CUET Mathematics 2022 7 Aug Shift 2 PYQs

1

2

4

8

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

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

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

(B), (C), (E) only

4

7

6

5

$4(1 - \log 2)$

$4(1 + \log 2)$

$2(1 + \log 2)$

$2(1 + \log 4)$

$\frac{27}{4}$

27

8

18

$f(x)$ is discontinuous at $x = 0$.

$f(x)$ is not a function as $f(0)$ is not defined.

$f(x)$ is a continuous function on its domain.

$f(x)$ is a discontinuous function on its domain.

$\frac{16}{3}$ square units

$\frac{32}{3}$ square units

$\frac{20}{3}$ square units

$\frac{4}{3}$ square units

$\frac{1}{3}(e - 1)$

$\frac{2}{3}(e - 1)$

$\frac{3}{4}(e - 1)$

$\frac{3}{7}(e - 1)$

$-2$

2

0

1

0

2

3

4

25

36

49

30

$e^x + e^y = c$

$y = e^{x+y} + c$

$e^x + e^{-y} = c$

$e^x - e^{-y} = c$

0

$-\frac{1}{5}$

$\frac{1}{5}$

1

1

$\frac{8}{3}$

$\frac{56}{3}$

$\frac{68}{3}$

$x = 3, y = 3, z = 24$

$x = 2, y = 2, z = 16$

$x = 2, y = 2, z = 20$

$x = 0, y = 4, z = 12$

One-one

Onto

One-one and onto both

Neither one-one nor onto

R is reflexive relation

R is symmetry relation

R is transitive relation

R is equivalence relation

(B) and (D) only

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

(B) and (E) only

(A) and (D) only

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

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

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

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

5

4

9

1

$\frac{9}{4}(\pi - 2)$ sq. units

$\frac{9}{2}(\pi + 1)$ sq. units

$\frac{9}{4}(\pi + 2)$ sq. units

$\frac{9}{2}(\pi + 2)$ sq. units

$\frac{-2}{(1 + \tan x)^2} + C$, where C is constant of Integration

$\frac{-4}{(1 + \tan x)^4} + C$, where C is constant of Integration

$\frac{-1}{2(1 + \tan x)^2} + C$, where C is constant of Integration

$\log(1 + \tan x)^3 + C$, where C is constant of Integration

32

16

08

04

$\frac{8a^3}{3}$

$\frac{16a^2}{3}$

$\frac{32a^2}{3}$

$\frac{64a^2}{3}$

$a - b$

$\frac{a + b}{2}$

$2b$

$\frac{b - a}{2}$

$\frac{\sin x}{x}$

$\sin x$

$\cos x$

$\frac{\cos x}{x}$

(A), (B), (C), (D), (E) only

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

(B), (C), (E) only

(B), (E) only

$e$

$e - 1$

$e^2 - (e + 1)$

$\frac{e^2 - (e + 1)}{e}$

$U(x) U(y) = U(c)$

$\frac{U(x)}{U(y)} = U(c)$

$U(x) - U(y) = U(c)$

$U(x) + U(y) = U(c)$

(where c is arbitrary constant)

$\frac{d^2 y}{dx^2} + y^2 = 0$

$\frac{d^2 y}{dx^2} + 4 \frac{dy}{dx} + 5y = 0$

$\frac{d^2 y}{dx^2} - 4 \frac{dy}{dx} - 5y = 0$

$\frac{d^2 y}{dx^2} - y^2 = 0$

$\left(\frac{8}{11}, \frac{24}{11}, \frac{-14}{11}\right)$

$\left(\frac{1}{11}, \frac{2}{11}, \frac{-7}{11}\right)$

$\left(\frac{17}{11}, \frac{18}{11}, \frac{-5}{11}\right)$

$\left(\frac{7}{11}, \frac{10}{11}, \frac{-10}{11}\right)$

4

5

3

6

$\vec{r} = (0, 0, 0) + \lambda(1, 0, 0)$

$\vec{r} = (0, 1, 0) + \mu(0, 1, 0)$

$\vec{r} = (0, 1, 0) + \mu(1, 1, 1)$

$\vec{r} = (0, 0, 0) + \lambda(0, 1, 0)$

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

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

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

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

$0^\circ$

$30^\circ$

$45^\circ$

$60^\circ$

$\frac{4}{\sqrt{29}}\hat{i} + \frac{3}{\sqrt{29}}\hat{j} + \frac{2}{\sqrt{29}}\hat{k}$

$\frac{4}{\sqrt{29}}\hat{i} + \frac{3}{\sqrt{29}}\hat{j} - \frac{2}{\sqrt{29}}\hat{k}$

$\frac{-4}{\sqrt{29}}\hat{i} - \frac{3}{\sqrt{29}}\hat{j} + \frac{6}{\sqrt{29}}\hat{k}$

$\frac{4}{\sqrt{29}}\hat{i} - \frac{3}{\sqrt{29}}\hat{j} - \frac{2}{\sqrt{29}}\hat{k}$

$2x + y - 1 = 0$

$2x + y + z = 0$

$2x + y - z - 1 = 0$

$4x + y + 4z - 1 = 0$

70

80

85

90

$\frac{35}{68}$

$\frac{33}{68}$

$\frac{1}{68}$

$\frac{1}{35}$

$\frac{1}{100}$

$\frac{1}{50}$

$\frac{1}{2}$

$\frac{1}{200}$