CUET Mathematics Question Paper 2024(Available): Download Set B Question paper with Answers PDF

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CUET Mathematics Question Paper 2024 (Set B) is available for download here. NTA conducted CUET 2024 Mathematics paper on 16 May in Shift 2B from 5:15 PM to 6:15 PM. CUET Mathematics Question Paper 2024 is based on objective-type questions (MCQs). Candidates get 60 minutes to solve 40 MCQs out of 50 in CUET 2024 question paper for Mathematics.

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CUET 2024 Mathematics Question Paper with Solution

Question 1:

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

Correct Answer: (2) zero matrix
View Solution

Question 2:

If A is a square matrix of order 4 and |A| = 4, then |2A| will be:

(1) 8
(2) 64
(3) 16
(4) 4

Correct Answer: (3) 16
View Solution

Question 3:

If [A]₃x₂ [B]xₓy = [C]₃x₁, then:

(1) x = 1, y = 3
(2) x = 2, y = 1
(3) x = 3, y = 3
(4) x = 3, y = 1

Correct Answer: (3) x = 3, y = 3 View Solution

Question 4:

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

Correct Answer: (2) 0
View Solution

Question 5:

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

Correct Answer: (3) 4/7
View Solution

Question 6:

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

List-I:

(A) Absolute maximum value
(B) Absolute minimum value
(C) Point of maxima
(D) Point of minima

List-II:

(I) 3
(II) 0
(III) -5
(IV) 4

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

Correct Answer: (3) (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
View Solution

Question 7:

Find the value of:

∫ (a – bx)² dx from 0 to 2

(1) (a – b)(a + b)
(2) a – b
(3) (a + b)²
(4) (1 / (a + b))

Correct Answer: (1) (a – b)(a + b)
View Solution

Question 8:

Find the second derivative of:

y = 5x logₑ 5

(1) 5x logₑ 5
(2) 5x (logₑ 5)²
(3) x e⁵ log 5
(4) x² e⁵ (log 5)

Correct Answer: (1) 5x logₑ 5
View Solution

Question 9:

What is the degree of the following differential equation?

(dy/dx)² + (dy/dx) = 1 - k

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

Correct Answer: (2) 2
View Solution

Question 10:

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

Correct Answer: (3) Skew symmetric matrix
View Solution

Question 11:

If A is a square matrix of order 4 and |A|= 4, then |2A| will be:

(1) 8
(2) 64
(3) 16
(4) 4

Correct Answer: (3) 16
View Solution

Question 12:

If [A]₃×₂ [B]ₓᵧ = [C]₃×₁, then:

(1) x = 1, y = 3
(2) x = 2, y = 1
(3) x = 3, y = 3
(4) x = 3, y = 1

Correct Answer: (4) x = 3, y = 1
View Solution

Question 13:

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

Correct Answer: (3) –2
View Solution

Question 14:

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

Correct Answer: (2) 1/3
View Solution

Question 15:

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

List-I
(A) Absolute maximum value
(B) Absolute minimum value
(C) Point of maxima
(D) Point of minima

List-II
(I) 3
(II) 0
(III) –5
(IV) 4

(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)

Correct Answer: (4) (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
View Solution

Question 16:

The rate of change (in cm²/s) of the total surface area of a hemisphere with respect to radius r at r = 3.31 cm is:

(1) 66π
(2) 6.6π
(3) 3.3π
(4) 4.4π

Correct Answer: (2) 6.6π
View Solution

Question 17:

The area of the region bounded by the lines:

x + (3/a)y = 4, x = 0, and y = 0 is:

(1) 56/3ab
(2) 56a
(3) ab/2
(4) 3ab

Correct Answer: (3) ab/2
View Solution

Question 18:

If A is a square matrix and I is an identity matrix such that A² = A, then A(I – 2A)³ + 2A³ is equal to:

(1) I + A
(2) I + 2A
(3) I – A
(4) A

Correct Answer: (1) I + A
View Solution

Question 19:

The value of the integral:

∫ (e²ˣ log₃(2x) – 1) dx from 1 to e is:

