0) and the eccentricity is is: 12806127
(a) + =
(b) + = 1
(c) + = 1
(d) None of these.
Q.128
The eccentricity of the
ellipse
+ = 1 if its latus-rectum be equal to one half of its
major axis is: 12806128
(a) (b)
(c) (d) None of these.
Q.129
The sum of
the focal distances of a point on an ellipse + = 1, a > b > 0 is:
(a) 2a + 2b (b) 2a
12806129
(c) 2b (d) None of these.
Q.130
The sum of
the focal distances of a point on an ellipse + = 1, a > b > 0 is equal to: 12806130
(a) length of minor axis
(b) length of major axis
(c) 2a + 2b
(d) None of these.
Q.131 ------------
are tangent to + = 1 for
all values of m. 12806131
(a) y = mx ±
(b) y = mx ±
(c) y = mx ±
(d) y = x ±
Q.132
For an ellipse 
which is true: 12806132
(a) 
(b) 
(c) 
(d) None
Q.133
The conic is an ellipse, if: 12806133
(a) e = 1 (b) e >1
(c) 0 < e < 1 (d) None
of these
Q.134
A second degree equation of the form ax+ by + 2gx + 2fy + c = 0 with
either a = 0 or b = 0 but not both zero, represents a\an: 12806134
(a) ellipse (b) parabola
(c) hyperbola (d) None
of these
Q.135
In equation of ellipse + = 1,
if a > b, then c = ----------. 12806135
(a) a + b (b) b - a
(c) a - b (d) b - a
Q.136
The vertices of the ellipse
+ = 1, a
> b is: 12806136
(a) (0, ± b) (b) (± b, 0)
(c) (± a, 0) (d) (0,
± a)
Q.137
The directrics of the ellipse
+ = 1, a
> b is: 12806137
(a) x = ± (b) x = ±
(c) y = ± (d) y = ±
Q.138
The length of latus-rectum of the ellipse + = 1, a
> b is equivalent to:
12806138
(a) (b) 2a
(c) (d) 2b
Q.139
In equation of ellipse + = 1,
if b > a, then c = 12806139
(a) a + b (b) b - a
(c) a - b (d) b - a
Q.140
Foci of a
hyperbola always lie on:
12806140
(a) x-axis
(b) y-axis
(c) conjugate-axis
(d) transverse-axis
Q.141
Asymptotes
are very helpful in graphing: 12806141
(a) Circle
(b) Parabola
(c) Ellipse
(d) Hyperbola
Q.142
In case of
hyperbola - = 1
12806142
(a) ae <
(b) ae >
(c) ae = (d) e < 1
Q.143
---------------- , y = X sin q + Y cos q are
equations of transformation for a rotation of axes through an angle
q, (0<q< 90°). 12806143
(a) x = X cos q + Y sin q
(b) x = X sin q - Y cos q
(c) x = X cos q - Y sin q
(d) None of these
Q.144
------------- is a tangent to y = 4ax for all non-zero
values of m. 12806144
(a) y = mx -
(b) y = - mx +
(c) y = mx +
(d) None of these
Q.145
The lines -------------- are called asymptotes of the
hyperbola 
.
12806145
(a) x = ± y (b) y = ± x
(c) y = ± x (d) None
Q.146
The transverse axis of the hyperbola - = 1 is: 12806146
(a) x = 0 (b) x = a
(c) y = 0 (d) y = - a
Q.147
The foci of the hyperbola
- = 1 is: 12806147
(a) (0, ± c) (b) (± c, 0)
(c) (± a, 0) (d) (0,
± a)
Q.148
- = 1 is the
standard equation of the: 12806148
(a) ellipse (b) parabola
(c) hyperbola
(d) None of these
Q.149
The conic is a hyperbola, if: 12806149
(a) e = 1 (b) e >1
(c) 0 < e < 1 (d) e
= 0
Q.150
In equation of the hyperbola
- = 1 the
value of c = ------- 12806150
(a) a + b (b) b - a
(c) a - b (d) b - a
Q.151
The vertices of the hyperbola
- = 1 is: 12806151
(a) (0, 0) (b) (± c, 0)
(c) (± a, 0) (d) (0,
± a)
Q.152
The eccentricity of the hyperbola
- = 1 is: 12806152
(a) e = > 1
(b) e = < 1
(c) e = ±
(d) None of these
Q.153
The general equation of second degree Ax+ By+ Gx + Fy + c = 0 is a\an
----------- if A ¹ B and both
are of opposite signs. 12806153
(a) ellipse (b) parabola
(c) hyperbola (d) circle
Q.154
----------- are tangent to - =1 for all
values of m. 12806154
(a) y = mx ±
(b) y = mx ±
(c) y = mx ±
(d) None of these
Q.155
The directrics of the hyperbola
- = 1 are: 12806155
(a) y = ± (b) x = ±
(c) y = ± (d) x = ±
Q.156
The centre of the hyperbola
- = 1 is: 12806156
(a) (0, 0) (b) (± c, 0)
(c) (± a, 0) (d) (0,
± a)
Q.157 The
eccentricity of the hyperbola
- = 1 is: 12806157
(a) e > 1
(b) e < 1
(c) e = 1
(d) None of these
Q.158
The general equation of second degree Ax+ By+ Gx + Fy + c = 0 is a\an
-------------- if A = B ¹ 0. 12806158
(a) circle (b) parabola
(c) hyperbola (d) ellipse
Q.159
The general equation of second degree ax + by + 2hxy + 2gx + 2fy + c=0 is a parabola if: 12806159
(a) h - ab = 0
(b) h - ab ¹ 0
(c) h - ab < 0
(d) h - ab > 0
