CUET Mathematics 2023 23 May Shift 3 PYQs

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

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

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

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

2, 1

-2, -1

2, -1

do not exist

9 cm$^2$/s

$\frac{9}{4}$ cm$^2$/s

$\frac{4}{9}$ cm$^2$/s

$\frac{9}{2}$ cm$^2$/s

$\frac{1}{1024}$

$\frac{17}{1024}$

$\frac{1023}{1024}$

$\frac{23}{1024}$

$\frac{680}{(221)^2}$

$\frac{6080}{(221)^2}$

$\frac{680}{221}$

$\frac{6800}{(221)^2}$

$\frac{e^x}{x} + C$, where C is constant of integration

$\frac{e^x}{2x} + C$, where C is constant of integration

$e^x x + C$, where C is constant of integration

$x^2 e^x + C$, where C is constant of integration

0

1

2

any order

$x^x$

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

$x^{x-1}$

$x^{x+1}$

(60, 0)

(0, 100)

(10, 50)

(0, 20)

$\frac{x^2}{2} + \log|x| + C$, (where C is constant of integration)

$\frac{x^2}{2} + \log|x| + 2x + C$, (where C is constant of integration)

$\frac{3}{2}\left(\sqrt{x} + \frac{1}{\sqrt{x}}\right) + C$, (where C is constant of integration)

$\frac{2}{3} x^{\frac{3}{2}} + 2\sqrt{x} + C$, (where C is constant of integration)

$(x^2 - y^2)dy - 2xy\, dx = 0$

$(x^2 + y^2)dy + 2xy\, dx = 0$

$(x^2 - y^2)dx + 2xy\, dy = 0$

$(x^2 + y^2)dy - 2xy\, dx = 0$

$\begin{bmatrix} 3 & 2 \\ -1 & 4 \end{bmatrix}$

$\begin{bmatrix} 4 & -1 \\ 2 & 3 \end{bmatrix}$

$\begin{bmatrix} -4 & 1 \\ -2 & -3 \end{bmatrix}$

$\begin{bmatrix} 4 & 1 \\ -2 & 3 \end{bmatrix}$

A, B, C only

B only

A, C only

D, C only

3|A|

$3^2$|A|

$|A|^3$

$3^3$|A|

$\begin{bmatrix} -2 & 3 \\ 1 & -2 \end{bmatrix}$

$\begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}$

$\begin{bmatrix} -2 & -3 \\ -1 & 2 \end{bmatrix}$

$\begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$

$\sin^{-1}\left(\frac{19}{21}\right)$

$\cos^{-1}\left(\frac{19}{23}\right)$

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

$\sin^{-1}\left(\frac{19}{23}\right)$

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

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

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

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

$2^n$

$n^2$

n!

(2n)!

$-\frac{70}{11}$

$\frac{70}{11}$

$\frac{11}{70}$

$-\frac{11}{70}$

$(-\infty, 1)$

$(-1, \infty)$

$(-\infty, -1) \cup (0, 1)$

$(-1, 0) \cup (1, \infty)$

1

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

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

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

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

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

60$^\circ$

90$^\circ$

120$^\circ$

30$^\circ$

4

-4

$-\frac{1}{4}$

0

$\frac{\pi}{3}$

$-\frac{\pi}{6}$

$\frac{1}{\sqrt{3}}$

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

Reflexive and symmetric

Neither reflexive nor symmetric

Transitive

Reflexive but not symmetric

$\pm 2$

$\pm 3$

$\pm 4$

0

$\frac{4}{9}$

$\frac{1}{18}$

$\frac{1}{3}$

$\frac{1}{2}$

zero matrix

Identity matrix

Scalar matrix

Diagonal matrix

A and B only

B only

C only

A and D only

$-\infty$

0

$\frac{1}{2}$

1

3k|A|

$k^3$|A|

$k^2$|A|

k|A|

all natural numbers

all rational numbers

all integers

all real numbers

$\tan^{-1}\frac{x}{a}$

$\tan^{-1}(ax)$

$a \tan^{-1}\frac{x}{a}$

$\sin^{-1}\frac{x}{a}$

2

1

$\frac{1}{2}$

$\frac{1}{3}$

$\tan^{-1} x = y + \frac{y^3}{3} + C$

$\tan^{-1} y = x + \frac{x^3}{3} + C$

$\tan^{-1} x = \tan^{-1} y + C$

$\tan^{-1} x + \tan^{-1} y = C$

$\frac{105}{512}$

$\frac{53}{128}$

$\frac{53}{64}$

$\frac{193}{512}$

If $|A| \neq 0$, then there exists a unique solution

If $|A| = 0$ and (adj A)B $\neq$ 0 then there is no solution

If $|A| \neq 0$ and (adj A)B $\neq$ 0 then there is no solution

If $|A| = 0$ and (adj A)B = 0 then system has infinitely many solutions

$\begin{bmatrix} x^{-1} & 0 & 0 \\ 0 & y^{-1} & 0 \\ 0 & 0 & z^{-1} \end{bmatrix}$

