The rate of change (in cm2/s ) of the total surface area of a hemisphere with respect to radius r at r=31.331 cm is :
Held on 16 May 2024 · Verified 13 Jul 2026.
66π
6.6π
3.3π
4.4π
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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
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