PUC II – TEXT BOOK MCQ’s
1. RELATIONS AND FUNCTIONS
NCERT MCQS:
1. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4),(1, 3), (3, 3),
(3, 2)}. Choose the correct answer.
(A) R is reflexive and symmetric but not transitive.
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive.
(D) R is an equivalence relation.
2.
Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choosethe correct answer.
(A) (2, 4) ∈ R
3.
5.
(C) (6, 8) ∈ R
(D) (8, 7) ∈ R
Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
(A) 1
4.
(B) (3, 8) ∈ R
(B) 2
(C) 3
(D) 4
Let f : R → R be defined as f(x) = x4. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.
Let f : R → R be defined as f (x) = 3x. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.
1
6.
If f : R → R be given by f (x) = f ( x)  (3  x3 ) 3 , then fof(x) is
1
(B) x3
(A) x 3
7.
Number of binary operations on the set {a, b} are
(A) 10
8.
(D) (3 – x3).
(C) x
(B) 16
(C) 20
(D ) 8
Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and
symmetric but not transitive is
(A) 1
9.
(B) 2
(C) 3
(D) 4
 4
4x
Let f : R –    → R be a function defined as f ( x) 
. The inverse of f is the map g :
3x  4
 3
 4
Range f → R –    given by
 3
(A) g ( y ) 
3y
3 4y
(B) g ( y ) 
4y
4  3y
(C) g ( y ) 
4y
3 4y
(D) g ( y ) 
3y
4  3y
-1-
2. INVERSE TRIGONOMETRIC FUNCTIONS
NCERT MCQS:
1.
tan 1 3  sec1 (2) is equal to [MQP]
B) 
A) π
2.
1
2
B)

B) 
B)
x
1 x
2
sin 1 (1  x)  2sin 1 x 
1
4
D) 1

D) 2 3
C) 0
2
5
6
C)

3
D)

6
1
2
1
B)

2
1 x
2
, then x is equal to
B) 1,
1
2
1
C)
1 x
2
x
D)
1  x2
[MQP]
C) 0
D)
1
2

4
D)
3
4
x
x y
tan 1    tan 1
is equal to [MQP]
x y
 y
A)
8.
C)
sin(tan-1 x), |x| < 1 is equal to [MQP]
A) 0,
7.
1
3

7
6
A)
6.
D)
7 

cos 1  cos
 is equal to
6 

A)
5.

3
tan 1 3  cot 1  3 is equal to (2022 M)
A) π
4.
3
2
3
C)

 1 
sin   sin 1     is equal to
 2 
3
A)
3.


2
B)

3
C)
If sin-1x=y, then
A) 0y
B) -/2y/2
C)0<y<
D)-/2<y</2
-2-
3. MATRICES
NCERT MCQS:
1.
Which of the given values of x and y make the following pair of matrices equal
5  0 y  2 
3 x  7
 y  1 2  3 x  , 8
4 

 
1
1
2
2
a) x  , y  7
b) Not possible to find c) y = 7, y 
d) x  , y 
3
3
3
3
2.
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is: [MQP]
a) 27
b) 18
c) 81
d) 512
Assume X, Y, Z, W &P matrices of order 2 × 𝑛, 3 × 𝑘, 2 × 𝑝, 𝑛 × 3 & 𝑝 × 𝑘 respectively
3.
The restriction on n, k and p so that PY + WY will be defined are:
A) k = 3, p = n
B) k is arbitrary, p = 2 C) p is arbitrary, k = 3 D) k = 2, p = 3
4.
If n = p, then the order of the matrix 7X – 5Z is:
A) p × 2
B) 2 × n
C) n × 3
D) p × n
  
5.
If A  
 is such that A² = I, then
   
(A) 1 + α² + βγ = 0
(B) 1 – α² + βγ = 0
(C) 1 – α² – βγ = 0
(D) 1 + α² – βγ = 0
2
6.
If A is square matrix such that A = A, then (I + A)³ – 7 A is equal to
(A) A
(B) I – A
(C) I
(D) 3A
7.
If A, B are symmetric matrices of same order, then AB – BA is a
(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix
cos   sin  
8.
If A  
 , then A + Aꞌ = I, if the value of α is
 sin  cos  


