(a) x=t2, y=t3: dxdy=23t, dx2d2y=4t3. At t=1: 43 -- (iii).
(b) f′(x)=2x1, f′′(x)=−4x3/21. f′′(1)=−41 -- (iv).
(c) Min of 9x2+12x+2 at x=−32: value =4−8+2=−2 -- (i).
(d) Point of inflexion of (x−2)4(x+1)3 is x=−1 -- (ii).
Match List-I with List-II
| List-I | List-II |
|---|---|
| (a) If x=t2 and y=t3, then dx2d2y at t=1 | (i) −2 |
| (b) If f(x)=x+1, then f′′(1) | (ii) −1 |
| (c) The minimum value of f(x)=9x2+12x+2 is | (iii) 43 |
| (d) The point of inflexion of the function f(x)=(x−2)4(x+1)3 is | (iv) −41 |
Choose the correct answer from the options given below
Held on 30 Aug 2022 · Verified 13 Jul 2026.
(a) - (i), (b) - (iii), (c) - (ii), (d) - (iv)
(a) - (ii), (b) - (iii), (c) - (i), (d) - (iv)
(a) - (iii), (b) - (iv), (c) - (i), (d) - (ii)
(a) - (iv), (b) - (i), (c) - (iii), (d) - (ii)
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.