CUET Mathematics Calculus > Application of Derivatives PYQs

(A), (B) and (C) only

(D) only

(B), (C) and (D) only

(B) and (C) only

$(0, \frac{1}{e})$

$(0, e)$

$(\frac{1}{e}, \infty)$

$(e, \infty)$

(A), (B) and (C) only

(A), (B) and (D) only

(B), (C) and (D) only

(C) and (D) only

$25\sqrt{3}$ cm²/sec

$50\sqrt{3}$ cm²/sec

$100\sqrt{3}$ cm²/sec

$15\sqrt{3}$ cm²/sec

(C) and (D) only

(A) and (B) only

(A) only

(B) only

2 cm/min decreasing

3 cm/min decreasing

2 cm/min increasing

3 cm/min increasing

6,10

7, 9

8, 8

5,11

Rs.50

Rs.100

Rs.150

Rs.200

$x = 0$

$x = 0, \frac{7}{6}$

$x = \frac{7}{6}$

$x = \frac{6}{7}$

(A) and (B) only

(B) and (C) only

(A) and (C) only

(C) and (D) only

decreasing on $\mathbb{R}$

increasing on $\mathbb{R}$

increasing on $(0, \infty)$

neither increasing nor decreasing on $(-\infty, 0)$

(A) and (B) only

(B) and (C) only

(C) and (D) only

(A), (B) and (D) only

42 cm²/s

168 cm²/s

84 cm²/s

252 cm²/s

(B), (C) and (D) only

(A), (B) and (C) only

(A) and (D) only

(A), (C) and (D) only

4

2

0

-1

(B) and (D) only

(B), (C) and (D) only

(A) and (D) only

(B) only

3r

$\frac{1}{3}r$

$\frac{1}{2}r$

2r

$(1, 2)$

$(2, 6)$

$(2, 3)$

$(3, \infty)$

$\alpha = \frac{-2}{3}, \beta = \frac{1}{6}$

$\alpha = \frac{-2}{3}, \beta = \frac{-1}{6}$

$\alpha = \frac{2}{3}, \beta = \frac{1}{6}$

$\alpha = \frac{2}{3}, \beta = \frac{-1}{6}$

1

5

6

3

increasing for all $x \in (-\infty, 0) \cup (0, \infty)$

decreasing for all $x \in (-\infty, 0) \cup (0, \infty)$

increasing for all $x \in (-\infty, \infty)$

neither increasing nor decreasing for $x \in (-\infty, \infty)$

$\frac{1}{e}$

$2e$

$e$

$\frac{2}{e}$

-4

2

4

-2

$\frac{1}{9\pi}$ cm/min

$\frac{1}{9}$ cm/min

$\frac{1}{18}$ cm/min

$\frac{1}{36}$ cm/min

(A), (B) and (D) only

(B), (C) and (D) only

(C) and (D) only

(A) and (D) only

$4x - y + 7 = 0$

$4x - y + 3 = 0$

$4x - y + 5 = 0$

$4x - y + 1 = 0$

10

21

16

5

decreasing in $(-\infty, -1]$

increasing in $(-\infty, -1]$

decreasing in $(-\infty, 2]$

increasing on $R$

2

$-\frac{6}{7}$

$\frac{2}{7}$

-2

(1, 13) only

(-1, 12) only

(1, 13) and (-1,11)

