CUET Mathematics 2022 4 Aug Shift 1 PYQs

$|A|$

$|A|^2$

$|A|^3$

$2|A|$

$\pm 4$

$\pm 2\sqrt{2}$

$\pm 7$

$\pm 3$

$\pm 1$

$\pm 2$

$\pm 4$

$\pm \frac{3}{2}$

$\frac{2\log_e x - 3}{x^3}$

$\frac{2\log_e x + 3}{x^3}$

$\frac{3 - 2\log_e x}{x^3}$

$\frac{3\log_e x - 3}{x^3}$

$[-2, 1]$

$(-\infty, 1]$

$(-\infty, -2) \cup (1, \infty)$

$(-\infty, -1] \cup [2, \infty)$

$\sqrt{x+1}$

$x + \sqrt{x+1}$

$-1 + x + \sqrt{x+1}$

$-1$

-1

0

1

2

$\frac{1}{2}\log\left(\frac{x^2+4}{x^2+3}\right) + C$

$\log\left(\frac{x^2+3}{x^2+4}\right) + C$

$\frac{1}{2}\log\left(\frac{x^2+3}{x^2+4}\right) + C$

$\log\left(\frac{x^2+4}{x^2+3}\right) + C$

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

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

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

$e^x \left(\frac{x^2-2}{x^3}\right) + C$

$\frac{3}{8}$ sq. unit

$\frac{5}{8}$ sq. unit

$\frac{7}{8}$ sq. unit

$\frac{9}{8}$ sq. unit

4

3

5

2

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

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

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

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

0.16

0.18

0.15

0.25

(0, 0)

(7, 0)

(3, 4)

(0, 2)

3

-3

7

-7

A and C only

B and D only

A and B only

B and C only

A and B only

A, B and D only

A, B, C and E only

B and D only

4

-2

2

-4

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

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

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

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

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

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

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

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

$\pi/4$

$\pi/3$

$\pi/6$

$\pi/2$

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

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

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

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

9

5

10

15

1

2

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{2}$

2

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

1

$-\frac{1}{2}$

-2

2

$\frac{1}{2}$

8

$\frac{16}{5}$

$\frac{14}{5}$

$-\frac{1}{8}$

$|y+1| = Ce^{\frac{x^2}{2} - x}$

$|y+1| = Ce^{x - \frac{x^2}{2}}$

$y = \frac{x^2}{2} - \frac{x^2 y^2}{2} - x + \frac{y^2}{2} + C$

$\frac{y^2}{2} + y = \frac{x^2}{2} - x + C$

$y = \frac{-\lambda^2}{x+y} + C$

$\frac{(x+y)^3}{3} = \lambda^2 x + C$

$\lambda \tan^{-1}\left(\frac{x+y}{\lambda}\right) = y + C$

$y = \frac{-2\lambda^2}{(x+y)^3} + C$

A and B only

B and D only

B and C only

A and D only

$\frac{x-2}{1} = \frac{y-2}{1} = \frac{z-1}{3}$

$\frac{x-1}{1} = \frac{y-1}{-1} = \frac{z-3}{2}$

$\frac{x}{-1} = \frac{y-1}{1} = \frac{z-2}{-2}$

$\frac{x-5}{5} = \frac{y-2}{1} = \frac{z}{-2}$

$\sqrt{26}$

$\sqrt{89}$

0

$\sqrt{27}$

$a = -\frac{13}{5}, c = \frac{26}{5}$

$a = 5, c = 10$

$a = 1, c = -2$

$a = 1, c = 10$

$\vec{r} = (\hat{i} + \hat{j} + \hat{k}) + \lambda(2\hat{i} - \hat{j} + \hat{k})$

$\vec{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})$

$\vec{r} = (-2\hat{i} + 3\hat{j} + 4\hat{k}) + \lambda(2\hat{i} - \hat{j} + \hat{k})$

$\vec{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(-2\hat{i} + 3\hat{j} + 4\hat{k})$

0

1

$\frac{3}{4}$

$\frac{3}{5}$

$-[\vec{a}, \vec{b}, \vec{c}]$

0

$2[\vec{a}, \vec{b}, \vec{c}]$

$[\vec{a}, \vec{b}, \vec{c}]$

72

112

100

110

$\frac{4}{5}$

$\frac{1}{15}$

$\frac{8}{15}$

$\frac{2}{3}$

$\frac{13}{50}$

$\frac{156}{625}$

$\frac{312}{625}$

$\frac{13}{25}$