CUET Mathematics 2023 15 June Shift 2 PYQs

$-\frac{1}{2}$

$\frac{5}{2}$

$-\frac{5}{2}$

$\frac{1}{2}$

$\frac{1}{28}\begin{bmatrix} 2 & -5 \\ 6 & -1 \end{bmatrix}$

$\frac{1}{32}\begin{bmatrix} -1 & 6 \\ -5 & -2 \end{bmatrix}$

$\frac{1}{32}\begin{bmatrix} -1 & -6 \\ 5 & -2 \end{bmatrix}$

$\frac{-1}{28}\begin{bmatrix} -1 & -6 \\ -5 & -2 \end{bmatrix}$

0

1

$\frac{\sqrt{3}}{2}$

$\frac{1}{2}$

2

4

8

16

$\frac{x^2}{e^4}$

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

$\frac{e}{x^2}$

$2x + \log 2$

$b = 2a$

$b = -2b$

$a = 2b$

$b = -2a$

$\left(\frac{-3}{2}, \frac{3}{2}\right)$

$\left(-\infty, \frac{-3}{2}\right)$

$\left(\frac{-3}{2}, \infty\right)$

$\left(-\infty, \frac{3}{2}\right)$

1

2

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{1}{2}\log\left(\frac{5}{17}\right)$

$\frac{1}{2}\log\left(\frac{17}{5}\right)$

$2\log\left(\frac{5}{17}\right)$

$2\log\left(\frac{17}{5}\right)$

2

3

4

5

$y = 9 + \frac{6}{x}$

$y = 9 - \frac{6}{x}$

$y = -9 + \frac{6}{x}$

$y = -3 - \frac{6}{x}$

0

1

$\frac{1}{6}$

$\frac{1}{2}$

1

$\frac{1}{2}$

$\frac{3}{2}$

2

Max. value $= \frac{2}{3}$

Max. value $= 5$

Max. value $= 11$

No Max. value

A LPP is an optimization problem

In a LPP the constraints and objective function are linear

Max $z = xy + 2x + 3y$ can be a valid objective function for a LPP

The optimal solution of a LPP is at one of the corner points of basic feasible solution

R is an equivalence relation.

R is transitive but neither reflexive nor symmetric.

R is reflexive but neither symmetric nor transitive.

R is symmetric & transitive but not reflexive.