Q.160
The general equation of second degree ax + by + 2hxy +
2gx + 2fy+c = 0 is an ellipse or a circle, if: 12806160
(a) h - ab = 0 (b) h - ab ¹ 0
(c) h - ab < 0 (d) h - ab > 0
Q.161
The general equation of second degree Ax + By + Gx + Fy +
c = 0 is a\an
-------------- if either A = 0 or B = 0. 12806161
(a) ellipse
(b) parabola
(c) hyperbola
(d) circle
Q.162
The general equation of second degree ax + by + 2hxy+2gx + 2fy + c = 0 is a hyperbola if: 12806162
(a) h - ab = 0
(b) h - ab < 0
(c) h - ab ¹ 0
(d) h - ab > 0
Q.163
The axes are rotated about the origin through an angle q of
ax + by +
2hxy + 2gx + 2fy + c = 0 is given
by ------, where 0 < q < 90°. 12806163
(a) tan 2q =
(b) tan 2q =
(c) tan 2q =
(d) None of these
Q.164
The radius of circle
is: (Board 2014)12806164
(a) 
(b) 
(c) 
(d) 
Q.165
The vertex of parabola
(x – 1)2 = 8(y + 2) is: (Board
2014)12806165
(a) (1, – 2) (b) (0, 1)
(c) (–1, –2) (d) (1, 2)
Q.166
The centre of circle
(x+3)2 + (y–2)2 = 16 equals: Board 2014)12806166
(a) (–3, 2) (b) (3, –2)
(c) (3,
2) (d) (–3, –2)
Q.167
The eccentricity of 
equals:
(Board
2014)12806167
(a) 
(b) 
(c) 
(d) 
Q.168
Centre of circle
(Board 2013)12806168
(a) 
(b) 
(c) 
(d) 
Q.169
Foci of ellipse 
are:
(Board
2013)12806169
(a) 
(b) 
(c) 
(d) 
Q.170
The set of all points in the plane that are equally distant from a
fixed point is called:
(Board
2015)12806170
(a) Ellipse (b)
Parabola
(c) Hyperbola (d)
Circle
Q.171
The parabola x2 = y passes through point: (Board
2015)12806171
(a) 
(b)
(c) (d) 
Q.172
Equation
of axis of the parabola x = 4ay is (Board
2015)12806172
(a) x = 0 (b) x = a
(c) y = 0
(d) y = a
Q.173
Length of
tangent from (0,1) to x2+ y2
+6x – 3y + 3 = 0 is: (Board 2015)12806173
(a) 2 (b) 3
(c) 4 (d) 1
Short Answer Questions
ONS & ANSWRS
Q.1
Give
original definition of conics. 12806174
Q.2
Define
conics in terms of eccentricity, focus, and directrix. 12806175
Q.3
Define
conics. 12806176
Q.4
Define
vertex of the cone. 12806177
Q.5
Define circle
as plane section of a cone. 12806178
Q.6
Define
parabola as plane section of a cone. 12806179
Q.7
Define
ellipse as plane section of a cone. 12806180
Q.8
Define
hyperbola as plane section of a cone. 12806181
Q.9
Give definition of parabola. 12806182
Q.10
Define
latus rectum of the parabola.
12806183
Q.11
Define the
axis of the cone. 12806184
Q.12
Define
translation of axes. 12806185
Q.13
Define
radius of the circle. 12806186
Q.14
Define
point circle.(Board 2012) 12806187
Q.15
Define
nappes. 12806188
Q.16
In cone how
the section of a circle is obtained. 12806189
Q.17
In cone how
the section of an ellipse is obtained. 12806190
Q.18
Write a
standard form of circle.
12806191
Q.19
Define a
diameter of the circle.
(Board 2012) 12806192
Q.20
Write a
general form of circle. 12806193
(Board 2012)
Q.21
Give
definition of a circle. 12806194
(Board 2012)
Q.22
Define
centre of the circle. 12806195
Q.23
Write the
conditions that the point
P(x, y) lies inside, on and outside the circle x + y+ 2gx + 2fy + c = 0. 12806196
Q.24
Define a chord of the
circle. 12806197
(Board
2012)
Q.25
Find the centre and radius
of the circle. 
(Board 2011)
12806198
Q.26
Find the
equation of circle with ends of a diameter at (-3, 2), (5, 6). 12806199
(Board 2008, 10)
Q.27
Find the centre and radius of the
circle
.(Board 2010) 12806200
Q.28
Derive the
equation of circle in standard form. (Board 2011) 12806201
Q.29
Write an
equation of the circle with centre (-3, 5) and radius 7. 12806202
Q.30
Show that
the equations 5x+ 5y
+ 24x + 36y + 10 = 0 represents a
circle. Also find its centre and radius. 12806203
(Board 2009)
Q.31
Determine
whether the point P(-5, 6) lies outside, on or inside the circle x+y+4x-6y-12=0 (Board 2012) 12806204
Q.32
Check the
position of the point
(5, 6) w.r.t. the circle x2 + y2 = 81. 12806205
(Board 2010)
Q.33
Find the
equation of the tangent and normal at
(4, 3) to the circle 
(Board 2010) 12806206
Q.34
Check the
position of the point
(5,6) w.r.t the circle 
(Board 2012) 12806207
Q.35
Find
the length of the tangent drawn from the point (–5, 4) to the circle 
.
