List of top Mathematics Questions

The slope of the curve \( y = -x^3 + 3x^2 + 8x - 20 \) is maximum at:

Assertion (A): $f(x) = \begin{cases} x \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}$ is continuous at $x = 0$.
Reason (R): When $x \to 0$, $\sin \frac{1}{x}$ is a finite value between -1 and 1.

Assertion (A): The set of values of $\sec^{-1} \left( \frac{\sqrt{3}}{2} \right)$ is a null set.
Reason (R): $\sec^{-1}x$ is defined for $x \in \mathbb{R} - (-1, 1)$.

The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

One of the values of $\sqrt{24-70i} + \sqrt{-24+70i}$ is

The set of all values of $\theta$ such that $\frac{1-i\cos\theta}{1+2i\sin\theta}$ is purely imaginary is

If $\cos\alpha+\cos\beta+\cos\gamma = 0 = \sin\alpha+\sin\beta+\sin\gamma$, then $\sin 2\alpha + \sin 2\beta + \sin 2\gamma =$

If $\alpha$ is a root of the equation $x^2-x+1=0$ then $(\alpha + \frac{1}{\alpha}) + (\alpha^2 + \frac{1}{\alpha^2}) + (\alpha^3 + \frac{1}{\alpha^3}) + \dots$ to 12 terms =

$\int e^x(x^3-2x^2+3x-4)dx =$

$\int_0^{\pi/2} \frac{1}{5\cos^2 x + 16\sin^2 x + 8\sin x \cos x} dx =$

$\int(1+\tan^2 x)(1+2x\tan x)dx =$

$\int_4^{18} \frac{1}{(x+2)\sqrt{x-3}}dx = $

If $[\cdot]$ denotes the greatest integer function, then $\int_1^2 [x^2] dx =$

Number of all possible ways of distributing eight identical apples among three persons is

$16 \sin 12^\circ \cos 18^\circ \sin 48^\circ =$

Number of solutions of the equation $\sin^2\theta + 2\cos^2\theta - \sqrt{3}\sin\theta\cos\theta = 2$ lying in the interval $(-\pi, \pi)$ is

If $3\sin\theta + 4\cos\theta = 3$ and $\theta \neq (2n+1)\frac{\pi}{2}$, then $\sin 2\theta =$