CUET Mathematics 2022 10 Aug Shift 1 PYQs

100

25

10

4

A and B only

B and C only

B and D only

A, C and D only

6

36

72

144

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{1}{4}$

$\frac{3}{4}$

$y = \sqrt{x^2 - 1} + \log|x + \sqrt{x^2 - 1}| + C$

$y = \sqrt{x^2 - 1} - \log|x + \sqrt{x^2 - 1}| + C$

$y = \sqrt{x^2 - 1} + \log|x + \sqrt{1 - x^2}| + C$

$y = \sqrt{1 - x^2} + \log|x + \sqrt{1 - x^2}| + C$

$(0, \pm 3)$

$(\pm 8, 0)$

$(0, \pm 8)$

$(\pm 3, 0)$

$\frac{1}{16}$

$\frac{10}{16}$

$\frac{4}{16}$

$\frac{15}{16}$

A & B only

B & C only

C & D only

A & D only

2

3

$\sqrt{5}$

$\sqrt{7}$

$\frac{\pi}{2} + \frac{1}{4}$

$\frac{\pi}{4} + \frac{1}{2}$

$\frac{3\pi}{4} + \frac{1}{6}$

$\frac{3\pi}{4} + \frac{1}{2}$

$e^{e-1}$

$e^{\frac{1}{e}}$

$e^{\frac{-1}{e}}$

$e^{\frac{-4}{e}}$

44

23

11

1

$\frac{31}{64}$

$\frac{15}{64}$

$\frac{103}{64}$

1

$\frac{\pi}{3\sqrt{3}}$

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

$\frac{\pi}{6\sqrt{3}}$

$\frac{\pi}{\sqrt{3}}$

2

3

5

13

$\frac{1}{x}$

$x$

$\frac{1}{x^2}$

$x^2$

B and C only

B, D and E only

A and D only

A and B only

4

6

2

0

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

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

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

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

$\pi ab$

$\frac{\pi ab}{2}$

$\frac{\pi ab}{4}$

$2\pi ab$

$\frac{e^x}{1+x^2} + C$

$\frac{-e^x}{1+x^2} + C$

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

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

$-\cos(\tan^{-1} x) + C$

$\cos(\tan^{-1} x) + C$

$\tan(\cos^{-1} x) + C$

$-\tan(\cos^{-1} x) + C$

1 unit

2 units

7 units

8 units

$2\sqrt{3}$

$12\sqrt{3}$

$8\sqrt{3}$

$6\sqrt{3}$

$-3, \frac{1}{7}, 2$

$-3, 2, 2$

$-3, \frac{2}{7}, 1$

$-21, 2, 14$

6

18

14

15

$\log(x^4 + 1) + C$

$\log\left(\frac{x^2 - 1}{x^2 + 1}\right) + C$

$\frac{1}{\sqrt{2}} \tan^{-1}\left(\frac{x^2 - 1}{\sqrt{2} \, x}\right) + C$

$\frac{1}{\sqrt{2}} \tan^{-1}\left(\frac{x^2 + 1}{\sqrt{2} \, x}\right) + C$

$4\pi$

$16\pi$

$32\pi$

$64\pi$

$\frac{3}{8}$

$\frac{4}{9}$

$\frac{5}{9}$

$\frac{5}{8}$

$\frac{{}^{20}C_2 \times {}^{10}C_2}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{10}C_2}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{11}C_3}{{}^{30}C_5}$

$\frac{{}^{19}C_2 \times {}^{11}C_2}{{}^{30}C_5}$

$\frac{54}{109}$

$\frac{51}{109}$

$\frac{64}{109}$

$\frac{54}{119}$

$\frac{1}{3}$

$\frac{4}{13}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{d^2y}{dx^2} + (m+n)\frac{dy}{dx} + y = 0$

$\frac{d^2y}{dx^2} + mn\frac{dy}{dx} + (m+n)y = 0$

$\frac{d^2y}{dx^2} - (m+n)\frac{dy}{dx} + mny = 0$

$\frac{d^2y}{dx^2} + (m+n)\frac{dy}{dx} - mny = 0$

$(-\infty, \infty)$

$(-2, \infty)$

$(-\infty, -2)$

$(-\infty, -2]$

$25\left(\frac{\pi}{4} - \frac{\sqrt{3}}{2}\right)$

$\frac{25}{12}(4\pi - 3\sqrt{3})$

$\frac{25}{12}(3\pi - 4\sqrt{3})$

$25\left(\frac{\sqrt{3}}{2} + \frac{\pi}{4}\right)$

$\pi$

$-1$

$\frac{\pi}{2}$

$\frac{3}{\sqrt{2}}$

A, C, D only

B, C, D only

C, D, E only

B, D, E only

14

$2\sqrt{7}$

28

25

512

64

32

8

$\frac{5\pi}{6}$

$\frac{-\pi}{3}$

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

$\frac{\pi}{3}$