List of top Mathematics Questions

$\int\sqrt{1+\cos\,x}\,dx$ is equal to

For what values of m can the expression $2x^2 + mxy + 3y^2 - 5y - 2$ be expressed as the product of two linear factors

The value of $\frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+........$ is

If $y =tan ^{-1} \sqrt {x^2-1}$ then the ratio $\frac {d^2y}{dx^2}: \frac {dy}{dx}$=_________

$ \displaystyle\lim _{n \rightarrow \infty} n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}$ is

Which of the following is NOT true?

The sides of a triangle are $6+\sqrt {12} , \sqrt {48} $ and $\sqrt {24}$. The tangent of the smallest angle of the triangle is

The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^2=-8y$ is _______

If $z$ satisfies the equation $|z|-z=1+2 i$, then $z$ is equal to

If $z=\frac{1-i \sqrt{3}}{1+i \sqrt{3}}$, then $\arg (z)$ is

The points $(1, 0), (0, 1), (0, 0) $ and $ (2k, 3k),k \neq 0$ are concyclic if $k$ = _____

The area bounded by the curve $ y= \begin{cases} x^2,x<0 & \quad\\ x,x \geq 0 & \quad \\ \end{cases} $ and the line $y = 4$ is

The eccentric angle of the point $(2,\sqrt{3})$ lying on $\frac {x^2}{16}+\frac{y^2}{4}-1$ is _________

If $x\neq n \pi ,\, x \neq\,(2n+1)\frac {\pi}{2}.n\in Z, $ then $\frac {Sin^{-1}(Cos x) + Cos^{-1}(Sin x)}{Tan ^{-1}(Cot x)+ Cot^{-1}(Tan x)} $ =

In $\Delta ABC$, if $a =2, B = \tan ^{-1} \frac {1}{2}$ and $C = \tan ^{-1}\frac{1}{3}$, then $(A,b)$ =

The condition for the line $y = mx +c$ to be a normal to the parabola $y = 4ax$ is _______

The set of real values of x for which $ f(x) = \frac {x}{log\, x}$ increasing, is

If $y'' - 3y' + 2y = 0$ where $y(0) = 1$, $y'(0) = 0$, then the value of $y$ at $x \,= log_e \,2$ is

$ \int e^{xloga }e^{x} dx $ is equal to

The complex number $ z = \begin{vmatrix}2&3+i&-3\\ 3-i&0&-1+i\\ -3&-1-i&4\end{vmatrix} $ is equal to

Let $ f : R $ - { $ \frac {5}{4} $ } $ \rightarrow R $ be a function defined as $ f(x) = \frac{5x}{4x+5} $ . The inverse of $ f $ is the map $ g : Range\,f\,\rightarrow R $ - { $ \frac {5}{4} $ } given by

Let $ * $ be a binary operation on the set $ Q $ of rational numbers defined by $ a*b $ = $ \frac{ab}{4} $ . The identity with respect to this operation is

For the equations $ x + 2y + 3z = 1 $ , $ 2x + y + 3z = 2 $ , $ 5x + 5y + 9z = 4 $

The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system A $\begin {bmatrix} x \\ y \\ z \end {bmatrix}-\begin {bmatrix} 1 \\ 0 \\ 0 \end {bmatrix}$ has exactly two distinct solutions, is