(Board 2007) 12806208
Q.36
Find the
co-ordinates of points of intersection of the line 2x + y = 5 and the circle x2+
y2+2x-9=0. Also find the length of the intercepted chord. 12806209
Q.37
Find the
length of the tangent from the point P(-5,10) to the
circle 5x+ 5y + 14x + 12y
- 10 = 0 (Board 2009) 12806210
Q.38
Prove that
the normal of the circle passes through the centre of circle. 12806211
(Board 2012)
Q.39
Tangents
are drawn from (- 3, 4) to the circle x+ y= 21. Find an equation of the line joining the points
of contact. 12806212
Q.40
Prove that
the tangent to a circle at any point of the circle is perpendicular to the
radial segment at that point. 12806213
Q.41
Find the
equation of parabola having focus at (a, 0) and directrix x+a=0
(Board
2010) 12806214
Q.42
Define a
focal chord of the parabola.
12806215
Q.43
In cone how
the section of a parabola is obtained. 12806216
Q.44
Define a
chord of the parabola. 12806217
Q.45
Define axis
of the parabola. 12806218
Q.46
Define vertex
of the parabola. 12806219
Q.47
Write an
equation of the parabola with given elements: Focus (2, 5); directrix y = 1. 12806220
Q.48
Write
equations of the tangent and normal to the parabola 12806221
x= 16y at the point whose abscissa is 8.
Q.49
Analyze the
parabola x= - 16y
12806222
Q.50
Find an
equation of the parabola whose focus is F(- 3, 4) and directrix is
3x - 4y + 5 = 0. 12806223
Q.51
Discuss and
sketch the graph of the parabola: y= – 12 x 12806224
Q.52
Discuss and
sketch the graph of the parabola: y= 8 x (Board 2012) 12806225
Q.53
Discuss and
sketch the graph of the parabola: x = - 16y 12806226
Q.54
Discuss and
sketch the graph of the parabola: x= 5 y (Board 2011, 12) 12806227
Q.55
Write an
equation of the parabola with given elements: Focus ( – 3, 1); directrix x = 3 12806228
Q.56
Write an
equation of the parabola with given elements: Focus (– 3, 1) ; directrix x – 2 y – 3 = 0 12806229
Q.57
Write an
equation of the parabola with given elements.
Focus (1, 2), vertex (3, 2) (Board 2008) 12806230
Q.58
Write an
equation of the parabola with given elements:
Focus (-1, 0), vertex (-1, 2) 12806231
Q.59
Write an
equation of the parabola with given elements. 12806232
Directrix x = - 2, focus (2, 2)
Q.60
Write an equation of the parabola with given elements: Directrix y = 3,
vertex (2, 2)
12806233
Q.61
Write an
equation of the parabola with given elements: Directrix y = 1, length of
latus-rectum is 8. Opens downward.
12806234
Q.62
Find the
equation of the parabola having its focus at the origin and directrix is
parallel to x-axis. 12806235
Q.63
Find the
equation of the parabola having its focus at the origin and directrix is
parallel to y – axis. 12806236
Q.64
Show that the ordinate at any point P of the parabola
is the mean proportional between the length of the latus rectum and the
abscissa of P. 12806237
Q.65
Find an
equation of the parabola formed by the cables of a suspension bridge whose span
is a m and the vertical height of the supporting towers is b m. 12806238
Q.66
A
suspension bridge with weight uniformly distributed along the length has two
towers of 100 m height above the road surface and are 400 m apart. The cables
are parabolic in shape and are tangent to road surface at the centre of the
bridge. Find the height of the cables at a point 100 m from the centre. 12806239
Q.67
Show that
the point of parabola which is closest to the focus is the vertex. 12806240
Q.68
Give
definition of an ellipse. 12806241
Q.69
Find an equation for the ellipse with given data: Foci (0, – 1)
and (0, – 5) and major axis of length 6 12806242
Q.70
Find an equation for the ellipse with given data: Vertices (0, ± 5), eccentricity =
(Board 2012) 12806243
Q.71
Find an equation for the ellipse with given data: Centre (0,0), focus (0,–3), vertex (0, 4)
(Board 2011) 12806244
Q.72
Find the
centre, foci, eccentricity, vertices and directrices of the ellipse whose
equation is x + 4y = 16 12806245
Q.73
Find the
centre, foci, eccentricity, vertices and directrices of the ellipse whose equation is 9x+ y = 18 12806246
(Board 2011)
Q.74
Prove that
the latus rectum of the ellipse + = 1, is 12806247
Q.75
The major
axis of an ellipse in standard form lies along the
x-axis and has length 4. The distance between the foci equals the length of
the minor axis. Write an equation of the ellipse.
12806248
Q.76
Show
that the equation 9x2 – 18x + 4y2 + 8y – 23 = 0 represents
an ellipse. 12806249
Q.77
An arch in
the form of half an ellipse is 40 m wide and 15 m high at the centre. Find the
height of the arch at a distance of 10 m from its centre. 12806250
Q.78
Analyze the
equation 4x+9y= 36
12806251
Q.79
Find an equation for the ellipse with given data. 12806252
Foci (± 3 , 0) and minor axis of length 10 .
Q.80
Find an equation for the ellipse
with foci (– 3 , 0) and vertices (± 6, 0). 12806253
(Board 2010)
Q.81
In cone how
the section of a hyperbola is obtained. 12806254
Q.82
Give
definition of a hyperbola.12806255
(Board 2011)
Q.83
Find an
equation of the hyperbola with the given data. Centre (0, 0), focus
(6, 0) , vertex (4, 0) 12806256
Q.84
Find an
equation of the hyperbola with the given data. (Board 2012) 12806257
Foci (± 5, 0) , Vertex (3, 0)
Q.85
Find
equations of tangents which passes through the given points to the given conic.
x– 2y=2 through
(1,– 2) 12806258
Q.86
Find the
eccentricity, the coordinates of the vertices and foci of the asymptotes of the
hyperbola - = 1 12806259
(Board 2010)
Q.87
Find
equations of tangents which pass through the given point to the given conic. x + y = 25 through
(7, – 1) 12806260
Q.88
Discuss the
equation
25x-16y= 400 12806261
Q.89
Find an
equation of the hyperbola with the given data.
