# Important MCQs For CBSE Class 12 Maths Board Exam 2023

In this post, I have provided CBSE Class 12th Maths Board Exam 2023 Important MCQs Questions With Answers.

The main purpose of these practice questions and answers is to help the CBSE Class 12 Maths students to prepare for their comming exams.

Given Below Are Important Questions with solution.

1 The number of equivalence relations that can be defined in the set A= {1,2,3} which containing the elements (1,2) is

(a) 0

(b) 1

(c) 2

(d) 3

2 The number of one-to-one functions that can be defined from the set {1,2,3,4,5} to {a, b}

a) 5

b) 0

c) 2

d) 3

3 What is the simplified form of cos-1(4x3 − 3x)

(a) 3sin−1 x

(b) 3cos−1 x

(c) π − 3 sin−1 x

(d) π − 3 cos−1 x

4 The number of all possible matrices of order2x3 with entry 1 or 2

1)16

2) 64

3) 6

4) 24

5 If the order of matrix P is 2×3 and the order of matrix Q is 3×4 , find the order of PQ.

1) 2×4

2) 2×2

3) 4×2

4) 3×3

6 Let A is a non – singular matrix of order 3 x 3 then | A ( adj A )| is equal to

a)| A |

b)| A |2

c)| A |3

d)3| A |

7 The function f(x) =[x] is continuous at

a)4

b)-2

c)1

d)1.5

8 The bottom of a rectangular swimming tank is 25 m by 40 m water is pumped into the tank at the rate of 500 cubic meters per minute. Find the rate at which the level of water in the tank is rising?

A) 1⁄4 m/min

B) 2/3 m/min

C) 1/3 m/min

D) 1⁄2 m/min

9 Area of region bound by circle x2+y2=1

a)2 sq units

b) sq units

c)3 sq units

d)4 sq units

10 Integrating factor of the differential equation dy/dx + y tan x – sec x = 0 is:

(A) cosx

(B) secx

(C) ecosx

(D) esecx

11 If points A (60 î+ 3 ĵ), (40 î– 8 ĵ) and C ( aî- 52ĵ) are collinear, then ‘a’ is equal to

a) 40

b) -40

c) 20

d) -20

12 Write direction cosines of a line parallel to z-axis.

(a) 1,0,0

(b) 0,0,1

(c) 1,1,0

(d) -1,-1,-1

13 Find the foot of the perpendicular drawn from the point (2,-3,4) on the y-axis.

(a) (2,0,4)

(b) (0.3.0)

(c) (0,-3,0)

(d) (-2,0,-4)

14 If α,β, Υ are the angles that a line makes with the positive direction of x,y,z axis respectively then the direction cosines of the line are

(a) cosα,sinβ, cosΥ

(b) cosα,cosβ, cosΥ

(c) sinα,sinβ, sinΥ

(d) 1, 1, 1

15 The feasible region of the inequality x+y≤1 and x–y≤1 lies in……… quadrants.

(a)Only I and II

(b)Only I and III

(c)Only II and III

(d)All four

16 Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3 is

a)1/18

b)5/18

c)1/5

d)2

17 The solution set of the inequality 3x + 5y < 4 is

a)an open half-plane not containing the origin.

b)an open half-plane containing the origin.

c)the whole XY-plane not containing the line 3x + 5y = 4.

d)a closed half plane containing the origin.

18 If A is a square matrix of order 3 and |A| = 5, then |adjA| =

(a) 5

(b) 25

(c) 125

(d) ⅕

19 The area of a triangle with vertices (2, −6), (5,4) and (k, 4) is 35 square units then , k is

A.12

B. −2

C. −12, −2

D. 12, −2

20 The vector having initial and terminal points as (2,5,0) and (-3,7,4) respectively is

A. 5î+ 2ĵ− 4k̂

B. −î+ 12ĵ+ 4k̂

C. −5î+ 2ĵ+ 4k̂

D.−5î+ 12ĵ+ 4k̂

21. Let A = { 1 , 2, 3 } and consider the relation R = {(1 , 1), (2 , 2), ( 3 , 3), (1 , 2), (2 , 3), (1,3)} Then , R is

(a) Reflexive but not symmetric

(b) Reflexive but not transitive

(c) Symmetric and transitive

(d)Neither symmetric nor transitive

22. If A is a skew – symmetric matrix , then A² is

(a) Symmetric

(b) Skew – symmetric

(c) A² = A

(d) A² ≠ A

23. The number of arbitrary constants in the general solution of a differential equation of fourth order are :

(a) 0

(b) 2

(c) 3

(d) 4

24. If y = log x/ (1+x) , then dy/ dx is equal to

(a) x/ (1+x)²

(b) 1/ (1+x) ²

(c) 2x/ (1+x)²

(d) 1/ x(1+x)

25. Corner points of the region for an LPP are (0, 2), (3, 0), (6, 0),(6, 8), and (0, 5) . Let F = 4x + 6y be the objective function. The minimum value of F occurs at

(a) (0,2) only

(b)(3,0) only

(c) The midpoint of the line segment joining the points (0,2) and ( 3, 0) only

(d) Any point on the line segment joining the points (0,2) and (3, 0) only.

26. f(x) = xˣ has a stationary point at

(a) x = e

(b) x = 1/ e

(c) x = 1

(d) x = √e

27. If A and B are events such that P ( A/ B) = P (B/ A) , then ………

(a) P(A) = P(B)

(b) P(A) ≠ P(B)

(c) P(A) + P(B) = 1

(d) None of these

28. If R = {(x , y ): x + 2y = 8 } is a relation N , then the range of R is :

(a){3, 2 , 1}

(b) { 3 , 2}

(c) {2 , 8 , 1}

(d) {3}

29. 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

30. The principal value of [tan-1 √3 − cot-1, (−√3)] is :

(a)π

(b) − π/2

(c) 0

(d) 2√3

31. If cos (sin-1 2/ 5 + cos-1 x) = 0 , then x is equal to

(a) 1/ 5

(b)2/ 5

(c) 0

(d) 1

32. The value of ∫ (cos 2x)/ (sinx +cosx)² dx is

(a) log | cos x + sin x | + C

(b) log | cos x − sin x | + C

(c) log | cos x + sin x |² + C

(d) log | cos x + sin x |-2 + C

33. The derivative of 3ˣ  w.r.t x is :

(a) log 3

(b) x. 3ˣ-1

(c) 0

(d) 3ˣ log 3

34. A is a square matrix of order 2, then adj(adj A) is :

(a) O

(b) I

(c) A-1

(d) A

35. The number of arbitrary constants in the general solution of a differential equation of fourth order is :

(a) 1

(b) 2

(c) 3

(d) 4

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