Match list I with list II, List - I, List - II, A. Slope of tangent to the curve y = x^3 - x at x = 2, I. -2, B. Slope of tangent to the curve y = 3x^3 - 4x at x = 0, II. 11, C. Slope of normal to the curve y = at = ()/3, III. 2, D. Slope of normal to the curve y = at = ()/6, IV. -4, Choose the correct answer from the option given below : Option 1: A-II, B-IV, C-I, D-III Option 2: A-II, B-III, C-I, D-IV Option 3: A-I, B-IV, C-II, D-III Option 4: A-I, B-III, C-II, D-IV

Answer: A-II, B-IV, C-I, D-III. Solution: A: y' = 3x^2 - 1, at x=2: 11 (II). B: y' = 9x^2 - 4, at x=0: -4 (IV). C: tangent slope = (/3) = 1/2, normal slope = -2 (I). D: tangent slope = -(/6) = -1/2, normal slope = 2 (III). Match: A-II, B-IV, C-I, D-III.

Calculus

Application of Derivatives

Medium

Match list I with list II

List - I List - II
A. Slope of tangent to the curve $y = x^3 - x$ at $x = 2$ I. $-2$
B. Slope of tangent to the curve $y = 3x^3 - 4x$ at $x = 0$ II. $11$
C. Slope of normal to the curve $y = \sin\theta$ at $\theta = \frac{\pi}{3}$ III. $2$
D. Slope of normal to the curve $y = \cos\theta$ at $\theta = \frac{\pi}{6}$ IV. $-4$

Choose the correct answer from the option given below :

List - I	List - II
A. Slope of tangent to the curve $y = x^3 - x$ at $x = 2$	I. $-2$
B. Slope of tangent to the curve $y = 3x^3 - 4x$ at $x = 0$	II. $11$
C. Slope of normal to the curve $y = \sin\theta$ at $\theta = \frac{\pi}{3}$	III. $2$
D. Slope of normal to the curve $y = \cos\theta$ at $\theta = \frac{\pi}{6}$	IV. $-4$

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

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

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

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

✅ Correct Option: 1

A: $y' = 3x^2 - 1$ , at $x=2$ : $11$ (II). B: $y' = 9x^2 - 4$ , at $x=0$ : $-4$ (IV). C: tangent slope $= \cos(\pi/3) = 1/2$ , normal slope $= -2$ (I). D: tangent slope $= -\sin(\pi/6) = -1/2$ , normal slope $= 2$ (III). Match: A-II, B-IV, C-I, D-III.

2022: 6 Aug Shift 2

The function $f(x) = 6(2x^4 - x^2)$ is strictly increasing in

2026: 18 May Shift 2

For the function $f(x)=2x^3-21x^2+36x-100$ ;

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Point of local maxima is	I. -208
B. Point of local minima is	II. -83
C. Local maximum value is	III. 6
D. Local minimum value is	IV. 1

Choose the correct answer from the options given below:

2025: 27 May Shift 1

A cylindrical drum of radius 7 cm and height 2 m is being kept in a vertical position filled with milk. If the milk is leaking at 14 cm³/sec from its lower base, then the rate of decrease in the level of milk is:

[Take $\pi = \frac{22}{7}$ ]

2023: 30 May Shift 3

The interval in which the function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is strictly decreasing is :

2025: 26 May Shift 2

The maximum value of the function $f(x) = x^2(60 - x)$ in [20, 80] is:

2026: 19 May Shift 1

The maximum area of a rectangle inscribed in a circle of radius $3\sqrt{2}$ cm, is:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)