3
(A)
(B)
(C) π
(D)
6
3
2
9.
If the matrix A is both symmetric and skew symmetric, then
(A) A is a diagonal matrix
(B) A is a zero matrix
(C) A is a square matrix
(D) None of these
10. Matrices A and B will be inverse of each other only if
(A) AB = B A
(B) AB = BA = 0
(C) AB = 0, BA = I
(D) AB = BA = I
[
]
11. 𝐴 = 𝑎𝑖𝑗 𝑚×𝑛 is a square matrix if
(A) 𝑚 < 𝑛
(B) 𝑚 > 𝑛
(C) 𝑚 = 𝑛
(D) None
4. DETERMINANTS
NCERT MCQ :
1.
If
x 2 6 2

, then x is equal to
18 x 18 6
(A) 6
2.
3.
(B) ±6
(C) -6
Let A be a square matrix of order 3 × 3, then | kA| is equal to
(A) k| A|
(B) k2 | A|
(C) k3 | A|
Which of the following is correct
(D) 0
(D) 3k | A |
(A) Determinant is a square matrix.
(B) Determinant is a number associated to a matrix.
(C) Determinant is a number associated to a square matrix.
(D) None of these
-3-
4.
5.
If area of triangle is 35 sq units with vertices (2, – 6), (5, 4) and (k, 4). Then k is
(A) 12
(B) –2
(C) –12, –2
a11 a12
If   a21 a22
a31 a32
a13
a23 and Aij is Cofactors of aij, then value of Δ is given by
a33
(A) a11 A31+ a12 A32 + a13 A33
(C) a21 A11+ a22 A12 + a23 A13
6.
(B) a11 A11+ a12 A12 + a13 A13
(D) a11 A11+ a21 A21 + a31 A31
x  2 x  3 x  2a
If a, b, c, are in A.P, then the determinant x  3 x  4 x  2b is
x  4 x  5 x  2c
(A) 0
7.
(B) 1
(C) x
(D) 2x
 x 0 0
If x, y, z are nonzero real numbers, then the inverse of matrix A   0 y 0 is
 0 0 z 
 x 1

(A)  0
 0

0
y 1
0
 x 1

(B) xyz  0
0

0 

0 
z 1 
 1
Let A    sin 
 1
(A) Det (A) = 0
sin 
1
 sin 
0
y 1
0
0

0
z 1 
1 0 0 
1 
0 1 0
(D)

xyz
0 0 1 
 x 0 0
1 
0 y 0
(C)

xyz
 0 0 z 
8.
(D) 12, –2
1 
sin   , where 0 ≤ θ ≤ 2π. Then
1 
(B) Det (A) ∈ (2, ∞)
(C) Det (A) ∈ (2, 4)
(D) Det (A) ∈ [2, 4]
9. Let A be a non singular square matrix of order 3 then det(adjA)=
(A) det(A)
(B) det(A2)
(C) det(A3)
(D)none
-1
10. If A is an invertible matrix of order 2 then det(A )=
(A) det(A)
(B) 1/det(A)
(C) 1
(D) 0
5. CONTINUITY AND DIFFERENTIABILITY
NCERT MCQ :
1. The function f(x) = [x] is continuous at x =
a) 4
b) -2
c) 1
d) 1.5
2. The function f(x) = |x + 1| + |x – 1| is
a) continuous at x = -1 as well as x = 1
b) continuous at x = -1 but not x = 1
c) continuous at x = 1 but not x = -1
d) None
3. The function f(x) = |x + 3| is not differentiable at x =
a) -3
b) 1
c) 2
d) 3
-4-
4. If f(x) = x sin
1
, x ≠ 0 then the value of the function at x = 0 so that the function is continuous at x = 0
x
is
a) 0
b) -1
c) 1
d) Indeterminate
 3x  4 ; 0  x  2
is continuous at x = 2 then λ =
2x   ; 2  x  3
5. If f(x)= 
a) -2
b) -1
c) 0
6. For what value of the function f(x)=
a) 5
3x  4 tan x
at
x
b) 6
 x 2  32
; x2
7. If f(x) =  x  2
k
; x2

a) 16
d) 2
x = 0 is continuous
c) 7
d) 4
is continuous at x = 2 then k =
b) 80
c) 32
d) 8