Foci (2 ± 5, - 7), length of the
transverse axis 10. 12806263
Q.90
Find an
equation of the hyperbola with the given data. 12806264
Foci (0, ± 9) , directrices y = ± 4
Q.91
Find an
equation of the hyperbola whose foci are (± 4, 0) and vertices (±2,0).
(Board 2011) 12806265
Q.92
Define
asymptote. 12806266
Q.93
What are
asymptotes of hyperbola
- = 1. 12806267
Q.94
Show that
the equation
4x- 8x - y- 2y - 1 = 0 represents a hyperbola. 12806268
Q.95
Find the
equation of the hyperbola referred to its axes as the axes of coordinates and
the distance between whose foci is 16 and whose eccentricity is .
12806269
Q.96
Find an
equation of the hyperbola with foci (0, ± 6), vertex (0, 3). 12806270
Q.97
Find an
equation of the hyperbola with centre (2, 2), horizontal transverse axis of
length 6 and eccentricity e = 2. 12806271
(Board 2011)
Q.98
Find the
centre, foci, eccentricity, vertices and directrices of the ellipse whose
equation is x– y= 9 12806272
Q.99
Find the
centre, foci, eccentricity, vertices and directrices of the ellipse whose
equation is – = 1 12806273
Q.100 Find the centre, foci, eccentricity, vertices and
directrices of the ellipse whose equation is
– = 1 12806274
Q.101 Find the centre, foci, eccentricity, vertices and
directrices of the ellipse whose equation is – x= 1 (Board 2012) 12806275
Q.102 Define slope of a tangent line to a curve. 12806276
Q.103 Define a normal line to a curve.
12806277
Q.104 Define a tangent line to a curve. 12806273
Q.105 Show that 2x - xy + 5x- 2y+ 2 = 0 represent a pair of lines. 12806278
Q.106 Write equations of the tangent and normal to the conic
+ = 1 at the point . 12806279
Q.107 Find the points of intersection of the ellipse + = 1 and the hyperbola
- = 1. 12806280
Q.108
Find
equations of the tangents of the ellipse
+ = 1 which are parallel to the line 3x + 8y + 1 = 0. 12806281
Q.109 Find equations of the common tangents to the two conic
+ = 1 and
+ = 1 12806282
Q.110 Transform the equation
x + 6x - 8y + 17 = 0. Referred to O¢(- 3, 1) as origin, axes remaining parallel to the old axes 12806283
Q.111
Write equations of the tangent and the normal to the
curve y = f(x) at a given point (x, y). 12806284
Q.112 Write
equation of the tangent to the curve whose parametric equations are
x = f(t) and y = f(t) at the point t. 12806285
Q.113 Write about translation of axes. 12806286
Q.114
Find an equation of the curve
x + 16y - 16 = 0 with
respect to new parallel axes obtained by shifting the origin to the point O¢(0, 1). 12806287
Q.115 Transform the equation x+6x-8y
+ 17 = 0. Referred to O¢(-
3, 1) as origin, axes remaining parallel to the old axes. 12806288
Q.116 Write about rotation of axes. 12806289
Q.117
Find equations of the tangent and normal to the given
curve at the indicated point: y = 4ax at
(at, 2at) 12806290
Q.118 Find equations of the tangent to the given curve at
the indicated point:
+ = 1 at (a cos q, b sin q) 12806291
Q.119 Find equations of tangents which passes through the
given points to the given conics: y = 12x through (1,
4) 12806292
Q.120 Find equations of the tangents to the ellipse + y= 1 which are parallel to the line 2x – 4y +
5 = 0. 12806293
|
Unit |
Vectors
|
|
07 |
Multiple Choice Questions
q Each question has four possible answers. Select the
correct answer and encircle it.
Q.1
Which of the following is a vector
quantity? 12807001
(a) work (b) temperature
(c) distance
(d) displacement
Q.2
For a vector
12807002
(Board 2005)
(a) 2A (b) A2
(c) 
(d)
Q.3
Length of the vector 
is:
(Board 2010) 12807003
(a) 3 (b) 4
(c) 6 (d)
5
Q.4
Which of the following is not a vector quantity? 12807004
(a) weight (b) mass
(c) force (d)
velocity
Q.5
If = 1, then
is a: 12807005
(a) free vector
(b) unit vector
(c) null vector
(d) None of these
Q.6
Let be a
non-zero vector, then is a: 12807006
(a) scalar quantity
(b) unit vector parallel to
(c) unit vector perpendicular to
(d) reciprocal vector
Q.7
12807007
(a) 0 (b) –1
(c) 2 (d)
1
Q.8
Mark the wrong statement. Two vectors can be: 12807008
(a) added (b) subtracted
(c) multiplied (d)
divided
Q.9
If P(x, y, z) be any point in space, then = x + y + z is called the:
12807009
(a) position vector of O
(b) position vector of P
(c) unit vector (d)
null vector
Q.10
If 
and 
then 
(Board
2008) 12807010
(a) 
(b) 
(c) 
(d)
Q.11
Two vectors are equal if they: 12807011
(a) passes through the same point
(b) are parallel to each other
(c) are parallel to each other and have same direction
(d) have equal magnitude and have same direction
Q.12
A scalar quantity is one that
possesses only: 12807012
(a) magnitude (b) direction
(c) both a and b
(d) none of these
Q.13
If 
and 
are parallel vectors, then 
(Board 2008) 12807013
(a) 0 (b) 1
(c) –1 (d) 2
Q.14
If vectors 
and 
are perpendicular, then x equals: 12807014
(Board 2009)
(a) 5 (b) 4
(c) 2 (d) 1
Q.15
If terminal point B of a vector coincides with its initial point A, then is known as: 12807015
(a) scalar (b) free
vector
(c) unit vector (d) null vector
Q.16
If
= , then |-
|
= ------------.