(1) logₑ 3
(2) logₑ 4 – logₑ 3
(3) logₑ 9 – logₑ 4
(4) logₑ 3 – logₑ 2

Correct Answer: (2) logₑ 4 – logₑ 3
View Solution

Question 20:

If a, b, and c are three vectors such that a + b + c = 0, where a and b are unit vectors and |c| = 2, then the angle between vectors b and c is:

(1) 60°
(2) 90°
(3) 120°
(4) 180°

Correct Answer: (3) 120°
View Solution

Question 21:

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

List-I
(A) |x – 1| + |x – 2|
(B) x – |x|
(C) x – [x]
(D) x |x|

List-II
(I) is differentiable everywhere except at x = 0
(II) is continuous everywhere
(III) is not differentiable at x = 1
(IV) is differentiable at x = 1

(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)

Correct Answer: (4) (A) - (II), (B) - (IV), (C) - (III), (D) - (I)
View Solution

Question 22:

Match List-I with List-II:

List-I
(A) Integrating factor of xdy – (y + 2x²)dx = 0
(B) Integrating factor of (2x² – 3y)dx = xdy
(C) Integrating factor of (2y + 3x²)dx + xdy = 0
(D) Integrating factor of 2xdy + (3x³ + 2y)dx = 0

List-II
(I) x¹
(II) x³
(III) x²
(IV) x

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

Correct Answer: (1) (A) - (I), (B) - (III), (C) - (IV), (D) - (II)
View Solution

Question 23:

If the function f: ℕ → ℕ is defined as f(n) = 1 – n if n is even, and f(n) = 1 + n if n is odd, then:

(1) (B) only
(2) (A), (B), and (D) only
(3) (A) and (C) only
(4) (A), (C), and (D) only

Correct Answer: (3) (A) and (C) only
View Solution

Question 24:

Evaluate the following integral:

∫₀^π (x cot x - 12) cos x dx

(1) 0
(2) 4π
(3) ∞
(4) 12π

Correct Answer: (1) 0
View Solution

Question 25:

If the random variable X has the following distribution:

X: 0, 1, 2, otherwise
P(X): k, 2k, 3k, 0

Match List-I with List-II:

List-I
(A) k
(B) P(X < 2)
(C) E(X)
(D) P(1 ≤ X ≤ 2)

List-II
(I) 6
(II) 3
(III) 2
(IV) 1

(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)

Correct Answer: (1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
View Solution

Question 26:

For a square matrix A_n×n, which of the following are true?

(1) |adj A| = |A|^n–1
(2) |A| = |adj A|^n–1
(3) A(adj A) = |A|
(4) |A^–1| = |A|^–1

Correct Answer: (3) (A), (C), and (D) only
View Solution

Question 27:

The matrix

    [ 1  0  0 ]
    [ 0  1  0 ]
    [ 0  0  1 ]

is a:

(1) Scalar matrix
(2) Diagonal matrix
(3) Skew-symmetric matrix
(4) Symmetric matrix

Correct Answer: (1) Scalar matrix, (2) Diagonal matrix, and (4) Symmetric matrix
View Solution

Question 28:

The feasible region represented by the constraints:

4x + y ≥ 80, x + 5y ≥ 115, 3x + 2y ≤ 150, x, y ≥ 0

is:

(1) Region A
(2) Region B
(3) Region C
(4) Region D

Correct Answer: (1) Region A
View Solution

Question 29:

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) 16/3 sq. units

Correct Answer: (3) 8/3 sq. units
View Solution

Question 30:

Evaluate the integral:

∫ dx / (x² + 1) * eˣ

(1) x² / (1 + eˣ) + C
(2) - eˣ x + C
(3) - x² / (1 + eˣ) + C
(4) eˣ x + C

Correct Answer: (3) - x² / (1 + eˣ) + C
View Solution

Question 31:

If the function f(x) is defined as:

f(x) = { kx + 1 for x ≤ π, cos x for x > π }

If f(x) is continuous at x = π, then the value of k is:

(1) 0
(2) π
(3) π/2
(4) -π/2

Correct Answer: (3) π/2
View Solution

Question 32:

If P and Q are matrices given by:

P = [ 1 2 1; -1 0 1 ] and Q = [ 2 -4 1 ]

Then the matrix (PQ)^ᵀ will be:

(1) [2 -3 -0; 0 3 -3; 7 5 4]
(2) [1 2 -4; 4 -8 -4; 2 4 -2]
(3) [0 7 -9; 7 6 5; 2 5 5]
(4) [6 2 -8; 7 5 2; 8 4 -7]

Correct Answer: (1) [2 -3 -0; 0 3 -3; 7 5 4]
View Solution

Question 33:

Δ = 1xcos–1–xcos1xcos–1xcos1
(A) Δ = 2(1 – cos²x)
(B) Δ = 2(2 – sin²x)
(C) Minimum value of Δ is 2
(D) Maximum value of Δ is 4

(1) (A), (C), and (D) only
(2) (A), (B), and (C) only
(3) (A), (B), (C), and (D)
(4) (B), (C), and (D) only

Correct Answer: (3) (A), (B), (C), and (D)
View Solution

Question 34:

If f(x) = sin(x) + 2cos²(x), in the interval [0, π/2], then:

(1) f'(x) = cos(x) – sin(2x)
(2) The critical points of the function are x = π/6 and x = π/2
(3) The minimum value of the function is 2
(4) The maximum value of the function is 4/3

Correct Answer: (1) (A), (B), and (D) only
View Solution

Question 35:

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

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

Correct Answer: (2) -3/2, -3/1, 3/2
View Solution

Question 36:

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.
P(X = x) =
For x = 1, P(X = x) = cx – 5
For x = 2, P(X = x) = 3x – 4
Otherwise, P(X = x) = 0

Match List-I with List-II:

List-I
(A) c
(B) P(X ≤ 2)
(C) P(X = 2)
(D) P(X ≥ 2)

List-II
(I) 0.75
(II) 0.3
(III) 0.55
(IV) 0.15

(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)

Correct Answer: (1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
View Solution

Question 37:

If sin y = x sin(a + y), then dx/dy is:

(1) sin(a + y) / sin y
(2) sin(a + y) / sin² y
(3) sin y / sin(a + y)
(4) sin² y / sin(a + y)

Correct Answer: (2) sin(a + y) / sin² y
View Solution

Question 38:

The unit vector perpendicular to each of the vectors a + b and a - b, where a = i + j + k and b = i + 2j + 3k, is:

(1) i/6 + j/6 + k/6
(2) -i/6 + j/6 - k/6
(3) -i/6 + j/2 + k/2
(4) -i/6 + j/2 - k/6

Correct Answer: (2) -i/6 + j/6 - k/6
View Solution

Question 39:

The distance between the lines

r = i - 2j + 3k + λ(2i + 3j + 6k) and r = 3i - 2j + k + μ(4i + 6j + 12k) is:

(1) 7√28
(2) 7√199
(3) 7√328
(4) 7√421

Correct Answer: (3) 7√328
View Solution

Question 40:

If f(x) = 2(π/4 – x)e^(tan x – 1), then f(x) is:

(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 (–∞, ∞)

Correct Answer: (2) Even and is strictly decreasing in (0, ∞)
View Solution

Question 41:

For the differential equation (x loge x)dy = (loge x – y)dx, the correct statements are:

(1) (A) and (C) only
(2) (A), (B), and (C) only
(3) (A), (B), and (D) only
(4) (A) and (D) only

Correct Answer: (2) (A), (B), and (C) only
View Solution

Question 42:

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, and if it shows a number divisible by 3, a ball is drawn from Bag-1; otherwise, a ball is drawn from Bag-2. If the ball drawn is not black in color, the probability that it was not drawn from Bag-2 is:

(1) 9/4
(2) 8/3
(3) 7/2
(4) 19/4

Correct Answer: (4) 19/4
View Solution

Question 43:

Which of the following cannot be the direction ratios of the straight line:

(2/3 – x) = (3/y – 2) = (1 – 4z)

(1) 2, –3, –1
(2) –2, 3, 1
(3) 2, 3, –1
(4) 6, –9, –3

Correct Answer: (4) 6, –9, –3
View Solution

Question 44:

Which one of the following represents the correct feasible region determined by the following constraints of an LPP?

x + y ≥ 10, 2x + 2y ≤ 25, x ≥ 0, y ≥ 0

(1) Image 1
(2) Image 2
(3) Image 3
(4) Image 4

Correct Answer: (1) Image 1
View Solution

Question 45:

Let R be the relation over the set A of all straight lines in a plane such that l1 R l2 if and only if l1 is parallel to l2. Then R is:

(1) Symmetric
(2) An Equivalence relation
(3) Transitive
(4) Reflexive

Correct Answer: (2) An Equivalence relation
View Solution

Question 46:

The probability of not getting 53 Tuesdays in a leap year is:

(1) 2/7
(2) 1/7
(3) 0
(4) 5/7

Correct Answer: (4) 5/7
View Solution

Question 47:

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

(1) π/3
(2) π
(3) π/6
(4) π/2

Correct Answer: (1) π/3
View Solution

Question 48:

If →b - →a = 27 and |→a| = 2|→b|, then |→b| is:

(1) 3
(2) 2
(3) 5/6
(4) 6

Correct Answer: (1) 3
View Solution

Question 49:

If tan^-1(x + 2) = cot^-1(x + 1), then which one of the following is true?

(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.

Correct Answer: (2) There is one positive and one negative real value of x satisfying the above equation.
View Solution

Question 50:

If A, B, and C are three singular matrices given by:

A =
[ 1 4 ]
[ 3 2a ]

B =
[ 3b 5 ]
[ a 2 ]

C =
[ a b c ]
[ c 1 a ]
[ a c c ]

Then the value of abc is:

(1) 15
(2) 30
(3) 45
(4) 90

Correct Answer: (2) 30
View Solution

Question 51:

A random variable X has the following probability distribution:

X: 1, 2, 3, 4, 5, 6, 7
P(X): k, 2k, 2k, 3k, k², 2k², 7k² + k

Match the options of List-I to List-II:

List-I
(A) k
(B) P(X < 3)
(C) P(X > 2)
(D) P(2 < X < 7)

List-II
(I) 7/10
(II) 53/100
(III) 1/10
(IV) 3/10

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

Correct Answer: (1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
View Solution

Question 52:

Match List-I with List-II:

List-I
(A) x⁵
(B) logₑ 5
(C) 5ˣ
(D) 5ˣ logₑ 5

List-II
(I) 5x (logₑ 5)
(II) 5x logₑ 5
(III) 5x
(IV) 0

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

Correct Answer: (1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
View Solution

Question 53:

For which one of the following purposes is CAGR (Compounded Annual Growth Rate) not used?

(1) To calculate and communicate the average growth of a single investment
(2) To understand and analyse the donations received by a non-government organisation
(3) To demonstrate and compare the performance of investment advisors
(4) To compare the historical returns of stocks with a savings account

Correct Answer: (2) To understand and analyse the donations received by a non-government organisation
View Solution

Question 54:

A flower vase costs ₹ 36,000. With an annual depreciation of ₹ 2,000, its cost will be ₹ 6,000 in ______ years.

(1) 10
(2) 15
(3) 17
(4) 6

Correct Answer: (2) 15
View Solution

Question 55:

Arun's speed of swimming in still water is 5 km/hr. He swims between two points in a river and returns back to the same starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 2 km/hr, then the distance between the two points is:

(1) 3 km
(2) 1.5 km
(3) 1.75 km
(4) 1 km

Correct Answer: (1) 3 km
View Solution

Question 56:

If e^y = x^x, then which of the following is true?

(1) d²y / dx² = 1
(2) d²y / dx² - y = 0
(3) d²y / dx² - dy / dx = 0
(4) d²y / dx² - dy / dx + 1 = 0

Correct Answer: (4) d²y / dx² - dy / dx + 1 = 0
View Solution

Question 57:

The probability of a shooter hitting a target is 3/4. How many minimum number of times must he fire so that the probability of hitting the target at least once is more than 90%?

