CUET Mathematics 2025 15 May Shift 2 PYQs

n × n

m × m

m × n

n × m

$f(x) \cdot log_e[f(x)] + C$; $C$ is a constant of integration

$\frac{log_e[f(x)]}{f(x)} + C$; $C$ is a constant of integration

$log_e(log_e[f(x)]) + C$; $C$ is a constant of integration

$\frac{log_e(log_e[f(x)])}{f(x)} + C$; $C$ is a constant of integration

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

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

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

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

100

± 1000

320

± 320

$\frac{4}{15}\left(1 - \frac{1}{x^3}\right)^{5/4} + C$; $C$ is a constant of integration

$\frac{4}{3}\left(1 - \frac{1}{x^3}\right)^{5/4} + C$; $C$ is a constant of integration

$\frac{4}{15}\left(1 - \frac{1}{x^3}\right)^{3/4} + C$; $C$ is a constant of integration

$\frac{4}{15}\left(1 - \frac{1}{x^2}\right)^{1/5} + C$; $C$ is a constant of integration

9

-1

7

3

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

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

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

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

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

(A), (D) and (E) only

(A) and (D) only

(B) and (C) only

63 sq. units

36 sq. units

27 sq. units

18 sq. units

0

$-\frac{9}{4}$

180

204

$\frac{x}{y}$

$\frac{y}{x}$

1

0

Region D

Region B

Region A

Region C

5

-3

-6

9

$b = 3a$

$a = 3b$

$a = 2b$

$a = b$

∞

0

1

2

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

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

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

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

(6,1,0)

(-3, -5,0)

(9,3,0)

(0, -3,0)

a symmetric matrix

a skew-symmetric matrix

neither a symmetric nor a skew-symmetric

always a diagonal matrix

$\frac{13}{20}$

$\frac{11}{20}$

$\frac{7}{20}$

$\frac{9}{20}$

1

2

3

4

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

(C) and (D) only

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

(A) and (D) only

0

2

$x$

$y$

[1,2]

[-1,1]

(1,2)

(-1,1)

$20\sqrt{3}$ cm²/sec

$10\sqrt{3}$ cm²/sec

$3\sqrt{5}$ cm²/sec

$5\sqrt{3}$ cm²/sec

$p = -7, q = 18$

$p = 7, q = -20$

$p = 7, q = -10$

$p = -7, q = 5$

$\frac{2\pi}{3}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$\frac{\pi}{6}$

$e - 1$ sq. units

$e$ sq. units

1 sq. units

0 sq. units

190

180

170

160

0

2

4

$\frac{5}{2}$

9

11

13

15

$2^n - 1$

$2^n - 2$

$^nP_2$

$n!$

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

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

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

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

$\frac{1}{8}$

$\frac{7}{8}$

$\frac{3}{8}$

$\frac{5}{8}$

$P(\bar{A} \cap \bar{B}) = [1-P(A)][1-P(B)]$

$P(A) + P(B) = 1$

$P(A) = P(B)$

$P(A) + P(B) = 0$

$\lambda = 5$ and $\mu \neq 9$

$\lambda \neq 9$ and $\mu = 5$

$\lambda = 5$ and $\mu = 9$

$\lambda = 5$ and $\mu = 5$

17 I

-17 I

15 I

-15 I

3

4

7

0

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

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

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

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

$\begin{bmatrix} 15 & 6 \\ 9 & 8 \end{bmatrix}$

$\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$

$\begin{bmatrix} 15 & 9 \\ -12 & -6 \end{bmatrix}$

$\begin{bmatrix} 15 & 9 \\ 6 & 12 \end{bmatrix}$

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

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

(A) and (C) only

(A) and (D) only

Reflexive

Symmetric

Transitive

Reflexive and transitive

72

-144

288

144

(A) only

(B) and (C) only

(A) and (C) only

(B) and (D) only

$y = \frac{x^3}{7} + cx^{-4}$; $c$ is arbitrary constant.

$y = \frac{x^3}{7} + cx^{-7}$; $c$ is arbitrary constant.

$y = \frac{x^7}{7} + cx^{-4}$; $c$ is arbitrary constant.

$y = \frac{x^7}{7} + cx^{-3}$; $c$ is arbitrary constant.

