CUET Mathematics 2022 30 Aug Shift 1 PYQs

$m = 3, n = 2$

$m = n$, $k$ is arbitrary

$m = k$, $n$ is arbitrary

$m = k = 2, n = 3$

$\begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} x & y \end{bmatrix} = \begin{bmatrix} 5 & -8 \end{bmatrix}$

$\begin{bmatrix} 3 & 6 \\ 4 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$

$\begin{bmatrix} x \\ y \end{bmatrix} \begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$

$\begin{bmatrix} x & y \end{bmatrix} \begin{bmatrix} 3 & 6 \\ 4 & 7 \end{bmatrix} = \begin{bmatrix} 5 & -8 \end{bmatrix}$

3

24

6

16

minimum value is $e^{\frac{1}{e}}$

maximum value is $e^{\frac{1}{e}}$

minimum value is $e^e$

maximum value is $\left(\frac{1}{e}\right)^e$

(a), (b) only

(a), (b), (c) only

(a), (b), (c), (d) only

(a), (c), (e) only

(a) - (i), (b) - (iii), (c) - (ii), (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)

$\frac{8}{3}a^2$

$\frac{4}{3}a^2$

$\frac{1}{3}a^2$

$\frac{1}{12}a^2$

$\frac{e^x}{x+1} + c$

$\frac{e^x}{x-1} + c$

$\frac{x}{x+1} + c$

$\frac{x}{x-1} + c$

$\frac{1+y+y^2}{1+x^2} = C$

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

$\frac{x+1}{y+1} = C$

$\log(1+y) - \frac{\sqrt{3}}{2}\log(x+1) = C$

1, 2 respectively

1, 1 respectively

1, 0 respectively

2, 1 respectively

$\frac{2x}{3}$

$\frac{x}{3}$

$\frac{x}{2}$

$\frac{3x}{2}$

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

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

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

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

intersection of the inequalities with the x-axis only

intersection of the inequalities with the axes only

corner points of the feasible region

intersection of the inequalities with the y-axis only

(a) and (d) only

(a), (b) and (c) only

(b) and (c) only

(a), (b) and (e) only

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

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

$x - 1 = 2y - 4 = z - 1$

$\frac{x-1}{2} = 2y - 4 = z - 1$

$\frac{2}{5}$

$\frac{1}{5}$

$\frac{3}{5}$

$\frac{2}{5}$

$-\frac{1}{2}$

$-1$

$0$

$1$

$\frac{x}{1+x}$

$\frac{1}{x}$

$\frac{1-x}{x}$

$\frac{1+x}{x}$

(a) and (b) only

(a) and (c) only

(a) only

(c) only

$2(\pi - 2)$

$\pi - 2$

$2\pi - 1$

$2\pi + 2$

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

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

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

$\frac{\pi}{6}, \frac{2\pi}{3}$

3

4

6

0

(e) only

(b) and (c) only

(a) and (d) only

(b) and (d) only

'f' is a function from $A \to B$

'f' is one-one function from $A \to B$

'f' is onto function from $A \to B$

'f' is not a function from $A \to B$

$\frac{7}{10}$

$\frac{3}{10}$

$\frac{7}{3}$

$\frac{10}{7}$

$\frac{120}{169}$

$\frac{-120}{169}$

$\frac{-60}{169}$

$\frac{60}{169}$

$ry$

$-ry$

$r^2 y$

$-r^2 y$

$\sec x$

$\cos x$

$\sec x + \tan x$

$\tan x$

order = 2, degree = 2

order = 2, degree = 4

order = 2, degree = 8

order = 1, degree = 1

$\frac{x}{2}\left(\sqrt{1 - 49x^2}\right) + \frac{1}{98}\sin^{-1}7x + C$

$\frac{7x}{2}\sqrt{1 + 49x^2} + \frac{1}{49}\sin^{-1}x + C$

$\frac{x}{2}\sqrt{1 + \frac{1}{7x^2}} - \frac{1}{49}\sin^{-1}7x + C$

$\frac{x}{2}\sqrt{1 - 49x^2} + \frac{1}{14}\sin^{-1}7x + C$

$1, 2, 3$

$\sqrt{5}, \sqrt{13}, \sqrt{10}$

$\sqrt{10}, \sqrt{13}, \sqrt{5}$

$\sqrt{13}, \sqrt{10}, \sqrt{5}$

$\sqrt{6}$ unit

$7$ unit

$\frac{5}{\sqrt{6}}$ unit

$\frac{4}{\sqrt{6}}$ unit

(a), (b) and (d) only

(a), (b) and (e) only

(b), (d) and (e) only

(a) and (b) only

$4\sqrt{11}$ sq. unit

$\sqrt{44}$ sq. unit

$\sqrt{11}$ sq. unit

$3\sqrt{11}$ sq. unit

$3$

$-\frac{3}{2}$

$\frac{3}{2}$

$-3$

$p = q$

$p = 2q$

$q = 3p$

$q = 2p$

$\frac{2}{5}(x+2)^{\frac{5}{2}} - \frac{4}{3}(x+2)^{\frac{3}{2}} + C$

$\frac{2}{5}(x+2)^{\frac{5}{2}} + \frac{4}{3}(x+2)^{\frac{3}{2}} + C$

$\frac{1}{5}(x+2)^{\frac{5}{2}} - \frac{2}{3}(x+2)^{\frac{3}{2}} + C$

$\frac{2}{5}(x+2)^{\frac{5}{2}} + \frac{4}{3}(x+2)^{\frac{3}{2}} + C$

$\frac{6}{10}$

$\frac{4}{10}$

$\frac{5}{10}$

$\frac{2}{5}$