List of top Mathematics Questions

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} \times \vec{b} = \vec{c}$, $\vec{a} \cdot \vec{c} = 2$ and $\vec{b} \cdot \vec{c} = 1$. If $|\vec{b}| = 1$, then the value of $|\vec{a}|$ is:
 

The area enclosed between the curve \( y = \sin x, y = \cos x \), \(\text{ for }\) \( 0 \leq x \leq \frac{\pi}{2} \) \(\text{ is:}\)

A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. What number of rows is not possible?
An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes:

The length of the projection of \( \mathbf{a} = 2\hat{i} + 3\hat{j} + \hat{k} \) \(\text{ on }\) \( \mathbf{b} = -2\hat{i} + \hat{j} + 2\hat{k} \) \(\text{ is equal to:}\)

There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals:
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
The general solution of the differential equation $(x^3-y^3)dx = (x^2y-xy^2)dy$ is
$\int_0^{\pi/2} \frac{1}{5\cos^2 x + 16\sin^2 x + 8\sin x \cos x} dx =$
$\int \frac{x\text{Tan}^{-1}x}{(1+x^2)^2}dx =$
$\int \frac{\log x}{(1+x)^2}dx = $
$\int(1+\tan^2 x)(1+2x\tan x)dx =$
$\int e^x(x^3-2x^2+3x-4)dx =$
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 = $
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
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
The approximate value of $\sqrt{6560}$ 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
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 $f(x) = \log_{(x-1)^2}(x^2-3x+2)$, $x \in \mathbb{R}-[1,2]$ and $x\neq0$, then $f'(3)=$
If $\{x\}=x-[x]$ where $[x]$ is the greatest integer $\le x$ and $\lim_{x\to 0^+} \frac{\text{Cos}^{-1}(1-\{x\}^2)\text{Sin}^{-1}(1-\{x\})}{\{x\}-\{x\}^3} = \theta$, then $\tan\theta=$
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 $f(0) =$
The values of x at which the real valued function $f(x)=7|2x+1|-19|3x-5|$ is not differentiable is
If $y=(1-x^2)\text{Tanh}^{-1}x$ then $\frac{d^2y}{dx^2}=$