 1  cos 4x
; x0

x2

a
; x  0 then the value of function f(x) is continuous at x = 0 is
8. If f (x)  

x

; x0
 16  x  4

a) 5
b) 8
9. How should we define f (x) 
a) a + b
c) 4
log(1  ax)  log(1  bx)
at x=0 so as to make it continuous at x = 0
x
b) logea + logeb
 log e x
; if

f
(x)

10. If
 x 1
 k
; if
a) 0
x 1
d) 3
d) log e a
c) a + b
b
is continuous at x = 1 then value of k is
x 1
b) -1
c) 1
d) e
7. INTEGRALS
.NCERT MCQ:
1.
2.
1 

The anti derivative of  x 
 equals
x

1
2 2 1 2
1 1
A) x 3  2 x 2  c
B) x 3  x  c
3
2
3
If
C)
1
2 32
x  2x 2  c
3
d
3
f ( x)  4 x 3  4 such that f(2) = 0. Then f(x) is
dx
x
4
A) x 
1 129

x3
8
3
B) x 
1 129

x4
8
4
C) x 
D)
3 32 1 12
x  x c
2
2
(CET)
1 129

x3
8
3
D) x 
1 129

x4
8
-5-
3.
10 x9  10 x log e 10
 x10  10x dx equals [CET]
A) 10x – x10 = c
4.
 sin
2
dx
equals
x cos 2 x
A) tan x + cot x + c
5.

dx
is equal to
e  e x
x
(A) tan-1(ex) + C
8.

B) tan x – cot x + c
B) tan (xex) + c
C) tan (ex) + c
D) cot (ex) + c
(B) tan-1(e-x) + C
(C) log(ex-e-x) + C
(D) log(ex + e-x) + C
[MQP]
(B) log |sin x + cos x| + C
(D)
If f (a  b  x)  f ( x), then a xf ( x)dx is equal to
b
1
(sin x  cos x) 2
[CET]
(A)
ab b
 f (b  x)dx
2 a
(B)
ab b
 f (b  x)dx
2 a
(C)
ba b
 f ( x)dx
2 a
(D)
ab b
 f ( x)dx
2 a
x

A)
12.
D) tan x + sec x + c
[MQP]
1
C
sin x  cos x
2
dx
equals
 2x  2
A) x tan-1 (x + 1) + c
11.
D) tan x – cot 2x + c
[MQP]
(C) log |sin x – cos x| + C
10.
C) tan x cot x + c
B) tan x + cosec x + c C) –tanx + cot x + c
cos 2 x
dx is equal to
(sin x  cos x) 2
(A)
9.
D) log(10x + x10) + c
e x (1  x)
equals [MQP]
cos 2 ( xe x )
A) – cot (exx) + c
7.
C) (10x – x10)-1 + c
[MQP]
sin 2 x  cos 2 x
 sin 2 x cos2 x dx is equal to
A) tan x + cot x + c
6.
B) 10x + x10 + c
dx
9 x  4 x2
[CET]
B) tan-1 (x + 1) + c
C) (x + 1) tan-1x + c
D) tan-1 x + c
equals
1 1  9 x  8 
1 1  9 x  8 
1 1  8 x  9 
1 1  9 x  8 
sin 
  c B) sin 
  c D) sin 
  c C) sin 
c
9
3
2
2
 8 
 8 
 9 
 9 
xdx
 ( x  1)( x  2) equals
A) log
( x  1)2
c
x2
B) log
( x  2)2
c
x 1
 x 1 
C) log 
 c
 x2
2
D) log ( x 1)( x  2)  c
-6-
13.
14.
dx
equals
2
 1)
 x( x
1
A) log | x |  log( x 2  1)  C
2
1
B) log | x |  log( x 2  1)  C
2
1
C)  log | x |  log( x 2  1)  C
2
D)
1
log | x |  log( x 2  1)  C
2
C)
1 x3
e c
2
x e
2 x3
1 x3
e c
3
A)
15.
dx equals
e
x