(-1, 13) only

2 cm²/cm

4 cm²/cm

6 cm²/cm

12 cm²/cm

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

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

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

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

$(0, 1)$

$(-1, 0)$

$(-1, 1)$

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

Rs.20

Rs.10

Rs.30

Rs.40

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

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

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

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

22

28

24

29

1 cm³/cm²

6 cm³/cm²

2 cm³/cm²

3 cm³/cm²

Increasing on $(\frac{-1}{2}, 1)$ and decreasing on $(0, \frac{1}{2})$

Increasing on $(\frac{1}{2}, \infty)$ and decreasing on $(-\infty, \frac{1}{2})$

Increasing on $(-\infty, \frac{1}{2})$ and decreasing on $(\frac{1}{2}, \infty)$

Increasing on $(-\infty, 1)$ and decreasing on $(1, \infty)$

(A) and (B) only

(A) and (C) only

(B) and (C) only

(A) and (D) only

$(-\infty, -3) \cup (3, \infty)$

$(-3, 0) \cup (0, 3)$

$(-\infty, \infty)$

$(0, \infty)$

$x = 4$

$x = 6$

$x = 5$

$x = 10$

$(-\infty, -4/3)$

$[0, \infty)$

$[-4/3, 0)$

$[-4/3, \infty)$

$x = 1$

$x = 2$

$x = 3$

$x = 5/2$

(B) and (D) only

(B), (C) and (D) only

(A) and (C) only

(A) and (B) only

$\frac{27}{8}(5x+7)^2$

$\frac{27}{16}(5x+7)^2$

$\frac{135\pi}{8}(5x+7)^2$

$\frac{135\pi}{16}(5x+7)^2$

(A), (D) and (C) only

(B), (C) and (D) only

(A) and (C) only

(B) and (D) only

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

$\left(-\infty, -\frac{1}{2}\right) \cup \left(\frac{4}{3}, \infty\right)$

$\left(-\infty, -\frac{1}{2}\right) \cap \left(\frac{4}{3}, \infty\right)$

$\left(-\infty, \frac{1}{2}\right) \cup \left(\frac{4}{3}, \infty\right)$

$\frac{2}{11}$ cm/sec

$\frac{1}{11}$ cm/sec

$\frac{3}{11}$ cm/sec

$\frac{4}{11}$ cm/sec decreases

is increasing on $\mathbb{R}$

is decreasing on $\mathbb{R}$

is decreasing on $(-\infty, 0)$

is neither increasing nor decreasing on $(0, \infty)$

16000

32000

64000

128000

525 cm²/s

225 cm²/s

255 cm²/s

252 cm²/s

120

60

0

-60

2.5 cm²/sec

2.66 cm²/sec

2.61 cm²/sec

2.59 cm²/sec

$(1, \infty)$

$(-\infty, 1)$

$(-\infty, \infty)$

$(-\infty, \infty) - \{0\}$

2856 cm³

3256 cm³

3656 cm³

3456 cm³

$(0, \infty)$

$(-4,4)$

$\left[\frac{-4}{3}, 0\right]$

$\left(-\infty, \frac{-4}{3}\right] \cup [0, \infty)$

$e$

$e^{1/e}$

$\left(\frac{1}{e}\right)^{1/e}$

$e^e$

26 m/min

13 m/min

52 m/min

6.5 m/min

$(-\infty, 8)$

$(-\infty, 4)$

$(4, \infty)$

$(8, \infty)$

(A) and (B) only

(B) and (C) only

(A) and (D) only

(A), (B) and (C) only

$6\pi$ $cm^2/cm$

$4\pi cm^2/cm$

$2\pi$ $cm^2/cm$

$3\pi$ $cm^2/cm$

1

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{8}$

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

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

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

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

$(-\infty,\infty)$

$(0, 1)$

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

$(1, \infty)$

$x = 0$ and $x = 3$

$x = -3$ and $x = -5$

$x = 0$ and $x = -5$

$x = -3$

64π $cm^3/cm^2$

32π $cm^3/cm^2$

$\frac{1}{2} cm^3/cm^2$

2 $cm^3/cm^2$

(A) and (D) only

(B) and (C) only

(A), (D) and (E) only

(B), (D) and (E) only

Rs.8

Rs.4

Rs.6

Rs.2

$4x - y - 1 = 0$

$4x - y - 4 = 0$

$x + 4y - 4 = 0$

$x + 4y - 1 = 0$

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

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

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

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

Strictly decreasing for $x < -\frac{3}{2}$

Strictly increasing for $x < \frac{3}{2}$

Strictly decreasing for $x > -\frac{3}{2}$

Strictly increasing for $x > \frac{3}{2}$

local maxima at $x = -1$

local minima at $x = -1$

local maxima at $x = 1$

neither local maxima nor local minima

$-2$

$-\frac{2}{e}$

$-e$

$-5e^3$

12

-15

27

-3

$0 < x < \frac{\pi}{3}$

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

$\frac{\pi}{4} < x < \frac{\pi}{2}$

$\frac{\pi}{2} > x > 0$

Rs. 750

Rs. 800

Rs. 640

Rs. 940

(A), (B) and (D) only

(B) and (D) only

(C) and (D) only

(A), (B) and (C) only

(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) - (III), (C) - (II), (D) - (I)

all positive real values of x

all negative real values of x

all non-positive real values of x

all real values of x

(B) and (C) only

(A) and (D) only

(A) and (C) only

(D) only

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

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

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

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

$(-\infty, -2) \cup (1, \infty)$

$(-\infty, 1)$

$(-\infty, -1) \cup (2, \infty)$

$(-2, 1)$

$(2, -4)$

$(2, 4)$

$(1, 2\sqrt{2})$

$(1, -2\sqrt{2})$

$(0, 3)$

$(2, 0)$

$(-2, 0)$