12807016
(a) - (b)
(c) || (d) - ||
Q.17
If 1 and 
are x and
y-components of a vector, then its angle with x-axis is: (Board 2009) 12807017
(a) 60o (b) 90o
(c) 30o (d) 45o
Q.18
If 2 and 2 are x and y-components of a
vector, then its angle with x-axis is: 12807018
(Board
2009)
(a) 30o (b) 45o
(c) 60o (d) 90o
Q.19
If = [x, y] and = [x¢,
y¢]
are two vectors, then difference between two vectors are -
= 12807019
(a) [ x - y, x¢ - y¢]
(b) [ x - y, x¢ - y¢]
(c) [ x + x¢, y + y¢]
(d) [ x - x¢, y - y¢]
Q.20
The vector = [1, 0] is
called unit vectors along: 12807020
(a) x-axis (b) z-axis
(c) y-axis
(d) None of these
Q.21
The vector = [0, 1] is
called ------- along y-axis. 12807021
(a) position vector
(b) null vector
(c) unit vector
(d) None of these
Q.22
The magnitude, length or norm of
vector = [x, y, z]
is ||
= ---------. 12807022
(a)
(b)
(c) x+
y + z
(d)
Q.23
cosa
+ cosb
+ cosg
= -----.12807023
(a) 0 (b) 2
(c) 1 (d) 3
Q.24
Two vectors are said to be negative of
each other if they have ----------- magnitude but ----------- direction. 12807024
(a) same, same
(b) opposite, same
(c) same, opposite
(d) None of these
Q.25
The law of parallelogram of
addition was used by Aristotle to describe the combined action of: 12807025
(a) one force (b) two forces
(c) three forces
(d) None of these
Q.26
If and have same direction, then 
= (Board
2005, 10) 12807026
(a) -AB (b) AB sinq
(c) AB (d) AB tanq
Q.27
Let A and B be two points whose
position vectors are and respectively.
If a point P divides AB in the ratio p : q, then the position vector of P is
given by
= -----------. 12807027
(a) (b)
(c) (d)
Q.28
The vector = [x, y] in R can be uniquely represented by: 12807028
(a) x + y (b) x - y
(c) y + x (d) y + x
Q.29
The null or zero vector in R is
= -------. 12807029
(a) [0] (b) [0,
0]
(c) [0, 0, 0]
(d) None of these
Q.30
Projection of vector 
along
is: (Board 2007) 12807030
(a) a (b) c
(c) b (d) a + b
Q.31
If ×
= × = × = 0, then × ( ´ ) is equal to: 12807031
(a)
(b) + +
(c)
(d) None of these.
Q.32
The vector = [0, 1, 0]
is called
----------- along y-axis. 12807032
(a) unit vector (b) null vector
(c) position vector
(d) None of these
Q.33
The vector = [0, 0, 1]
is called
------------ along z-axis. 12807033
(a) unit vector
(b) null vector
(c) free vector
(d) None of these
Q.34
If the vectors 
and 
are perpendicular to each other, then the
value of 
is:
(Board 2008) 12807034
(a) 3 (b) 
(c) 
(d)
Q.35
. = ------- ,
where q
is the angle between and and lies in
[0, p]. 12807035
(a) . cos q
(b) || . ||
(c) || . || cos q
(d) None of these
Q.36
Two vectors 
are collinear if 
implies:
(Board 2006) 12807036
(a) p = 0, q ¹ 0
(b) p ¹ 0, q = 0
(c) p = 0, q = 0
(d) p ¹ 0, q ¹ 0
Q.37
The dot product of unit vector with unit
vector is: 12807037
(a) 0 (b) 2
(c) 1 (d) 3
Q.38
The angle between the vectors 
and 
is:(Board2007) 12807038
(a) 
(b) 
(c) 
(d) 
Q.39
Two non-zero
vectors and are perpendicular if and only if . is equal to:
12807039
(a) 0 (b) 2
(c) 1 (d) None of these
Q.40
If q
= ------------ between two vectors and , then and are
perpendicular to each other. 12807040
(a) 0 (b)
(c) p (d)
Q.41
The projection of along is equal to: (Board 2006)
12807041
(a) (b)
(c)
(d) None of these
Q.42
´
= 12807042
(a) 0 (b)
(c) (d)
Q.43
´
= 12807043
(a) 0 (b)
(c) (d)
Q.44
If and be any two
vectors and
´
= 0, then: 12807044
(a) = 0 or = 0
(b) = 0 and = 0
(c) = 0 or ¹ 0
(d) ¹ 0 or = 0
Q.45
If =[x1,y1,z1] and =[x,y2,z2],
then ´
=
------------------, which is known as determinant formula for ´
. 12807045
(a) 
(b) 
(c) 
(d) None of these
Q.46
Zero vector is perpendicular to:
(Board 2011) 12807046
(a) every vector
(b) unit vector only
(c) position vector only
(d) not any vector
Q.47
Area of parallelogram of two vectors and along two
adjacent sides of parallelogram is equal to: 12807047
(a) ´ (b) | ´ |
(c) | . | (d) | ´ |
Q.48
The -------------------------- is of the volume
of the parallelepiped. 12807048
(a) volume of the tetrahedron
(b) volume of the parallelepiped
(c) volume of the triangle
(d) None of these
Q.49
If any two vectors of scalar triple
product are equal, then its value is equal to:
(a) 0 (b) 2 12807049
(c) 1
(d) None of these
Q.50
If q
is the angle between two vectors and , then q
= 12807050
(a) cos
(b) cos(
.)
