List of top Mathematics Questions

The function $f\left(x\right) = \sec \left[\log\left(x+\sqrt{1+x^{2}}\right)\right]$ is

The value of $\frac{\log_{3} 5 \times \log_{25} 27 \times \log_{49} 7}{\log_{81} 3}$ is

If $f(5)=7$ and $f^{'}(5)=7$ then $\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}$ is given by

The general solution of the different equation $100\frac{d^{2}y}{dx^{2}}-20 \frac{dy}{dx}+y = 0 $ is

The degree of the differential equation $x = 1+\left(\frac{dy}{dx}\right)+\frac{1}{2!}\left(\frac{dy}{dx}\right)^{2}+\frac{1}{3!}\left(\frac{dy}{dx}\right)^{3} + .........$

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