mathematics CUET 2024

1.An objective function Z = ax + by is maximum at points (8, 2) and (4, 6). If a > 0 and b > 0 and ab = 25, then the maximum value of the function is equal to :
(1) 60

(2) 50

(3) 40

(4) 80

ANS 2

2.The area of the region bounded by the lines x+2y=12, x = 2, x = 6 and x-axis is:
(1) 34 sq units

(2) 20 sq units

(3) 24 sq units

(4) 16 sq units

ANS 4

3.A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the second throw of dice and a number less than 4 in the third throw?
(1)1/3

(2) 1/6

(3)1/9

(4) 1/28

ANS 4

4.The corner points of the feasible region determined by x + y ≤8, 2x + y ≥ 8, x 20, y≥0 are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is:

(1) 8a+ 4 = b

(2) a = 2b

(3) b=2a

(4) 8b+ 4 = a

ANS 2

(1) 0

(2) 4t

ANS 1

6.If A and B are symmetric matrices of the same order, then AB - BA is a :

(1) symmetric matrix

(2) zero matrix

(3) skew symmetric matrix

(4) identity matrix

ANS 3

7.If A is a square matrix of order 4 and |A|= 4, then |2A| will be:
(1) 8

(2) 64

(3) 16

(4) 4

ANS 2

(1) x = 1,y=3

(2) x=2,y=1

(3) x=3, y=3

(4) x=3, y=1

ANS 2

9. If a function f(x) = x²+bx+ 1 is increasing in the
interval [1, 2], then the least value of b is :
(1) 5

(2) 0

(3)- 2

(4) -4

ANS 3

10.Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be:

(1)5/9

(2)1/3

(3)4/7

(4)3/8

ANS 2

11. For the function f(x) = 2x³ - 9x² + 12x-5, x = [0,3], match List-I with List-II :

Choose the correct answer from the options given below:
(1) (A) - (IV), (B) - (II), (C) - (I), (D) - (III)

(2) (A)-(II), (B) - (III), (C) - (I), (D) - (IV)

(3) (A)-(IV), (B) - (III), (C) - (II), (D) - (I)

(4) (A)-(IV), (B) - (III), (C) - (I), (D) - (II)

ANS 4

12.The second order derivative of which of the
following functions is 5x ?

ANS 4

13.The degree of the differential equation (1−

(1) 1

(2)2

(3) 3

(4)3/2

ANS 2

ANS 1

ANS 4

ANS 4

17. Let X denote the number of hours you play during a randomly selected day. The probability that X can take values x has the following form, where c is some constant.

Match List-I with List-II :

Choose the correct answer from the options given below:

(1) (A)-(I), (B) - (II), (C) - (III), (D) - (IV)

(2)(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(3) (A)-(I), (B) - (II), (C) - (IV), (D) - (III)

(4) (A)-(III), (B) - (IV), (C) - (I), (D) - (II)

ANS 2

ANS 4

ANS 3

(1) even and is strictly increasing in (0, ∞)

(2) even and is strictly decreasing in (0, ∞)

(3) odd and is strictly increasing in (-∞, ∞)

(4) odd and is strictly decreasing in (-∞, ∞)

ANS 3

21. For the differential equation (x log_e x)dy = (loge x - y)dx
(A) Degree of the given differential equation is 1.

(B) It is a homogeneous differential equation. 

(C) Solution is 2y loge x + A = (loge x)², where A is an arbitrary constant

(D) Solution is 2y log_e x + A=log_e (log_e x), where A is an arbitrary constant

Choose the correct answer from the options given below:
(1) (A) and (C) only

(2) (A), (B) and (C) only

(3) (A), (B) and (D) only

(4) (A) and (D) only

ANS 1

22. There are two bags. Bag-1 contains 4 white and 6 black balls and Bag-2 contains 5 white and 5 black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2. If the ball drawn is not black in colour, the probability that it was not drawn from Bag-2 is:

(1) 4/9

(2) 3/8

(3) 2/7

(4) 4/14 

ANS 3

23.Which of the following cannot be the direction ratios of the straight line the direction ratios of the straight line x-3/3 = 2-y/3 = z+4/-1 ? 

(1) 2,-3,-1

(2) -2,3,1

(3)2,3,-1

(4) 6,-9,-3

ANS 3

24.Which one of the following represents the correct feasible region determined by the following constraints

x+y≥ 10, 2x + 2y ≤ 25, x≥0, y ≥0

(1)

(2)

(3)

(4)

ANS 3

25.Let R be the relation over the set A of all straight lines in a plane such that l₂ Rl₂ ↔ l₂, is parallel to l₂.Then R is:

(1) Symmetric

(2) An Equivalence relation

(3) transitive 

(4) Reflexive

ANS 2

26.The probability of not getting 53 Tuesdays in a leap year is :
(1) 2/7

(2) 1/7

(3) O

(4) 5/7

ANS 4

27.The angle between two lines whose direction ratios are proportional to 1, 1, -2 and(√3 −1). (- √3-1) 4 is:

(1) π/3

(2) π

(3) π/6

(4) π/2

ANS 1

(1) 3

(2) 2

(3) 5/6

(4) 6

ANS 1

(1) There is no real value of x satisfying the above
equation.

(2) There is one positive and one negative real value of x satisfying the above equation.

(3) There are two real positive values of x satisfying the above equation.

(4) There are two real negative values of x satisfying the above equation.

ANS 2

(1) 15

(2) 30

(3)45

(4) 90

ANS 3

(1) log_e 3

(2) log_e 4 - log_e 3

(3) log_e 9- log_e 4

(4) log_e 3- log_e 2

ANS 2

ANS 4

33. Let [x] denote the greatest integer function. Then match List-I with List-II :

Choose the correct answer from the options given below:
(1) (A)- (I), (B) - (II), (C) - (III), (D) - (IV)

(2) (A) - (I), (B) - (III), (C) - (II), (D) - (IV)

(3) (A) - (II), (B) - (I), (C) - (III), (D) - (IV)

(4) (A) - (II), (B) - (IV), (C) - (III), (D) - (I)

ANS 3

(1) 66π

(2) 6.6π

(3) 3.3π

(4) 4.4π

ANS 2

ANS 1

36. If A is a square matrix and I is an identity matrix such that A = A² then A(I-2A)³ + 2A³

(1) I + A

(2) I+2A

(3) I-A

(4) A

ANS 4

37.Match List-I with List-II :

Choose the correct answer from the options given below:

(1) (A) - (1), (B) - (III), (C) - (IV), (D) - (II)

(2) (A) - (1), (B) - (IV), (C) - (III), (D) - (II)

(3) (A)-(II), (B) - (I), (C) - (III), (D) - (IV)

(4) (A)-(III), (B) - (IV), (C) - (II), (D) - (I)

ANS 2

(A) f is injective

(B) f is into

(C) f is surjective

(D) fis invertible

Choose the correct answer from the options given below:

(1) (B) only

(2) (A), (B) and (D) only

(3) (A) and (C) only

(4) (A), (C) and (D) only

ANS 4

ANS 1

40. If the random variable X has the following
distribution :

Match List-I with List-II:

Choose the correct answer from the options given below:

(1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(2) (A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(3) (A)-(I), (B) - (II), (C) - (IV), (D) - (III)

(4) (A)-(III), (B) - (IV), (C) - (I), (D) - (II)

ANS 2

41. For a square matrix Anxn
(A) |adj A| = |A|n−1

(B) |A| = |adj A|n−1

(C) A(adj A) = |A|

(D) |A-1|= 1/A

Choose the correct answer from the options given below:

(1) (B) and (D) only

(2) (A) and (D) only

(3) (A), (C) and (D) only

(4) (B), (C) and (D) only

ANS 2

(A) scalar matrix

(B) diagonal matrix

(C) skew-symmetric matix

(D)symmetric matrix

Choose the correct answer from the options given below:
(1) (A), (B) and (D) only

(2) (A), (B) and (C) only

(3) (A), (B), (C) and (D)

(4)(B), (C) and (D) only

ANS 1

43.The feasible region represented by the constraints 4x + y ≥ 80, x+5y ≥ 115, 3x + 2y ≤ 150, x, y ≥0

(1) Region A

(2) Region B

(3) Region C

(4) Region D

ANS 3

44.The area of the region enclosed between the curves 4x2 = y and y = 4 is :
(1) 16 sq. units

(2) 32/3 sq. units

(3) 8/3 sq. units

(4) 16

ANS 4

ANS 4

ANS 4

ANS 2

(A) Δ=2(1-cos² x) 

(B) Δ=2(2 - sin² x)

(C) Minimum value of Δ is 2

(D) Maximum value of Δ is 4

Choose the correct answer from the options given below:

(1) (A). (C) and (D) only

(2) (A), (B) and (C) only

(3) (A), (B). (C) and (D) only

(4) (A) (B), (C) and (D) only

ANS 4

(A) f'(x) = cos x - sin 2x/

(B) The critical points of the function are x =Π/6 and x= Π/2 

(C) The minimum value of the function is 2

(D) The maximum value of the function is 3/4

Choose the correct answer from the options given below:

(1) (A), (B) and (D) only

(2) (A), (B) and (C) only

(3) (A), (B), (C) and (D)

(4) (B), (C) and (D) only

ANS 1

50. The direction cosines of the line which is
perpendicular to the lines with direction ratios 1, -2, -2 and 0, 2, 1 are:

(1) 2/3, −1/3, 2/3

(2) −2/3, −1/3, 2/3

(3) 2/3, −1/3, −2/3

(4) 2/3, 1/3, 2/3

ANS 1