1
A)
17.
2
3
0
3
D)
1 x2
e c
2
sec x(1  tan x)dx equals [MQP]
A) ex cos x + c
16.
1 x2
e c
3
B)
B) ex sec x + c
C) ex sin x + c
D) ex tan x + c
dx
equals
1  x2

3
2
3
B)

dx
equals
4  9x2
A)

6
C)

6
D)

12
C)

24
D)

4
(2017M)
2
12
B)
1
18.
( x  x3 ) 3
dx is [CET]
The value of the integral 1
x4
3
1
A) 6
19.
If f(x) =
B) 0

x
0
t sin t dt , the f′(x) is
A) cosx + x sin x
20.
C) 3
D) 4
C) x cosx
D) sinx + x cosx
(C) -1
(D)
[CET]
B) x sinx
 2x 1 
1
dx is
The value of 0 tan 1 
2 
 1 x  x 
(A) 1
21. The value
A) 0
(B) 0

2

2


4
( x3  x cos x  tan 5 x  1)dx is [CET]
B) 2

 4  3sin x 
22. The value 0 2 log 
 dx is
 4  3cos x 
3
A) 2
B)
4
C) π
D) 1
C) 0
D) -2
[CET]
-7-
23. ∫ √1 + 𝑥 2 𝑑𝑥 is equal to
A)
B)
C)
D)
𝑥
2
1
√1 + 𝑥 2 + 2 log | (𝑥 + √1 + 𝑥 2 ) | + 𝐶
3
2
(1 + 𝑥 2 )2 + 𝐶
3
3
2
𝑥 (1 + 𝑥 2 )2 + 𝐶
3
𝑥2
2
1
√1 + 𝑥 2 + 2 x 2 log | (𝑥 + √1 + 𝑥 2 ) | + 𝐶
24. ∫ √𝑥 2 − 8𝑥 + 7 𝑑𝑥 is equal to
A)
B)
C)
D)
1
2
1
2
1
2
1
2
(𝑥 − 4)√𝑥 2 − 8𝑥 + 7 + 9 log|𝑥 − 4 + √𝑥 2 − 8𝑥 + 7| + 𝐶
(𝑥 + 4)√𝑥 2 − 8𝑥 + 7 + 9 log|𝑥 + 4 + √𝑥 2 − 8𝑥 + 7| + 𝐶
(𝑥 − 4)√𝑥 2 − 8𝑥 + 7 − 3√2 log|𝑥 − 4 + √𝑥 2 − 8𝑥 + 7| + 𝐶
(𝑥 − 4)√𝑥 2 − 8𝑥 + 7 −
9
2
log|𝑥 − 4 + √𝑥 2 − 8𝑥 + 7| + 𝐶
10. VECTORS ALGEBRA
NCERT MCQ:
1.
2.
In triangle ABC given below, which of the following is not true:
(A) AB  BC  CA  0
(B) AB  BC  AC  0
(C) AB  BC  CA  0
(D) AB  CB  CA  0
If a and b are two collinear vectors, then which of the following are incorrect:
(A) b  a , for some scalar λ
(B) a  b
(C) the respective components of a and b are proportional
(D) both the vectors a and b have same direction, but different magnitudes.
3.
If a is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λ a is unit vector if
(A) λ = 1
4.
(B) λ = – 1
(C) a = | λ|
Let the vectors a and b be such that | a | 3 and | b |
(D) a = 1/| λ|
2
, then a  b is a unit vector, if the angle
3
between a and b is
(A) π/6
(B) π/4
(C) π/3
(D) π/2
-8-
5.
1
1
Area of a rectangle having vertices A, B, C and D with position vectors iˆ  ˆj  4kˆ , iˆ  ˆj  4kˆ and
2
2
1
1
iˆ  ˆj  4kˆ , iˆ  ˆj  4kˆ respectively is
2
2
(A)
6.
1
2
(B) 1

(D) 3
If θ is the angle between any two vectors a and b , then a  b  a  b whenθ is equal to
(B)

4
(C)

2
(D) π
If θ is the angle between two vectors a and b , then a  b  0 only when
(A) 0 <θ<
9.
(C) 1

(B) –1
(A) 0
8.

