List of top Mathematics Questions

Choose the figure which is different from the rest.

Which region in the Venn diagram represents students who play Volleyball or Football or both but Basketball?

Choose the number pair/group which is different from the others.
A) 70–80 B) 54–62 C) 28–32 D) 21–24 E) 14–16

The system of equations \[ x + y + z = 6, \] \[ x + 2y + 5z = 9, \] \[ x + 5y + \lambda z = \mu, \] has no solution if:

Let $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + p\hat{k}$ be two vectors. If $(\vec{a}, \vec{b}) = 60^\circ$, then $p =$

The general solution of the differential equation $(x^3-y^3)dx = (x^2y-xy^2)dy$ is

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2x$ and eccentricity is $\sqrt{3}$ is

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

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

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

$\int \frac{\log x}{(1+x)^2}dx = $

$\int \frac{x\text{Tan}^{-1}x}{(1+x^2)^2}dx =$

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

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

If a normal is drawn at a variable point P(x, y) on the curve $9x^2+16y^2-144=0$, then the maximum distance from the centre of the curve to the normal is

A real valued function
$f:[4, \infty) \to \mathbb{R}$ is defined as $f(x) = (x^2+x+1)^{(x^2-3x-4)}$, then f is

The approximate value of $\sqrt{6560}$ is

If a balloon flying at an altitude of 30 m from an observer at a particular instant is moving horizontally at the rate of 1 m/s away from him, then the rate at which the balloon is moving away directly from the observer at the 40th second is (in m/s)

If the normal drawn at the point P on the curve $y^2 = x^2-x+1$ makes equal intercepts on the coordinate axes, then the equation of the tangent drawn to the curve at P is

If $y=(1-x^2)\text{Tanh}^{-1}x$ then $\frac{d^2y}{dx^2}=$

The values of x at which the real valued function $f(x)=7|2x+1|-19|3x-5|$ is not differentiable is

If $y^3=x$ then the value of $\frac{dy}{dx}$ at $x=1$ is

For $a\neq0$ and $b\neq0$, if the real valued function $f(x) = \frac{\sqrt[4]{625+4x}-5}{\sqrt[4]{625+5bx}-5}$ is continuous at $x=0$, then $f(0) =$