A: y′=3x2−1, at x=2: 11 (II). B: y′=9x2−4, at x=0: −4 (IV). C: tangent slope =cos(π/3)=1/2, normal slope =−2 (I). D: tangent slope =−sin(π/6)=−1/2, normal slope =2 (III). Match: A-II, B-IV, C-I, D-III.
Match list I with list II
| List - I | List - II |
|---|---|
| A. Slope of tangent to the curve y=x3−x at x=2 | I. −2 |
| B. Slope of tangent to the curve y=3x3−4x at x=0 | II. 11 |
| C. Slope of normal to the curve y=sinθ at θ=3π | III. 2 |
| D. Slope of normal to the curve y=cosθ at θ=6π | IV. −4 |
Choose the correct answer from the option given below :
Held on 23 Aug 2022 · Verified 13 Jul 2026.
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
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
The derivative of x³ + 2x² - 5x + 1 is:
For $y \neq 0$, the particular solution of the differential equation $2ye^{x/y}dx + (y - 2xe^{x/y})dy = 0$ at the point (1, 1) is
The value of ∫₀¹ x·eˣ dx is:
Match List-I with List-II | List-I | List-II | | --- | --- | | (A) $f(x) = x \sin x$ | (I) is not continuous at $x = -3$ | | (B) $f(x) = \frac{\vert x\vert }{x}, x \neq 0$ and $f(x) = 1 \text{ at } x = 0$ | (II) is continuous everywhere | | (C) $f(x) = x - [x]$, $[x]$ denotes greatest integer function | (III) is not differentiable at $x = 1$ | | (D) $f(x) = e^{\vert x - 1\vert }$ | (IV) is not continuous at $x = 0$ | Choose the correct answer from the options given below:
The area (in sq. units) of the region enclosed by the curve $9x^2 + 4y^2 = 36$ is
Work through every CUET UG Calculus PYQ, year by year.