(c) cos
(d) cos
Q.51
Area of triangle = ------------------
, if and are vectors
along two adjacent sides of the triangle. 12807051
(a) | ´ | (b) | ´ |
(c) | . | (d)
Q.52
A unit vector is defined as a vector
whose magnitude is: 12807052
(a) 0
(b) 2
(c) 1
(d) None of these
Q.53
A vector, whose initial point is the
origin O and whose terminal point P, is called the --------------- of the point
P and is
written as . 12807053
(a) unit vector
(b) null vector
(c) position vector
(d) None of these
Q.54
The position vector of any point in xy-plane is: (Board 2009) 12807054
(a) 
(b) 
(c) 
(d) 
Q.55
If = [x, y] and = [x, y], are any two
non-zero vectors in the plane, then dot product of and is . = -----. 12807055
(a) xx- yy
(b) xx+ yy
(c) x y+ xy
(d) x y- xy
Q.56
. =
-----------, where and are any
vectors. 12807056
(a) - .
(b) .
(c) - .
(d) None of these
Q.57
For any three vectors , and
, . ( ´
) is also
written as: 12807057
(a) ´ ( ´ ) (b) ( ´ ) .
(c) . ( . ) (d) . ( ´ )
Q.58
The position vector of a point
P(-1,
2, 3) is: (Board 2007) 12807058
(a) 
(b) 
(c) 
(d) 
Q.59
If
and are unit vectors and q
is the angle between them, then the vector
+
is a unit vector if q
= 12807059
(a) (b)
(c) (d)
Q.60
If q
= ---------- between two vectors and , then and are
collinear. 12807060
(a) 0 (b) 1
(c) (d)
Q.61
The magnitude of dot and cross
products of two vectors are 6 and 
respectively, the angle between the vectors
is: (Board 2009)
12807061
(a) 90o (b) 30o
(c) 60o (d) 0o
Q.62
If q
is the angle between and , then q
is equal to: 12807062
(a) sin
(b) sin
(c) cos
(d) sin
Q.63
: 12807063
(Board
2008)
(a) either 
or 
(b) 
are parallel
(c) 
are perpendicular
(d) both 
and 
are nonzero
Q.64
The value of 
is: 12807064
(Board
2011)
(a) 1 (b) 
(c) 0 (d) 
Q.65
If = [x,
y,
z]
and = [x, y, z] are any
three non-zero vectors, then . =
12807065
(a) xx+
y z+
zy
(b) xz + yy+
zx
(c) x y+
x y+
zz
(d) xx+
yy+
zz
Q.66
A constant force 
acting on a body, displaces it from A to B.
The work done by is equal to: (Board 2007) 12807066
(a) 
(b) 
(c) 
(d) 
Q.67
The cross product or vector product of
two vectors is defined: 12807067
(a) only in plane
(b) both a and c
(c) only in space
(d) None of these
Q.68
If and be any two
vectors, then
´
v is equal to: 12807068
(a) - ´ (b) ´
(c) - ´
(d) None of these
Q.69
If 
and 
are coterminous edges of a tetrahedron, then
volume = 12807069
(a) 
(b) 
(c) 
(d) 
Q.70
The vectors , and are coplanar
if and only if [ ] is equal to: 12807070
(a) 0 (b) 2
(c) 1 (d) None of these
Q.71
(Board 2006)
12807071
(a) 1 (b) 0
(c) 
(d) 
Q.72
If l, m, n are the
direction cosines of a vector , then: 12807072
(a) 
– m+
n= 1
(b) + m+
n= 0
(c) + m+
n= 1
(d) + m–
n= 0
Q.73
(Board
2007, 11,15) 12807073
(a) 
(b)
(c) 1 (d)
Q.74
If = k ,
where k is a scalar, then: 12807074
(a) A, B, C form a triangle.
(b) and have the same
magnitude.
(c) A, B, C are collinear.
(d) A, B, C are coincident.
Q.75
Sine of the angle between two vectors and is
given by: 12807075
(a)
(b)
(c)
(d)
Q.76
In DABC,= ,= , = , then: 12807076
(a) + + = 
(b) - + =
(c) + - =
(d) + - =
Q.77
Magnitude of vector 
is:
(Board 2014) 12807077
(a) 29 (b) 
(c) 28 (d) 
Q.78
: (Board 2014) 12807078
(a) 1 (b) 2
(c) 0 (d) – 1
Q.79
equals:
(Board
2014,15) 12807079
(a) 0 (b) 2
(c) 4 (d) 6
Q.80
Work done by a constant force F during displacement d
is equal to:
(Board 2014) 12807080
(a) 
(b) 
(c) 
(d)
Q.81
Moment of
force F about (r) is :
(Board 2015) 12807081
(a)
r ´ F
(b) F ´ r
(c) r .
