CUET UG 2024 / Mathematics

CUET UG 2024 Mathematics Previous Year Solved Paper

CUET UG 2024 Mathematics previous year paper with easy solutions. This page keeps the original questions and presents student-friendly explanations in a clean table format for quick revision, practice, and topic-wise mock preparation.

Subject: Mathematics
Year: 2024
Questions extracted: 50
Source format: previous year paper with solution section

Student-Friendly Solutions Table

Each question is shown with its original wording from the source paper and an easier explanation designed for quick understanding.

Q.No. Question Easy Solution
1 If A and B are symmetric matrices of the same order, then AB - BA is a:
Options:
A. symmetric matrix
B. zero matrix
C. skew symmetric matrix
D. identity matrix		 Option C Option C follows the relevant matrix or determinant property.
2 If A is a square matrix of order 4 and |A|=4, then |2A| will be:
Options:
A. 8
B. 64
C. 16
D. 4		 Option B Option B follows the relevant matrix or determinant property.
3 If [A]3×2 [B]x×y = [C]3×1, then:
Options:
A. x=1, y=3
B. x=2, y=1
C. x=3, y=3
D. x=3, y=1		 Option B Option B is the correct answer according to the provided key.
4 If a function f(x)=x²+bx+1 is increasing in the interval [1,2], then the least value of b is:
Options:
A. 5
B. 0
C. -2
D. -4		 Option C Option C is the correct answer according to the provided key.
5 Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be:
Options:
A. 5/9
B. 1/3
C. 4/7
D. 3/8		 Option B Option B follows the correct probability calculation.
6 For the function f(x)=2x³-9x²+12x-5, x ∈ [0,3], match List-I with List-II:






List-IList-II
(A) Absolute maximum value(I) 3
(B) Absolute minimum value(II) 0
(C) Point of maxima(III) -5
(D) Point of minima(IV) 4

Options:
A. (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
B. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
C. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
D. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)		 Option D Option D gives the correct matching of values or properties.
7 An objective function z=ax+by is maximum at points (8,2) and (4,6). If a > 0 and b > 0 and a+b=10, then the maximum value of the function is equal to:
Options:
A. 60
B. 50
C. 40
D. 80		 Option B Option B is the correct result from the graph or linear programming condition.
8 The area of the region bounded by the lines x+2y=12, x=2, x=6 and x-axis is:
Options:
A. 34 sq units
B. 20 sq units
C. 24 sq units
D. 16 sq units		 Option D Option D is the correct result from the graph or linear programming condition.
9 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?
Options:
A. 1/3
B. 1/6
C. 1/9
D. 1/18		 Option D Option D follows the correct probability calculation.
10 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:
Options:
A. 8a+4=b
B. a=2b
C. b=2a
D. 8b+4=a		 Option C Option C is the correct result from the graph or linear programming condition.
11 If t=e^2x and y=log_e t² then d²y/dx² is:
Options:
A. 0
B. 4t
C. 4e^2t/t
D. e^2t(4t-1)/t²		 Option A Option A is the correct answer according to the provided key.
12 ∫ n/(x^(n+1)-x) dx =
Options:
A. (1/n) log_e |(x^n-1)/(x^n)| + C
B. log_e |(x^n+1)/(x^n-1)| + C
C. (1/n) log_e |(x^n+1)/(x^n)| + C
D. log_e |x^n/(x^n-1)| + C		 Option A Option A is the correct calculus result for the given expression.
13 The value of ∫₀¹ (a-bx²)/(a+bx²)² dx is:
Options:
A. (a-b)/(a+b)
B. 1/(a-b)
C. (a+b)/2
D. 1/(a+b)		 Option D Option D is the correct calculus result for the given expression.
14 The second order derivative of which of the following functions is 5^x (ln 5)^2?
Options:
A. 5^x ln 5
B. 5^x (ln 5)^2
C. 5^x/(ln 5)
D. 5^x/(ln 5)^2		 Option B Option B is the correct answer according to the provided key.
15 The degree of the differential equation (1-(dy/dx)²)^(3/2) = k d²y/dx² is:
Options:
A. 1
B. 2
C. 3
D. 3/2		 Option B Option B is the correct calculus result for the given expression.
16 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:
Options:
A. Symmetric
B. An Equivalence relation
C. Transitive
D. Reflexive		 Option B Option B is the correct answer according to the provided key.
17 The probability of not getting 53 Tuesdays in a leap year is:
Options:
A. 2/7
B. 1/7
C. 0
D. 5/7		 Option D Option D follows the correct probability calculation.
18 The angle between two lines whose direction ratios are proportional to 1, 1, 2 and (√3-1), (-√3-1), -4 is:
Options:
A. π/3
B. π
C. π/6
D. π/2		 Option D Option D follows the required vector or 3D geometry relation.
19 If (a-b)·(a+b) = 27 and |a| = 2|b|, then |a| is:
Options:
A. 3
B. 2
C. 5
D. 6		 Option D Option D is the correct answer according to the provided key.
20 If tan⁻¹(2/(3^-x+1)) = cot⁻¹(3/(3^x+1)), then which one of the following is true?
Options:
A. There is no real value of x satisfying the above equation.
B. There is one positive and one negative real value of x satisfying the above equation.
C. There are two real positive values of x satisfying the above equation.
D. There are two real negative values of x satisfying the above equation.		 Option A Option A is the correct answer according to the provided key.
21 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:
Options:
A. 15
B. 30
C. 45
D. 90		 Option D Option D is the correct answer according to the provided key.
22 The value of the integral ∫ from ln2 to ln3 of (e^2x-1)/(e^2x+1) dx is:
Options:
A. ln 3
B. ln 4 - ln 3
C. ln 9 - ln 4
D. ln 3 - ln 2		 Option B Option B is the correct calculus result for the given expression.
23 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 a and b is:
Options:
A. 60°
B. 90°
C. 120°
D. 0°		 Option D Option D follows the required vector or 3D geometry relation.
24 Let [x] denote the greatest integer function. Match List-I with List-II:






List-IList-II
(A)x-1+x-2(I) is differentiable everywhere except at x=0
(B) x-x(II) is continuous everywhere
(C) x-[x](III) is not differentiable at x=1
(D) x²(IV) is differentiable at x=1

Options:
A. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
B. (A)-(I), (B)-(III), (C)-(II), (D)-(IV)
C. (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
D. (A)-(II), (B)-(IV), (C)-(III), (D)-(I)		 Option C Option C gives the correct matching of values or properties.
25 The rate of change (in cm²/s) of the total surface area of a hemisphere with respect to radius r = cube root of 1.331 cm is:
Options:
A. 66Ï€
B. 6.6Ï€
C. 3.3Ï€
D. 4.4Ï€		 Option B Option B is the correct result from the graph or linear programming condition.
26 The area of the region bounded by the lines x/(7√3) + y/b = 4, x=0 and y=0 is:
Options:
A. 56√3ab
B. 56ab
C. ab/2
D. 3ab		 Option A Option A is the correct result from the graph or linear programming condition.
27 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:
Options:
A. I+A
B. I+2A
C. I-A
D. A		 Option D Option D follows the relevant matrix or determinant property.
28 Match List-I with List-II regarding Integrating Factors:






List-I (Differential Equation)List-II (Integrating Factor)
(A) xdy - (y+2x²)dx = 0(I) 1/x
(B) (2x²-3y)dx = xdy(II) x
(C) (2y+3x²)dx + xdy = 0(III) x²
(D) 2xdy + (3x³+2y)dx = 0(IV) x³

Options:
A. (A)-(I), (B)-(III), (C)-(IV), (D)-(II)
B. (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
C. (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
D. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)		 Option C Option C gives the correct matching of values or properties.
29 If the function f : N → N is defined as f(n) = n-1, if n is even; n+1, if n is odd, then:
Options:
A. (B) only
B. (A), (B) and (D) only
C. (A) and (C) only
D. (A), (C) and (D) only		 Option D Option D is the correct answer according to the provided key.
30 ∫₀^(π/2) (1-cot x)/(csc x + cos x) dx =
Options:
A. 0
B. π/4
C. 8
D. π/12		 Option A Option A is the correct calculus result for the given expression.
31 If the random variable X has the following distribution:



X012otherwise
P(X)k2k3k0

Match List-I with List-II:






List-IList-II
(A) k(I) 5/6
(B) P(X<2)(II) 4/3
(C) E(X)(III) 1/2
(D) P(1≤X≤2)(IV) 1/6

Options:
A. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
B. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
C. (A)-(I), (B)-(II), (C)-(IV), (D)-(III)
D. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)		 Option B Option B gives the correct matching of values or properties.
32 For a square matrix Aₙ×ₙ:
(A) |adj A| = |A|^(n-1)
(B) |A| = |adj A|^(n-1)
(C) A(adj A) = |A|I
(D) |A^-1| = 1/|A|
Options:
A. (B) and (D) only
B. (A) and (D) only
C. (A), (C) and (D) only
D. (B), (C) and (D) only		 Option C Option C follows the relevant matrix or determinant property.
33 The matrix [[1,0,0],[0,1,0],[0,0,1]] is a:
(A) scalar matrix
(B) diagonal matrix
(C) skew-symmetric matrix
(D) symmetric matrix
Options:
A. (A), (B) and (D) only
B. (A), (B) and (C) only
C. (A), (B), (C) and (D)
D. (B), (C) and (D) only		 Option A Option A follows the relevant matrix or determinant property.
34 The feasible region represented by the constraints 4x+y≥80, x+5y≥115, 3x+2y≤150, x,y≥0 is:
Options:
A. Region A
B. Region B
C. Region C
D. Region D		 Option C Option C is the correct result from the graph or linear programming condition.
35 The area of the region enclosed between the curves y=4x² and y=4 is:
Options:
A. 16 sq. units
B. 32/3 sq. units
C. 8/3 sq. units
D. 16/3 sq. units		 Option D Option D is the correct result from the graph or linear programming condition.
36 ∫ e^x((2x+1)/(2√x))dx =
Options:
A. e^x/(2√x)+C
B. -e^x√x+C
C. -e^x/(2√x)+C
D. e^x√x+C		 Option D Option D is the correct calculus result for the given expression.
37 If f(x) = kx+1, if x ≤ π; cos x, if x > π is continuous at x = π, then the value of k is:
Options:
A. 0
B. π
C. 2/Ï€
D. -2/Ï€		 Option D Option D is the correct answer according to the provided key.
38 If P = [[-1],[2],[1]] and Q = [[2,-4,1]] are two matrices, then (PQ)^T will be:
Options:
A. [[4,5,7],[-3,-3,0],[0,-3,-2]]
B. [[-2,4,-1],[4,-8,2],[2,-4,1]]
C. [[5,5,2],[7,6,7],[-9,-7,0]]
D. [[-2,4,8],[7,5,7],[-8,-2,6]]		 Option B Option B is the correct answer according to the provided key.
39 If Δ = | 1 cosx 1 ; -cosx 1 cosx ; -1 -cosx 1 |, then:
(A) Δ = 2(1+cos²x)
(B) Δ = 2(2-sin²x)
(C) Minimum value of Δ is 2
(D) Maximum value of Δ is 4
Options:
A. (A), (C) and (D) only
B. (A), (B) and (C) only
C. (A), (B), (C) and (D)
D. (B), (C) and (D) only		 Option C Option C is the correct answer according to the provided key.
40 For f(x) = sin x + 1/2 cos 2x in [0, π/2]:
(A) f'(x) = cos x - sin 2x
(B) The critical points are x = π/6 and x = π/2
(C) The minimum value of the function is 1/2
(D) The maximum value of the function is 3/4
Options:
A. (A), (B) and (D) only
B. (A), (B) and (C) only
C. (A), (B), (C) and (D)
D. (B), (C) and (D) only		 Option C Option C is the correct answer according to the provided key.
41 The direction cosines of the line which is perpendicular to the lines with direction ratios 1, -2, -2 and 0, 2, 1 are:
Options:
A. 2/3, -1/3, 2/3
B. -2/3, -1/3, 2/3
C. 2/3, -1/3, -2/3
D. 2/3, 1/3, 2/3		 Option A Option A follows the required vector or 3D geometry relation.
42 Given P(X=x) = 0.1 if x=0; cx if x=1,2; c(5-x) if x=3,4, match List-I with List-II:






List-IList-II
(A) c(I) 0.75
(B) P(X≤2)(II) 0.3
(C) P(X=2)(III) 0.55
(D) P(X≥2)(IV) 0.15

Options:
A. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
B. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
C. (A)-(I), (B)-(II), (C)-(IV), (D)-(III)
D. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)		 Option B Option B gives the correct matching of values or properties.
43 If sin y = x · sin(a+y), then dy/dx is:
Options:
A. sin²a / sin(a+y)
B. sin(a+y) / sin²a
C. sin(a+y) / sin a
D. sin²(a+y) / sin a		 Option D Option D is the correct calculus result for the given expression.
44 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:
Options:
A. 1/√6 i + 2/√6 j + 1/√6 k
B. -1/√6 i + 1/√6 j - 1/√6 k
C. -1/√6 i + 2/√6 j + 2/√6 k
D. -1/√6 i + 2/√6 j - 1/√6 k		 Option D Option D follows the required vector or 3D geometry relation.
45 The distance between the lines r=i-2j+3k+λ(2i+3j+6k) and r=3i-2j+1k+μ(4i+6j+12k) is:
Options:
A. √28/7
B. √199/7
C. √328/7
D. √421/7		 Option C Option C follows the required vector or 3D geometry relation.
46 If f(x)=2(tan⁻¹(e^x)-π/4), then f(x) is:
Options:
A. even and is strictly increasing in (0, ∞)
B. even and is strictly decreasing in (0, ∞)
C. odd and is strictly increasing in (-∞, ∞)
D. odd and is strictly decreasing in (-∞, ∞)		 Option C Option C is the correct answer according to the provided key.
47 For the differential equation (x log_e x)dy = (log_e x-y)dx:
(A) Degree is 1
(B) It is a homogeneous differential equation
(C) Solution is 2y log_e x + A = (log_e x)^2
(D) Solution is 2y log_e x + A = log_e(log_e x)
Options:
A. (A) and (C) only
B. (A), (B) and (C) only
C. (A), (B) and (D) only
D. (A) and (D) only		 Option A Option A is the correct calculus result for the given expression.
48 Bag-1 has 4 white, 6 black balls. Bag-2 has 5 white, 5 black balls. Die divisible by 3 draws from Bag-1, else Bag-2. If drawn ball is white, probability it was from Bag-1 is:
Options:
A. 4/9
B. 3/8
C. 2/7
D. 4/19		 Option D Option D follows the correct probability calculation.
49 Which of the following cannot be the direction ratios of the line (x-3)/2 = (2-y)/3 = (z+4)/-1?
Options:
A. 2, -3, -1
B. -2, 3, 1
C. 2, 3, -1
D. 6, -9, -3		 Option C Option C follows the required vector or 3D geometry relation.
50 Correct feasible region for x+y≥ 10, 2x+2y≤ 25, x≥ 0, y≥ 0 is:
Options:
A. Shaded region between parallel lines
B. Triangular region at origin
C. Empty region (No intersection)
D. Infinite region		 Option A Option A is the correct result from the graph or linear programming condition.

FAQs

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