CUET Mathematics Question Paper 2024 Set C(Available): Download Solutions and Answer Key pdf

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CUET Mathematics Question Paper 2024 (Set C) is available with detailed solution. NTA is going to conduct 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 Mathematics Question Paper with Solutions 2024 (Set C)

Question 1:

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

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

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

Question 2:

The degree of the differential equation (d²y)/(dx)² = (1 - k)(dy)/(dx)

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

Correct Answer: (1) 1
View Solution

Question 3:

n¹ (x - x_π) + ∫ dx = ?

(1) n eⁿ (x - 1) log C
(2) n eⁿ x log C
(3) n eⁿ x log C x - 1
(4) n eⁿ (x log C) x - 1

Correct Answer: (1) n eⁿ (x - 1) log C

View Solution

This is an indefinite integral problem. To solve, use standard integral properties and the appropriate substitutions to simplify the equation.

When dealing with integrals and derivatives, carefully follow the integration rules for each term and solve sequentially.

Question 4:

The value of ∫ (a - bx)/(a + bx) dx is:

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

Correct Answer: (4) 1/(a + b)
View Solution

Question 5:

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 6:

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 7:

If [A]_3×2 [B]_x×y = [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 8:

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 9:

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 10:

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 11:

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

Correct Answer: (2) 50
View Solution

Question 12:

The area of the region bounded by the lines x + 2y = 12, x = 2, x = 6, and the x-axis is:

(1) 34 sq units
(2) 20 sq units
(3) 24 sq units
(4) 16 sq units

Correct Answer: (3) 24 sq units
View Solution

Question 13:

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

(1) 1/3
(2) 1/6
(3) 1/9
(4) 1/18

Correct Answer: (3) 1/9
View Solution

Question 14:

The corner points of the feasible region determined by x + y ≤ 8, 2x + y ≥ 8, x ≥ 0, 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

Correct Answer: (3) b = 2a
View Solution

Question 15:

If t = e^2x and y = loge t², then d²y/dx² is:

(1) 0
(2) 4t
(3) 2t^4e
(4) 2t²e (4t – 1)

Correct Answer: (2) 4t

View Solution

Question 16:

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

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

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

Question 17:

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) 4

(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 18:

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: (2) diagonal matrix
View Solution

Question 19:

The feasible region represented by the constraints:

4x + y ≥ 80,
x + 5y ≥ 115,
3x + 2y ≤ 150,
x, y ≥ 0
of an LPP is:

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

Correct Answer: (3) Region C
View Solution

Question 20:

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: (2) 32/3 sq. units
View Solution

Question 21:

∫ dx / (x² + e^x) is:

(1) x² / (1 + e^x) + C
(2) – e^x x + C
(3) – x² / (1 + e^x) + C
(4) e^x x + C

Correct Answer: (3) – x² / (1 + e^x) + C
View Solution

Question 22:

If f(x) is defined as:
f(x) = { kx + 1, if x ≤ π
cos x, if x > π
For f(x) to be continuous at x = π, the value of k is:

(1) 0
(2) π
(3) π/2
(4) -π/2

Correct Answer: (3) π/2
View Solution

Question 23:

If P = [1 2; 1 -1] and Q = [2 -4; 1 1] are two matrices, then (PQ)^' will be:

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

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

Question 24:

Δ = 1xcos⁻¹(xcos1xcos) where:

(1) Δ = 2(1 – cos²x)
(2) Δ = 2(2 – sin²x)
(3) Minimum value of Δ is 2
(4) Maximum value of Δ is 4

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

View Solution

Question 25:

f(x) = sin x + 2 cos²x in [0, π/2].

(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: (3) (A), (B) and (D) only
View Solution

Question 26:

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, 3/2)
(2) (–3/2, –3, 3/2)
(3) (3/2, –3, –3/2)
(4) (3/2, 3, 3/2)

Correct Answer: (3) (3/2, –3, –3/2)
View Solution

Question 27:

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) = c * x for x = 3, 4
Otherwise, P(X = x) = 0

(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 28:

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

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

Correct Answer: (2) asin(y + a)
View Solution

Question 29:

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 30:

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: (1) 7/28
View Solution

Question 31:

If f(x) = 2(e^(π/4) - tan x), 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: (3) odd and is strictly increasing in (–∞, ∞)
View Solution

Question 32:

For the differential equation (x log(x))dy = (log(x) - y)dx:

Choose the correct answer from the options below:

(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 33:

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: (3) 7/2
View Solution

Question 34:

Which of the following cannot be the direction ratios of the straight line:
(2x – 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 35:

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

Correct Answer: (1)
View Solution

Question 36:

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

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

Correct Answer: (3) Transitive
View Solution

Question 37:

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 38:

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 39:

If a vector (b - a) + (b + a) = 27 and |a| = 2|b|, then |b| is:

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

Correct Answer: (2) 2
View Solution

Question 40:

If tan⁻¹( – x / √(3 + x²)) = cot⁻¹( x / √(3 + x²)), 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 41:

If A, B and C are three singular matrices given by A = [1 4; 3 2a], B = [3b 5; a 2], and C = [a + b + c c + 1; a + c c], then the value of abc is:

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

Correct Answer: (2) 30
View Solution

Question 42:

The value of the integral ∫ (e^(2x log 3) * e^(2x log 2)) dx from e to 1 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 43:

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 the vectors b and c is:

(1) 60°
(2) 90°
(3) 120°
(4) 180°

Correct Answer: (3) 120°
View Solution

Question 44:

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

Question 45:

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: (1) 66π
View Solution

Question 48:

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) x
(II) x²
(III) x³
(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 49:

If the function f : ℕ → ℕ is defined as f(n) = 1 + n if n is odd, and f(n) = 1 - n if n is even, then which of the following is true?

(1) f is injective
(2) f is into
(3) f is surjective
(4) f is invertible

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

Question 50:

∫ (x cos x + e^x cos x) dx from 0 to π is:

(1) 0
(2) π/4
(3) ∞
(4) π/12

Correct Answer: (1) 0

View Solution

By evaluating the integral using standard methods of integration and applying the limits, the result is 0.

In definite integrals, always apply the limits after performing the integration, and check the result for any cancellations or symmetries.

Question 51:

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 52:

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: (1) 15, 25, 21
View Solution

Question 53:

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: (1) maximize Z = 0.08x + 0.09y
View Solution

Question 54:

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. Given the formula for EMI:
EMI = P * r * (1 + r)ⁿ / ((1 + r)ⁿ – 1), where
P is the principal loan amount, r is the monthly interest rate, and n is the number of months.

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 55:

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 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 56:

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 57:

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 58:

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 61:

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: (2) 1
View Solution

Question 62:

The equation of the tangent to the curve (5/2)x + (5/2)y = 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 63:

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: (3) 1.89
View Solution

Question 64:

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 the bond is:
(Use (1.05)¹⁰ ≈ 1.6)

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

Correct Answer: (2) ₹ 68,500
View Solution

Question 65:

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

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

Correct Answer: (2) 3
View Solution

Question 66:

If (12x + 103y) / (78x + 5) = (5x + 1) / (y + 32), then the value of 5x + 3y is equal to:

(1) –1
(2) 8
(3) 2
(4) 0

Correct Answer: (2) 8
View Solution

Question 67:

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

Correct Answer: (1) 15/41
View Solution

Question 68:

Which of the following are components of a time series?
(A) Irregular component
(B) Cyclical component
(C) Chronological Component
(D) Trend Component

(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)
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Question 69:

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: (2) 30
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Question 70:

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%
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Question 71:

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: (1) 4
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Question 72:

For I = [10, 0; 0, 1], 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
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Question 73:

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:

(1) 512/5
(2) 21/2
(3) 1024/45
(4) 21/2 210

Correct Answer: (1) 512/5
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Question 74:

If a 95% confidence interval for the population mean was reported to be 160 to 170 and σ = 25, then the size of the sample used in this study is:
(Use Z_0.025 = 1.96)

(1) 96
(2) 125
(3) 54
(4) 81

Correct Answer: (4) 81
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Question 75:

Two pipes A and B together can fill a tank in 40 minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in:

(1) 1 hour
(2) 2 hours
(3) 80 minutes
(4) 20 minutes

Correct Answer: (4) 20 minutes
View Solution

Question 77:

Match List-I with List-II:

List-I
(A) e^x
(B) log_e 5
(C) 5^x log_e 5
(D) 5^x

List-II
(I) 5^x (log_e 5)
(II) 5^x log_e 5
(III) 5^x
(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: (2) (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
View Solution

Question 78:

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 + 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 79:

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
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Question 80:

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: (3) 17
View Solution

Question 81:

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 82:

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
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Question 83:

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: (3) 3
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Question 84:

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)
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Question 85:

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