F (d) F . r
Short Answer Questions
Q.1
Define Vector quantity. 12807082
Q.2
Define Scalar quantity. 12807083
Q.3
Define a position vector. 12807084
Q.4
State parallelogram law of addition of
vectors. 12807085
Q.5
Define a Unit vector. 12807086
Q.6
Define equal vectors. 12807087
Q.7
Define a null or zero vector.
12807088
Q.8
What do you mean by negative of a vector? 12807089
Q.9
If
O is the origin
and = , find the point P when A and B are
(-3, 7) and (1, 0) respectively. 12807090
Q.10
What is set of vectors in R? 12807091
Q.11
Let be a vector in the plane or in space and let c be a real
number. Then
(i)
|| ³ 0, and || = 0 if and only if
= 12807092
(ii) |c| = |c| ||
Q.12
Let A and B be two points whose position vectors are and respectively. If a point P divides AB in the ratio p : q,
then the position vector of P is given by
= 12807093
Q.13
Find the position vector of a point which divides the line segment
joining the points C and D with position vectors 
and 
in the ratio 3:4. 12807094
(Board 2009)
Q.14
Find a unit vector parallel to 
? (Board 2009) 12807095
Q.15
Write a unit vector in the direction of the vector 
. (Board 2010) 12807096
Q.16
If = [1, - 3] and = [2, 5], then find - 12807097
Q.17
Find the unit vector in the direction as the vector = 2 + 6 12807098
(Board 2009)
Q.18
If = 2 + 3 + , = 4 + 6 + 2 and = - 6 - 9 - 3, then find |--|
12807099
Q.19
What is set of vectors in R? 12807100
Q.20
If ABCD is a parallelogram such that the points A, B and C are
respectively (- 2, - 3), (1, 4) and (0, - 5). Find the coordinates of D. 12807101
Q.21
Prove that the line segment joining the
midpoints of two sides of a triangle is parallel to the third side and half as
long. 12807102
Q.22
If
u = 2i + 3 + 4k, v = -i + 3 - k and w = i + 6 + zk represents the sides of a
triangle. Find the value of z. 12807103
Q.23
Use vectors, to prove that the diagonals of a parallelogram bisect
each other. (Board 2007) 12807104
Q.24
If and be the position
vectors of A and B respectively w.r.t. origin O, and C be a point on 
such that 
= , then show that
C is the mid-point of AB. 12807105
Q.25
Define direction angles. 12807106
Q.26
Find the direction cosines of the
vector
. 12807107
Q.27
Find the direction cosines of the vector 
(Board 2010) 12807108
Q.28
Find the vector whose magnitude is 5
and has direction angles: 12807109
a = , b = , g =
Q.29
If = 2 -
4 + 5 and
= 4 -
3 -
4, then find . 12807110
Q.30 Find a, so that |a i + (a+1) j + 2k|=3
(Board 2008, 09) 12807111
Q.31
Define dot product of two vectors.
12807112
Q.32
If =3 - - 2 and = +2- , then find . 12807113
Q.33
For the vectors: = 2– 3+ 4,
= – + 2, = 3+ 2–
Verify
that ×
( + ) = × + ×
12807114
Q.34
Calculate the projection of 
and projection of 
when: (Board 2008) 12807115
Q.35 Find the angle between the vectors
= 2 - + and = - + (Board 2009)
12807116
Q.36
Show that the vectors 2 - + , - 3 - 5 and 3 - 4 - 4 form the sides of a right triangle. 12807117
Q.37
Prove that cos (a - b) = cos a
cos b + sin a sin b (Board 2010) 12807118
Q.38
Find a scalar a so that the vectors
2
+ a + 5
and 3
+ + a
are perpendicular. (Board 2008, 09)
12807119
Q.39
Prove that in any triangle ABC
a = b cos C + c cos B (Projection Law)
12807120
Q.40
Prove that in any triangle ABC
a= b+ c- 2bc cos A
(Cosine Law) 12807121
Q.41
If
+ + = , || = 3, || = 5,
|| = 7. Find the angle between
and .
12807122
Q.42
Show that the components of a vector are the projections of that
vector along , and respectively. 12807123
Q.43
Use scalar products to prove that the
triangle whose vertices are A (1, 0, 1),
B (1, 1, 1) and C (1, 1, 0) is a right isosceles triangle. 12807124
Q.44
Find x for which
the angle between
= x+ – and = + x– is .
12807125
Q.45
If is vector for which v
. 
= 0, v. 
= 0 and v . 
= 0 , find vector v.
(Board 2009) 12807126
Q.46
Define a cross product of two vectors. 12807127
Q.47
If
=2– 3– , = +4– 2,
Q.48
Compute the cross product: 12807129
(2– 3+ 5) ´ (6+ 2– 3).
Q.49
Compute the cross
product:
(2– 5) ´ . 12807130
Q.50
Find a unit
vector perpendicular to both = + + and = 2+ 3–. 12807131
Q.51
Find a unit vector perpendicular to
each of the vectors +2+2, &3–2 –4. Also
calculate the sine of the angle between these vectors. 12807132
Q.52
Find a unit vector
perpendicular to both = + + and = 2+ 3–. 12807133
Q.53
Find a vector perpendicular to the two vectors and
given the four points A (0, 2, 4), B (3, – 1, 2), C (2, 0, 1) and D (4,
2, 0) 12807134
Q.54
Find a vector of magnitude 7 and
perpendicular to = 4+ 3– 6,
= – 6– 2+ 7 12807135
Q.55
If = 2 + 3 + , = 4 + 6 + 2 and = - 6 - 9 - 3, then show that , , and are parallel to each other. 12807136
Q.56
If = 2 - + , then find by determinant formula ´ 12807137
Q.57
If =2 - + and = 4 +2 -
, then find by
determinant formula ´
12807138
Q.58
If =2 - + and = 4 +2 - , then find by determinant formula ´
12807139
Q.59 Find
a and b so that 3
+ 4 and a
+ 
- 2 are
parallel. (Board 2009) 12807140
Q.60
Prove that the area of triangular
region whose vertices are A(), B(), C() is
. 12807141
Q.61
Find
the area of the triangle with vertices A(1,-1,1), B(2,1,-1) & C(- 1,1,2). Also find a unit vector
perpendicular to plane ABC. 12807142
Q.62
Find
area of the parallelogram whose vertices are P(0, 0, 0), Q(- 1, 2, 4),
R(2, - 1, 4 ) and S(1, 1, 8). 12807143
Q.63
If
a, b, g are the direction angles of a vector
, then
show that 
(Board 2008) 12807144
Q.64
Which of the following triples can be the
direction angles of a single vector.
12807145
Q.65
Let , and be vectors in the space.
Then show that (+)+=+(+). 12807146
Q.66
Find a vector perpendicular to the two
vectors and given the four points A (0, 2, 4), B (3, – 1,
2), C (2, 0, 1) and D (4, 2, 0). 12807147
Q.67
Find a vector perpendicular to each of the vectors. = 2 + + and
= 4 + 2 - (Board
2008, 09) 12807148
Q.68
Find the area of triangle with two adjacent sides =3+2 and =2– 4.
12807149
Q.69
Find the area enclosed by the triangle
ABC whose vertices are A(0,0, 0), B(1, 1, 1) and C(0, 2, 3). 12807150
Q.70
Find the area of a parallelogram having diagonals. 12807151
= 3+ – 2 , = – 3+ 4
Q.71
Find
the area of a parallelogram whose vertices are A(1, 3, – 2) , B(5, 1 ,7) , C(8,
– 4, 11) and D(4, – 2, 2) 12807152
Q.72
Prove that:
(Board 2005, 09) 12807153
Q.73
If +
+ = , show that
´ = ´ = ´ (Board
2015)12807154
Q.74
In
any triangle ABC, prove that
= = (Law
of Sines) 12807155
Q.75
Show that sin
(a + b) = sin a
cos b+cos a sin b 12807156
Q.76
If = 0 and, what do you know about (Board
2007)
12807157
Q.77
Define a scalar triple product. 12807158
Q.78
If
= 3– +5, = 4+ 3
– 2, = 2+5+ .Verify that: ×
´
= × ´ = ×
´
12807159
Q.79
Find
the volume of parallelepiped whose edges are
= 2– 3+ ,
= – + 2,
= 2+ –
12807160
Q.80
Find the volume of the
parallelepiped with edges (Board 2005) 12807161
Q.81
Find the volume of parallelepiped whose edges are =2–3+,=–+2, = 2+ – 12807162
Q.82
Find the volume of the parallelepiped determined by = +2 -,
= -2+3, = -7 - 4 12807163
Q.83
Compute the cross product:
(2– 5) ´ . 12807164
Q.84
Find the value of 
(Board 2005) 12807165
Q.85
Prove that [– – – ] = 0
12807166
Q.86
Prove that [–––] = 0
12807167
Q.87
Find the value of 
12807168
(Board
2006)
Q.88
Compute the cross
product:
´ (2+ 3). 12807169
Q.89
Find the value of ×
´
12807170
Q.90
Find the volume of the tetrahedron whose vertices are A(2,1,8),
B(3, 2, 9), C(2, 1, 4) and D(3, 3,
10). 12807171
Q.91
Find the volume of tetrahedron that
has the following vertices.
(0,
1, 2) , (5, 5, 6) , (1, 2, 1) , (3, 2, 1) 12807172
Q.92
Find the value of a, so that a + ,
+ + 3 and 2 + - 2 are coplanar.
12807173
Q.93
Do the points (4, –2, 1), (5, 1, 6),
(2, 2, –5) and (3, 5, 0) lie in a plane? 12807174
Q.94
Prove that the points whose position vectors are A(-6+3+2), B(3 - 2 + 4), C(5 + 7 + 3) and D(- 13 + 17 - ) are coplanar. 12807175
Q.95
Prove that four points A(-3,5, - 4),
B(- 1, 1, 1), C( - 1, 2, 2) and D(- 3, 4, - 5) are coplanar. 12807176
Q.96
Show that the vectors –2+ 2, – 2+ 3– 4 and – 3+ 5 are coplanar. 12807177
Q.97
Find the value of l which makes
+ – , – 2+ and l+ – lcoplanar. (Board 2007) 12807178
Q.98
Find the work done in moving an object along a straight line from
(5, 3, – 2) to (1, – 2, 4) in a force field given by
=
2– + 3× 12807179
Q.99
Find
the work done by a constant force =2+ 4, if its points of application to a body
moves it from A(1, 1) to B(4, 6).
(Assume that || is measured
in Newton and |d| in meters.) 12807180
Q.100 The constant forces 2 + 5 + 6 and --2- act on a body, which is displaced from
position P(4,-3,-2) to Q(6, 1,-3). Find the
total work done. 12807181
Q.101 Find the moment about the
point M(-2, 4, -6) of the force represented by , where
coordinates of points A and B are
(1, 2, - 3) and (3, - 4, 2) respectively. 12807182
Q.102 Prove that
(Board 2011) 12807183
Q.103
Find the moment about A(1, 1, 1) of each of the
concurrent forces where P(2, 0, 1) is their point of concurrency. (Board
2009) 12807184