-7

-14

7

14

$\frac{x^3}{3} + \frac{x^2}{2} + C$; $C$ is a constant of integration

$\frac{x^3}{3} - \frac{x^2}{2} + C$; $C$ is a constant of integration

$\frac{x^3}{6} + \frac{x^2}{4} + C$; $C$ is a constant of integration

$\frac{x^3}{6} - \frac{x^2}{4} + C$; $C$ is a constant of integration

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

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

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

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

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

(B) and (E) only

(B), (D) and (E) only

(A), (C) and (E) only

$(4, \infty)$

$\left(\frac{1}{4}, \infty\right)$

$\left(-\infty, \frac{1}{4}\right)$

$\left(0, \frac{1}{4}\right)$

(C) and (D) only

(A) only

(B) only

(C) only

$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} ; s = \sqrt{\frac{n_1s_1^2 + n_2s_2^2}{n_1 + n_2 - 2}}$

$t = \frac{\bar{x}_1 - \bar{x}_2}{s\sqrt{\frac{1}{n_1^2} + \frac{1}{n_2^2}}} ; s = \sqrt{\frac{n_1^2s_1^2 + n_2^2s_2^2}{n_1 + n_2 - 2}}$

$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} ; s = \sqrt{\frac{n_1s_1^2 + n_2s_2^2}{n_1 + n_2 - 2}}$

$t = \frac{\bar{x}_1 - \bar{x}_2}{s\sqrt{\frac{1}{n_1^2} + \frac{1}{n_2^2}}} ; s = \sqrt{\frac{n_1s_1^2 + n_2s_2^2}{n_1 + n_2 - 2}}$

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

(B) and (D) only

(A) and (C) only

(C) and (D) only

70.96

73.12

76.12

75.54

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

(A) and (D) only

(B) and (C) only

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

1/3

1/729

728/729

665/729

0

1

2

3

0.6767

0.3233

0.18044

0.9753

$\frac{d^2y}{dx^2} = 2\frac{dy}{dx}$

$\frac{d^2y}{dx^2} = 2\left(\frac{dy}{dx}\right)^2$

$\frac{d^2y}{dx^2} = 2\left(\frac{dy}{dx}\right)^{1/2}$

$\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$

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

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

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

(A) and (C) only

Rs. 8000

Rs. 6000

Rs. 5000

Rs. 7500

A statistical hypothesis is a statement about the population parameter which may be true or false.

The standard deviation of the sampling distribution of a statistics is known as its standard error.

If sufficiently large random samples with replacement are drawn from a population, then the sampling distribution of the sample means approaches a binomial distribution.

In a statistical hypothesis testing, a Type-I error is made when null hypothesis is rejected when it is true.

0

1

2

3

$x + 2y - 3 = 0$

$2y - x - 3 = 0$

$2y - x + 3 = 0$

$3x + 2y - 3 = 0$

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

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

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

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

Nominal rate of return is the total amount of money earned by an investment without considering various expenses.

The compound annual growth rate is calculated by the final and beginning value of the investment.

The compound annual growth rate describes the effect of compounding.

The actual rate of return can be calculated by adding the various expenses into the total money earned.

Rs. 35998

Rs. 34996

Rs. 33998

Rs. 34448

48

64

76

72

(0, 1]

[1, 0)

(0, 1)

[0, 1]

5 minutes

8 minutes

12 minutes

7.5 minutes

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

(B) and (D) only

(A) and (C) only

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

2 km

1.9 km

1.8 km

2.1 km

(AB+BA) is skew symmetric matrix.

(AB+BA) is always a diagonal matrix.

(AB+BA) is a symmetric matrix.

(AB-BA) is a symmetric matrix.

Rs. 31250

Rs. 37285

Rs. 27880

Rs. 30280

(A) and (D) only

(A) and (C) only

(B) and (D) only

(C) and (D) only

(A) and (D) only

(C) and (D) only

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

(A) and (C) only

2.5

1.5

2.36

0.512

0

31

36

40

1

4

6

2

$(-\infty, e)$

$(0, e)$

$(0, e) - \{1\}$

$(e, \infty)$

$\alpha = 2\beta$

$2\alpha = \beta$

$\alpha = \beta$

$\alpha = 3\beta$

$\log_e|y| + \frac{1}{x} + \frac{1}{y} - x = c$, where $c$ is constant of integration

$\log_e|y| - \frac{1}{x} + \frac{1}{y} + x = c$, where $c$ is constant of integration

$\log_e|x| - \frac{1}{x} + \frac{1}{y} + x = c$, where $c$ is constant of integration

$\log_e|x| + \frac{1}{x} + \frac{1}{y} + x = c$, where $c$ is constant of integration

Compound annual growth rate

Annual average growth rate

Nominal rate

Linear depreciation rate

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

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

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

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

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

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

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

(C) and (D) only