(D) 4
The value of iˆ. ˆj  kˆ  ˆj  iˆ  kˆ  kˆ  iˆ  ˆj is
(A) 0
7.
  
(C) 2

2
(B) 0   

2
(C) 0 < θ < π
(D) 0 ≤ θ ≤ π
Let a and b be two unit vectors and θ is the angle between them. Then a  b is a unit vector if
(A)  

4
(B)  

3
(C)  

2
(D)  
2
3
11.THREE DIMENSIONAL GEOMETRY
NCERT MCQ :
1.
Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is
(A) 2 units
2.
(B) 4 units
(C) 8 units
(D)
2
units
29
The planes: 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are
(A) Perpendicular
(B) Parallel
(C) intersect y-axis
5

(D) passes through  0, 0, 
4

12. LINEAR PROGRAMMING PROBLEM
NCERT MCQ:
1.
The corner points of the feasible region determined by the following system oflinear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). LetZ = px + qy, where p, q > 0.
Condition on p and q so that the maximum of Zoccurs at both (3, 4) and (0, 5) is
(A) p = q
(B) p = 2q
(C) p = 3q
(D) q = 3p
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13.PROBABILITY
NCERT MCQs
1.
2.
3.
4.
5.
6.
1
, P(B) = 0, then P (A|B) is
2
1
(A) 0
(B)
(C) not defined
(D) 1
2
If A and B are events such that P(A|B) = P(B|A), then
(A) A ⊂ B but A ≠ B
(B) A = B
(C) A ∩ B = ∅
(D) P(A) = P(B)
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
1
1
1
(A) 0
(B)
(C)
(D)
12
3
36
Two events A and B will be independent, if
(A) A and B are mutually exclusive
(B) P(A′B′) = [1 – P(A)] [1 – P(B)]
(C) P(A) = P(B)
(D) P(A) + P(B) = 1
4
Probability that A speaks truth is . A coin is tossed. A reports that a headappears. The probability
5
that actually there was head is(2018J)
1
1
4
2
(A)
(B)
(C)
(D)
5
5
5
2
If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of thefollowing is correct?
If P (A) =
(A) P(A| B) = P(B)
(B) P(A|B) < P(A)
(C) P(A|B) ≥ P(A)
(D) None of these
P(A)
7.
8.
9.
The mean of the numbers obtained on throwing a die having written 1 on threefaces, 2 on two faces
and 5 on one face is
8
(A) 1
(B) 2
(C) 5
(D)
3
Suppose that two cards are drawn at random from a deck of cards. Let X be thenumber of aces
obtained. Then the value of E(X) is
37
1
5
2
(A)
(B)
(C)
(D)
13
13
13
221
In a box containing 100 bulbs, 10 are defective. The probability that out of asample of 5 bulbs, none is
defective is
1
(B)  
2
(A) 10-1
10.
5
 
9
(C)  
10

The probability that a student is not a swimmer is
5
(D)

9
10
1
. Then the probability thatout of five students, four
5
are swimmers is (2016M)
4
4 1
(A) 5 C4  
5 5
11.
12.
13.
4
4 1
(B)  
5 5
1 4
(C) 5 C1  
5 5
 
4
(D) None of these
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then
(A) A ⊂ B
(B) B ⊂ A
(C) B = ∅
(D) A = ∅
If P(A|B) > P(A), then which of the following is correct :
(A) P(B|A) < P(B)
(B) P(A ∩ B) < P(A) . P(B)
(C) P(B|A) > P(B)
(D) P(B|A) = P(B)
If A and B are any two events such that P(A) + P(B) – P(A and B) = P(A), then
(A) P(B|A) = 1
(B) P(A|B) = 1
(C) P(B|A) = 0
(D) P(A|B) = 0
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