$xyz \begin{bmatrix} x^{-1} & 0 & 0 \\ 0 & y^{-1} & 0 \\ 0 & 0 & z^{-1} \end{bmatrix}$

$\frac{1}{xyz} \begin{bmatrix} x^{-1} & 0 & 0 \\ 0 & y^{-1} & 0 \\ 0 & 0 & z^{-1} \end{bmatrix}$

$\frac{1}{xyz} \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

$\hat{i} + 0\hat{j} + \hat{k}$

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

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

$\frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}$

2

$\sqrt{2}$

$\frac{1}{\sqrt{2}}$

Not known

$x^{x \cos x}$

$x^{(x \sin x)}[\sin x + \sin \log x]$

$x^{(x \sin x)}[\sin (1 + \log x) + x \log x \cos x]$

$x^{(x \sin x)}[\sin \log x + x \log x \cos x]$

$\tan^{-1} x$

$x$

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

$\sqrt{1+x^2}$

0

(a + b + c)

(a - b)(b - c)(c - a)

$a^2 + b^2 + c^2$

$\frac{\pi}{6}$

$\frac{\pi}{12}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{x}{2}\sqrt{4x^2 + 9} + \frac{9}{2}\log|2x + \sqrt{4x^2 + 9}| + C$

$\frac{x}{2}\sqrt{4x^2 + 9} + \frac{3}{2}\log|2x + \sqrt{4x^2 + 9}| + C$

$2x\sqrt{4x^2 + 9} + \frac{9}{2}\log|2x + \sqrt{4x^2 + 9}| + C$

$x\sqrt{4x^2 + 9} + \frac{9}{4}\log|2x + \sqrt{4x^2 + 9}| + C$

{3, 2, 1, 0}

{0, -1, -2, -3}

{0, 1, 8, 27}

{0, -1, -8, -27}

$8\sqrt{3}$

$4\sqrt{3}$

$16\sqrt{3}$

$2\sqrt{3}$

Maximize Z = 800x + 1200y

Subject to constraints,

$3x + 4y \leq 60$

$x + 3y \leq 30$

$x, y \geq 0$

Maximize Z = 800x + 1200y

Subject to constraints,

$3x + 4y \geq 60$

$x + 3y \geq 30$

$x, y \geq 0$

Minimize Z = 800x + 1200y

Subject to constraints,

$3x + 4y \leq 60$

$x + 3y \geq 30$

$x, y \geq 0$

Minimize Z = 800x + 1200y

Subject to constraints,

$3x + 4y \geq 60$

$x + 3y \leq 30$

$x, y \geq 0$

(0, 10)

(20, 0)

(12, 6)

(0, 0)

$\frac{5}{6}$

$\frac{3}{4}$

1

$\frac{1}{2}$

$\begin{bmatrix} -2 & 5 \\ 1 & 10 \end{bmatrix}$

$\begin{bmatrix} 8 & 13 \\ -2 & 12 \end{bmatrix}$

$\begin{bmatrix} -8 & 13 \\ 3 & 12 \end{bmatrix}$

$\begin{bmatrix} 7 & 10 \\ -3 & 12 \end{bmatrix}$

A, B, E only

B, C, E only

C, B , D only

A, D, E only

5%

2.5%

3%

4.5%

+1.54

-1.54

-1.74

-1.10

$x = 30, y = 30$

$x = 20, y = 40$

$x = 15, y = 45$

$x = 55, y = 5$

Rs.2,000

Rs.1,200

Rs.600

Rs.200

0.0005

0.002

0.27

0.027

$A = R\left[\frac{(1+i)^n - 1}{i}\right]$

$A = R\left[\frac{(1-i)^n - 1}{i}\right]$

$A = R\left[\frac{(1+i)^n}{i} - 1\right]$

$A = R\left[i^{n-1} - 1\right]$

Rs.40/L

Rs.58/L

Rs.60/L

Rs.62/L

Rs.23,888.88

Rs.24,000

Rs.21,500

Rs.21666.66

$\frac{4}{5}$

$\frac{7}{8}$

$\frac{15}{16}$

$\frac{4}{7}$

81

27

64

512

2 hours

6 hours

7 hours

12 hours

a = b

a = 2b

b = 2a

b = 3a

(0, 24)

(0, 20)

(8, 12 )

(16, 0)

Rs.30 per kg

Rs.35 per kg

Rs.40 per kg

Rs.42 per kg

Rs.30,000

Rs.50,000

Rs.35,000

Rs.40,000

$\sqrt{6}$

$\sqrt{7}$

$2\sqrt{3}$

$2\sqrt{2}$

100 m

500 m

125 m

120 m

0.5

1.2

1.6

2.4

35 points

25 points

15 points

20 points

88.9

115.4

144.4

86.7