CUET Mathematics 2022 25 May Shift 1 PYQs

$x = 2k$

$x = k^2$

$x = k^3$

$x = 3k$

$15\pi$

$54\pi$

$18\pi$

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

not an LPP

an LPP, with unbounded feasible region and no solution

an LPP, and Max $Z = 18$, at $x = 3, y = 4$

an LPP, and Max $Z = 12$, at $x = 0, y = 4$

$x^2 - y^2 = C$

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

$xy = C$

$x^2 + y^2 = C$

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

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

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

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

$\frac{7}{10}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{7}{11}$

$\frac{1}{4}$

$\frac{1}{2}$

$1$

$0$

$x = 0, y = 20$, Max $Z = 60$

$x = 10, y = 15$, Max $Z = 65$

$x = 10, y = 20$, Max $Z = 70$

$x = 15, y = 10$, Max $Z = 60$

1

3

2

4

$\frac{2}{9}$

$\frac{3}{2}$

$\frac{2}{27}$

$\frac{3}{8}$

AB, BA both are defined and are equal

AB is defined but BA is not defined

AB is not defined but BA is defined

AB, BA are defined but are not equal

Diagonal matrix

Symmetric matrix

Skew-symmetric matrix

Scalar matrix

decreasing

constant

increasing

neither decreasing nor increasing

$10^{-1}$

$\left(\frac{1}{2}\right)^5$

$\left(\frac{9}{10}\right)^5$

$\left(\frac{9}{10}\right)$

1 and 3

1 and 2

2 and 3

3 and 0

reflexive only

reflexive and transitive

symmetric and transitive

neither symmetric nor transitive

$x = 10$

$x = 30$

$x = 0$

$x = -10$

$\cos^{-1}\left(\frac{8}{21}\right)$

$\sin^{-1}\left(\frac{8}{21}\right)$

$\cos^{-1}\left(\frac{21}{82}\right)$

$\sin^{-1}\left(\frac{21}{82}\right)$

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

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

$\tan^{-1} y = x^2 + \frac{x^3}{3} + c$

$\tan^{-1} y = x^2 - \frac{x^3}{3} + c$

$\begin{bmatrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \end{bmatrix}$

$\begin{bmatrix} \cos^2\theta & \sin^2\theta \\ -\sin^2\theta & \cos^2\theta \end{bmatrix}$

$\begin{bmatrix} \cos\theta^2 & \sin\theta^2 \\ -\sin\theta^2 & \cos\theta^2 \end{bmatrix}$

$\begin{bmatrix} \cos\theta+\sin\theta & \cos\theta-\sin\theta \\ \sin\theta-\cos\theta & \cos\theta+\sin\theta \end{bmatrix}$

$e^x + e^{-y} = 2$

$e^{-x} + e^y = 2$

$e^x + e^y = 2$

$e^{-x} + e^{-y} = 2$

$x + y \geq 50$

$2x + y \leq 80$

$x, y \geq 0$

$x + y \leq 50$

$2x + y \geq 80$

$x, y \geq 0$

$x + y \leq 50$

$2x + y \leq 80$

$x, y \geq 0$

$x + y \geq 50$

$2x + y \geq 80$

$x, y \geq 0$

$\frac{2e^{2x} \sin(\tan^{-1} e^{2x})}{1 + e^{4x}}$

$\frac{2e^{2x} \cos(\tan^{-1} e^{2x})}{1 + e^{4x}}$

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

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

$1.04 a^3$ m$^3$

$1.004 a^3$ m$^3$

$1.12 a^3$ m$^3$

$1.12 a^2$ m$^3$

Bounded in first quadrant but has no solution

Unbounded in first quadrant but has a solution

Unbounded in first quadrant and has no solution

Bounded and has a solution $x = 0, y = 0, Z = 0$

$\frac{5}{18}$

$\frac{7}{18}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{4a^2}{3}$ sq. units

$\frac{8a^2}{3}$ sq. units

$\frac{2a^2}{3}$ sq. units

$\frac{9a^2}{5}$ sq. units

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

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

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

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

$x = 2, y = 1, z = 0$

$x = 2, y = 2, z = 0$

$x = -2, y = -1, z = 0$

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

A, E only

A, C, D only

C, D, E only

E only

$2\sin x + 2x$

$\sin^2 x + x^2$

$\sin(\sin x + x) + \sin x + x$

$\sin^2 x + 2\sin x + x$

$|B|^2$

$|B|$

$\sin^2\theta |B|$

$\cos^2\theta |B|$

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

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

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

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

$D = 0$

$D = \pm 1$

$D^2 = 0$ or $1$

$D = (a_1 + a_2 + a_3) - (b_1 + b_2 + b_3)$

4 sq. units

6 sq. units

8 sq. units

$\frac{3}{2}$ sq. units

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

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

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

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

$0$

$\frac{\pi}{2}$

$1$

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

$\sqrt{\frac{1-x^2}{1-y^2}}$

$\sqrt{\frac{1-y^2}{1-x^2}}$

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

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

$|A|$

$|A|^2$

$|A|^3$

$3|A|$

0

12

16

32

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

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

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

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

Exactly one point

Exactly two points

Exactly three points

No point

$\frac{1}{24}$

$\frac{1}{4}$

$\frac{23}{24}$

$\frac{3}{4}$

A row matrix has only one row.

A diagonal matrix has all diagonal elements equal to zero.

A symmetric matrix is a square matrix satisfying certain conditions.

A skew-symmetric matrix has all diagonal elements equal to zero.

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$\left[\frac{1}{4}, \frac{1}{2}\right]$

$\left[\frac{1}{2}, 1\right]$

$\left[\frac{1}{4}, \frac{3}{4}\right]$

$\left[\frac{1}{2}, \frac{3}{4}\right]$

$4x - 2y = 7$

$2x - y = 7$

$2x - y = 5$

$4x - 2y = 5$

$y = 2x^3 + c x^{\frac{1}{2}}$

$y = x^3 + c x^{\frac{1}{2}}$

$y = 2x^3 + c x^{-\frac{1}{2}}$

$y = x^3 + c x^{-\frac{1}{2}}$

$-1$

$1$

$-2$

$2$

$\frac{5}{8}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

$25\left(\frac{1}{2}\right)^{24}$

$\left(\frac{1}{2}\right)^{24}$

$24\left(\frac{1}{2}\right)^{24}$

$24\left(\frac{1}{2}\right)^{23}$

$x = 6, y = 8$

$x = 8, y = 4$

$x = 6, y = 6$

$x = 5, y = 10$

$\left(\frac{13}{24}, \frac{17}{24}\right)$

$\left(\frac{24}{25}, \frac{32}{25}\right)$

$\left(\frac{5}{24}, \frac{7}{24}\right)$

$\left(1, \frac{5}{4}\right)$

$14 + 162x$

$126 + 15x$

$128 + 14x$

$162 + 14x$

$0.5e^{-5}$

$5e^{-5}$

$e^{-5}$

$25e^{-5}$

50

30

25

60

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

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

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

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

Rs 24,000

Rs 20,000

Rs 16,000

Rs 28,000

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

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

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

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

15

34

25

16

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

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

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

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

$\begin{bmatrix} 5 & 4 \\ -2 & 4 \end{bmatrix}$

$\begin{bmatrix} 25 & 4 \\ -2 & 4 \end{bmatrix}$

$\begin{bmatrix} 21 & 4 \\ -2 & 4 \end{bmatrix}$

$\begin{bmatrix} 31 & 4 \\ -2 & 4 \end{bmatrix}$

5 cm

6 cm

7 cm

8 cm

$\frac{1}{30}$

$\frac{1}{20}$

$\frac{1}{40}$

$\frac{1}{10}$

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

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

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

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

$x = 12, y = 13$

$x = 15, y = 10$

$x = 17, y = 8$

$x = 18, y = 7$

Rs 11,990

Rs 12,300

Rs 11,890

Rs 12,000

2 litres

1 litre

3 litres

0.5 litres

$\left(-\frac{3}{4}, -\frac{1}{4}\right)$

$(-1, 3)$

$(3, -1)$

$(-4, -3)$

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

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

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

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

60 units

120 units

20 units

40 units

160

200

150

170