CUET Mathematics Question Paper 2024 (Set A) is available here for download. 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 2024 Mathematics Question Paper with Solution
Question 1:
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:
If t = e²ˣ and y = logₑ t², then d²y/dx² is:
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:
The area of the region bounded by the lines x + 2y = 12, x = 2, x = 6, and the x-axis is:
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?
Evaluate the integral:
∫ (x + 1)ⁿ dx = ?
Find the value of:
∫ (a – bx)² dx from 0 to 2
Find the second derivative of:
y = 5x logₑ 5
What is the degree of the following differential equation?
(dy/dx)² + (dy/dx) = 1 - k
If A and B are symmetric matrices of the same order, then AB – BA is a:
If A is a square matrix of order 4 and |A|= 4, then |2A| will be:
If [A]₃×₂ [B]ₓᵧ = [C]₃×₁, then:
If a function f(x) = x² + bx + 1 is increasing in the interval [1, 2], then the least value of b is:
Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be:
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
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:
The area of the region bounded by the lines:
x + (3/a)y = 4, x = 0, and y = 0 is:
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:
The value of the integral:
∫ (e²ˣ log₃(2x) – 1) dx from 1 to e is:
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:
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
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
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:
Evaluate the following integral:
∫0π (x cot x - 12) cos x dx
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
For a square matrix An×n, which of the following are true?
The matrix
[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]
is a:
The feasible region represented by the constraints:
4x + y ≥ 80, x + 5y ≥ 115, 3x + 2y ≤ 150, x, y ≥ 0
is:
The area of the region enclosed between the curves 4x² = y and y = 4 is:
Evaluate the integral:
∫ dx / (x² + 1) * eˣ
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:
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:
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
If f(x) = sin(x) + 2cos²(x), in the interval [0, π/2], then:
The direction cosines of the line which is perpendicular to the lines with direction ratios (1, -2, -2) and (0, 2, 1) are:
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
If sin y = x sin(a + y), then dx/dy is:
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:
The distance between the lines
r = i - 2j + 3k + λ(2i + 3j + 6k) and r = 3i - 2j + k + μ(4i + 6j + 12k) is:
If f(x) = 2(π/4 – x)e^(tan x – 1), then f(x) is:
For the differential equation (x loge x)dy = (loge x – y)dx, the correct statements are:
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:
Which of the following cannot be the direction ratios of the straight line:
(2/3 – x) = (3/y – 2) = (1 – 4z)
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
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:
The probability of not getting 53 Tuesdays in a leap year is:
The angle between two lines whose direction ratios are proportional to (1, 1, -2) and (3, -1, -4) is:
If →b - →a = 27 and |→a| = 2|→b|, then |→b| is:
If tan-1(x + 2) = cot-1(x + 1), then which one of the following is true?
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:
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
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
For which one of the following purposes is CAGR (Compounded Annual Growth Rate) not used?
A flower vase costs ₹ 36,000. With an annual depreciation of ₹ 2,000, its cost will be ₹ 6,000 in ______ years.
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:
If ey = xx, then which of the following is true?
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%?
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
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 =
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)?
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:
For the given five values 12, 15, 18, 24, 36; the three-year moving averages are:
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
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:
The solution set of the inequality |3x| ≥ |6 – 3x| is:
If the matrix:
[ 0, -1, 3x ]
[ 1, y, -5 ]
[ -6, 5, 0 ]
is skew-symmetric, then the value of 5x – y is:
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:
If A =
[ 2 4 ]
[ 4 3 ] , X =
[ n 1 ] , B =
[ 8 ]
[ 11 ]
and AX = B, then the value of n will be:
The equation of the tangent to the curve 5/2x + 5/2y = 33 at the point (1, 4) is:
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:
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)
The least non-negative remainder when 351 is divided by 7 is:
If
[ 12x 10y ] = [ 5x 32 ], then the value of 5x + 3y is equal to:
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:
Which of the following are components of a time series?
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:
For an investment, if the nominal rate of interest is 10% compounded half yearly, then the effective rate of interest is:
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:
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:
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:
If a 95% confidence interval for the population mean is reported to be 160 to 170 and σ = 25, then the size of the sample used in this study is:
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:
An even number is the determinant of:
List-I
(A)
[ 1 -1 ]
[ -1 5 ]
(B)
[ 13 -1 ]
[ -1 15 ]
(C)
[ 16 -1 ]
[ -11 15 ]
(D)
[ 6 -12 ]
[ 11 15 ]
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