(A) and (D) only

(B) and (D) only

(B) and (C) only

(A) and (C) only

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

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

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

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

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

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

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

$\frac{3x + x^3}{1 + 3x^2}$

12

$-10$

6

$-5$

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

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

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

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

24

09

12

6

$\frac{-5}{3}$

1

$-1$

$\frac{2}{7}$

$(a^2 + b^2)c$

$(a^2\cos^2\theta + b^2\sin^2\theta)c$

$(a^2\cos^2\theta - b^2\sin^2\theta)c$

$(a^2 + b^2)c^2$

1, 2

3, 0

0

2, 1

0 and 1

1 and 2

1

2

$\frac{\cos^2(a+y)}{\sin a}$

$\frac{\sin^2(a+y)}{\sin a}$

$\frac{\cos^2(a+y)}{\cos a}$

$\frac{\sin^2(a+y)}{\cos a}$

$\frac{\pi}{5}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$0°$

$45°$

$60°$

$90°$

6 unit

3 unit

$6\pi$ unit

$2\pi$ unit

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

$\left(0, \frac{\pi}{4}\right) \cup \left(\frac{5\pi}{4}, 2\pi\right)$

$\left(\frac{3\pi}{4}, \frac{7\pi}{4}\right)$

$\left(0, \frac{3\pi}{4}\right) \cup \left(\frac{7\pi}{4}, 2\pi\right)$

$-\frac{9}{4}$

$\frac{19}{2}$

9

$-3$

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

$(x^4+1)^{\frac{1}{4}} + C$

$-(x^4+1)^{\frac{1}{4}} + C$

$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}} + C$

$\left(\pi - \frac{8}{3}\right)$ sq. units

$\left(\frac{8}{3} + \pi\right)$ sq. units

$\left(\frac{\pi}{2} - \frac{4}{3}\right)$ sq. units

$\left(\frac{\pi}{2} + \frac{4}{3}\right)$ sq. units

$\frac{13}{4}$ sq. units

$\frac{15}{4}$ sq. units

$\frac{17}{4}$ sq. units

$\frac{19}{4}$ sq. units

(D) Only

(C) and (D) Only

(B) and (D) Only

(A) Only

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

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

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

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

(B) and (C) Only

(C) and (D) Only

(D) Only

(B) and (D) Only

0

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$x + y + z = 3$

$x + y - z = 1$

$x + y + z = 1$

$x + y + z = 0$

3

$-2$

$-1$

5

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

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

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

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

(A) and (D) Only

(B) and (D) Only

(B) and (C) Only

(A), (B) and (D) Only

$\frac{1}{16}$

$\frac{1}{81}$

$\frac{1}{27}$

$\frac{1}{8}$

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{1}{5}$

$\frac{4}{5}$

$2(x + 7)$

$\frac{x + 7}{2}$

$x - 7$

$\frac{x - 7}{2}$

is continuous at $x = 3$

has removable discontinuity at $x = 3$

has irremovable discontinuity at $x = 3$

continuous at every real number

$\frac{1}{(n+2)(n+3)}$

$\frac{1}{(n+1)(n+2)}$

$\frac{1}{n(n+1)}$

$\frac{1}{(n-1)(n-2)}$

$\left(0, \frac{1}{2}\right)$

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

$\left(\frac{1}{2}, \frac{1}{3}\right)$

$(0, 1)$

$\frac{197}{\sqrt{179}}$

$\frac{197}{\sqrt{191}}$

$\frac{197}{\sqrt{189}}$

$\frac{197}{\sqrt{237}}$

7

5

9

11

12 litres

10 litres

15 litres

20 litres

0.5 km/hr

5 km/hr

8 km/hr

7.5 km/hr

10 minutes

7.5 minutes

15 minutes

12.5 minutes

₹ 1,000

₹ 1,500

₹ 500

₹ 2,500

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

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

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

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

$x = -2$, $y = 6$

$x = 12$, $y = 5$

$x = -4$, $y = 7$

$x = 10$, $y = -2$

125

625

75

375

5

6

0

$-2$

$\frac{-5}{x^2}$

$\frac{-20}{x^4}$

$\frac{x^3}{e^2}$

$\frac{-20x^3}{e^2}$

(2, 4)

(3, 2)

(1, 4)

(2, 3)

6

3

10

5

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

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

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

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

25 units

50 units

49 units

$\frac{49}{2}$ units

$\frac{1}{25}$

$\frac{1}{5}$

$\frac{1}{22}$

1

0.2

0.1

0.4

0.3

$15e^{-5}$

$\frac{118}{3}e^{-5}$

$\frac{15}{4}e^{-5}$

$\frac{13}{3}e^{-4}$

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

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

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

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

150

200

300

80

320

360

140

260

$y = 0.7 + 9.5x$

$y = 10.3 + 0.5x$

$y = 9.2 + 0.7x$

$y = 11.5 + 0.6x$

1.85

$-2.05$

$-2.15$

1.65

$\sqrt{\frac{3}{2}}$

$\sqrt{3}$

2.5

$\sqrt{2}$

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

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

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

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

4500

7500

9000

4250

₹ 20,50,000

₹ 19,50,000

₹ 22,00,000

₹ 18,50,000

6 years

12 years

10 years

8 years

225

180

270

250

0, 28

50, 0

20, 18

0, 30

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

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

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

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

{8, 16, 24, 32, 40, 48}

{11, 22, 33, 44}

{8, 19, 30, 41}

{8, 19, 27, 35, 43}