(1) 1
(2) 2
(3) 3
(4) 4

Correct Answer: (4) 4
View Solution

Question 58:

Match List-I with List-II:

List-I
(A) Distribution of a sample leads to becoming a normal distribution
(B) Some subset of the entire population
(C) Population mean
(D) Some assumptions about the population

List-II
(I) Central Limit Theorem
(II) Hypothesis
(III) Sample
(IV) Parameter

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

Correct Answer: (1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
View Solution

Question 59:

Ms. Sheela creates a fund of ₹ 1,00,000 for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of r % per annum. If the scholarship amount is taken as ₹ 8,000, then r =

(1) 1 8 2%
(2) 16 8 23%
(3) 17 8 25%
(4) 2 8 5%

Correct Answer: (3) 17 8 25%
View Solution

Question 60:

A person wants to invest an amount of ₹ 75,000. He has two options A and B yielding 8% and 9% return respectively on the invested amount. He plans to invest at least ₹ 15,000 in Plan A and at least ₹ 25,000 in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where x and y are investments in Plan A and Plan B respectively)?

(1) maximize Z = 0.08x + 0.09y
x ≥ 15000, y ≥ 25000, x + y ≥ 75000, x ≤ y, x, y ≥ 0
(2) maximize Z = 0.08x + 0.09y
x ≥ 15000, y ≤ 25000, x + y ≥ 75000, x ≤ y, x, y ≥ 0
(3) maximize Z = 0.08x + 0.09y
x ≥ 15000, y ≥ 25000, x + y ≤ 75000, x ≥ y, x, y ≥ 0
(4) maximize Z = 0.08x + 0.09y
x ≥ 15000, y ≥ 25000, x + y ≤ 75000, x ≤ y, x, y ≥ 0

Correct Answer: (4) maximize Z = 0.08x + 0.09y
x ≥ 15000, y ≥ 25000, x + y ≤ 75000, x ≤ y, x, y ≥ 0
View Solution

Question 61:

In a 700 m race, Amit reaches the finish point in 20 seconds and Rahul reaches in 25 seconds. Amit beats Rahul by a distance of:

(1) 120 m
(2) 150 m
(3) 140 m
(4) 100 m

Correct Answer: (3) 140 m
View Solution

Question 62:

For the given five values 12, 15, 18, 24, 36; the three-year moving averages are:

(1) 15, 25, 21
(2) 15, 27, 19
(3) 15, 19, 26
(4) 15, 19, 30

Correct Answer: (3) 15, 19, 26
View Solution

Question 63:

A property dealer wishes to buy different houses given in the table below with some down payments and balance in EMI for 25 years. Bank charges 6% per annum compounded monthly.

Property type Price of the property (in ₹) Down Payment (in ₹)

Property Type	Price of the Property (in ₹)	Down Payment (in ₹)
P	45,00,000	5,00,000
Q	55,00,000	5,00,000
R	65,00,000	10,00,000
S	75,00,000	15,00,000

Match List-I with List-II:

List-I
(A) P
(B) Q
(C) R
(D) S

List-II
(I) ₹25,600
(II) ₹38,400
(III) ₹32,000
(IV) ₹35,200

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

Correct Answer: (1) (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
View Solution

Question 64:

The corner points of the feasible region for an L.P.P. are (0, 10), (5, 5), (5, 15) and (0, 30). If the objective function is Z = αx + βy, α, β > 0, the condition on α and β so that the maximum of Z occurs at corner points (5, 5) and (0, 20) is:

(1) α = 5β
(2) 5α = β
(3) α = 3β
(4) 4α = 5β

Correct Answer: (2) 5α = β
View Solution

Question 65:

The solution set of the inequality |3x| ≥ |6 – 3x| is:

(1) (-∞, 1]
(2) [1, ∞)
(3) (-∞, 1) ∪ (1, ∞)
(4) (-∞, -1) ∪ (-1, ∞)

Correct Answer: (1) (-∞, 1]
View Solution

Question 66:

If the matrix:
[ 0, -1, 3x ]
[ 1, y, -5 ]
[ -6, 5, 0 ]
is skew-symmetric, then the value of 5x – y is:

(1) 12
(2) 15
(3) 10
(4) 14

Correct Answer: (3) 10
View Solution

Question 67:

A company is selling a certain commodity ‘x’. The demand function for the commodity is linear. The company can sell 2000 units when the price is ₹ 8 per unit and it can sell 3000 units when the price is ₹ 4 per unit. The Marginal revenue at x = 5 is:

(1) ₹ 79.98
(2) ₹ 15.96
(3) ₹ 16.04
(4) ₹ 80.02

Correct Answer: (3) ₹ 16.04
View Solution

Question 70:

If A =
[ 2 4 ]
[ 4 3 ] , X =
[ n 1 ] , B =
[ 8 ]
[ 11 ]
and AX = B, then the value of n will be:

(1) 0
(2) 1
(3) 2
(4) not defined

Correct Answer: (3) 2
View Solution

Question 71:

The equation of the tangent to the curve 5/2x + 5/2y = 33 at the point (1, 4) is:

(1) x + 8y – 33 = 0
(2) 12x + y – 8 = 0
(3) x + 8y – 12 = 0
(4) x + 12y – 8 = 0

Correct Answer: (3) x + 8y – 12 = 0
View Solution

Question 72:

A random variable X has the following probability distribution:

X: -2, -1, 0, 1, 2
P(X): 0.2, 0.1, 0.3, 0.2, 0.2

The variance of X will be:

(1) 0.1
(2) 1.42
(3) 1.89
(4) 2.54

Correct Answer: (2) 1.42
View Solution

Question 73:

A Multinational company creates a sinking fund by setting a sum of ₹ 12,000 annually for 10 years to pay off a bond issue of ₹ 72,000. If the fund accumulates at 5% per annum compound interest, then the surplus after paying for bond is:

(Use (1.05)¹⁰ ≈ 1.6)

(1) ₹ 78,900
(2) ₹ 68,500
(3) ₹ 72,000
(4) ₹ 1,44,000

Correct Answer: (1) ₹ 78,900
View Solution

Question 74:

The least non-negative remainder when 351 is divided by 7 is:

(1) 2
(2) 3
(3) 6
(4) 5

Correct Answer: (3) 6
View Solution

Question 75:

If
[ 12x 10y ] = [ 5x 32 ], then the value of 5x + 3y is equal to:

(1) -1
(2) 8
(3) 2
(4) 0

Correct Answer: (4) 0
View Solution

Question 76:

There are 6 cards numbered 1 to 6, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then P(X > 3) is:

(1) 15/41
(2) 15/1
(3) 21/11
(4) 21/1

Correct Answer: (1) 15/41
View Solution

Question 77:

Which of the following are components of a time series?

(1) (A), (B), and (D) only
(2) (A), (B), and (C) only
(3) (A), (B), (C), and (D)
(4) (B), (C), and (D) only

Correct Answer: (3) (A), (B), (C), and (D)
View Solution

Question 78:

The following data is from a simple random sample:
15, 23, x, 37, 19, 32
If the point estimate of the population mean is 23, then the value of x is:

(1) 12
(2) 30
(3) 21
(4) 24

Correct Answer: (4) 24
View Solution

Question 79:

For an investment, if the nominal rate of interest is 10% compounded half yearly, then the effective rate of interest is:

(1) 10.25%
(2) 11.25%
(3) 10.125%
(4) 11.025%

Correct Answer: (3) 10.125%
View Solution

Question 80:

A mixture contains apple juice and water in the ratio 10 : x. When 36 litres of the mixture and 9 litres of water are mixed, the ratio of apple juice and water becomes 5 : 4. The value of x is:

(1) 4
(2) 4.4
(3) 5
(4) 8

Correct Answer: (3) 5
View Solution

Question 81:

For I =
[ 10 01 ] , if X and Y are square matrices of order 2 such that XY = X and YX = Y, then (Y² + 2Y) equals to:

(1) 2Y
(2) I + 3X
(3) I + 3Y
(4) 3Y

Correct Answer: (3) I + 3Y
View Solution

Question 82:

A coin is tossed K times. If the probability of getting 3 heads is equal to the probability of getting 7 heads, then the probability of getting 8 tails is: