CUET Mathematics 2022 23 Aug Shift 1 PYQs

64

81

12

24

Skew symmetric matrix

Null matrix

Symmetric matrix

Unit matrix

$2 \times 3$

$3 \times 3$

$2 \times 2$

$3 \times 2$

$[-2, 2]$

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

$(-2, 0) \cup (0, 2)$

$(-2, 2)$

$-\frac{1}{t^2}$

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

$1$

$-\frac{1}{2at^3}$

$(0, 1)$

$(0, 3)$

$\left(-\frac{1}{3}, 0\right)$

$\left(\frac{1}{3}, 0\right)$

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

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

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

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

$\frac{9}{8}$

$\frac{9}{4}$

$\frac{9}{2}$

$\frac{9}{7}$

$x + 1$

$1 - x$

$e^x + 1$

$e^x - 1$

$\frac{3}{4}$

$\frac{1}{4}$

$-\frac{1}{4}$

$\frac{9}{4}$

$2 \log |C(x-1)(x-3)|$

$\log_e |C(x-1)(x-3)|$

$\frac{1}{2}\log_e |C(x-1)(x-3)|$

$\frac{1}{2}\log_e |C(x+2)(x-3)|$

$(1 + y^2)|1 - x^2| = C$

$(1 + y^3)|1 - x^2| = C$

$(1 + y^4)|1 - x^2| = C$

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

$\frac{1}{2}$

$\frac{1}{2^{10}}$

$\frac{5}{2^9}$

$\frac{1}{2^9}$

$(0, 6)$

$(4, 4)$

$(6, 0)$

$(0, 4)$

$\frac{63}{256}$

$\frac{63}{512}$

$\frac{193}{512}$

$\frac{193}{256}$

Reflexive

Symmetric

Transitive

Equivalence

6

7

8

9

$I - A$

$A - I$

$A + I$

$A$

$\begin{bmatrix} -24 & 144 \\ 24 & -25 \end{bmatrix}$

$\begin{bmatrix} -8 & -8 \\ -2 & -9 \end{bmatrix}$

$\begin{bmatrix} 112 & -168 \\ -42 & 91 \end{bmatrix}$

$\begin{bmatrix} -8 & -168 \\ -42 & -9 \end{bmatrix}$

B, C, E only

A, B, D only

C, D, E only

A, D, E only

$-1$

$1$

$0$

$\pi$

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

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

$e^x + C$

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

$\tan x + \cot x + C$

$\tan x - \cot x + C$

$\tan x \cot x + C$

$\tan x - \cot 2x + C$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \frac{1}{2}\log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \frac{1}{4}\log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \frac{3}{4}\log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

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

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

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

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

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

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

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

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

$-\pi \leq x \leq 0$

$0 \leq x \leq \pi$

$-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$

$-\frac{\pi}{4} \leq x \leq \frac{3\pi}{4}$

$x$

$\frac{1}{x}$

$e^{-x}$

$e^x$

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

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

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

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

A, B, C, D only

B, C, D only

A, B, C, E only

C, D, E only

$(\alpha, -\beta, -\gamma)$

$(-\alpha, \beta, \gamma)$

$(0, \beta, \gamma)$

$(\alpha, -\beta, \gamma)$

$45°$

$90°$

$60°$

$0°$

$[-6, 2]$

$[0, 2]$

$[0, 6]$

$[-3, 1]$

$\theta = \cos^{-1}\left(\frac{\sqrt{19}}{21}\right)$

$\theta = \cos^{-1}\left(\frac{\sqrt{19}}{\sqrt{21}}\right)$

$\theta = \cos^{-1}\left(\frac{19}{21}\right)$

$\theta = \cos^{-1}\left(\frac{9}{21}\right)$

$-2\hat{i} - 3\hat{j} + 2\hat{k}$

$\hat{i} + \hat{j} + \hat{k}$

$2\hat{i} - \hat{j} - \hat{k}$

$\hat{i} - 2\hat{j} + 2\hat{k}$

$\frac{15}{\sqrt{2}}$

$15\sqrt{2}$

$15\sqrt{3}$

$\frac{15}{\sqrt{3}}$

$2$

$3$

$4$

$5$

BCGB and optimal solution occurs at $(12, 0)$

ABCDEA and optimal solution occurs at $(4, 4)$

ABCDEA and optimal solution occurs at $(0, 6)$

FDCF and optimal solution occurs at $(0, 12)$

E and G are independent events

E and F are independent events

F and G are independent events

E and F are dependent events

$1$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{9}$