List of top Mathematics Questions

If $y= \sin^{-1} (3^{-x})$, then $\frac{dy}{dx} = $
If $ f(x) = x^m$, where $m$ is a positive integer then the value of $m$ for which $f'(\alpha + \beta) = f'(\alpha ) + f'(\beta)$ for all $ \alpha , \beta > 0$ is
The points of discontinuities of $f(x) = \left(\frac{\pi x}{x+1} \right)$ other than $x = -1$ are
$f(x) = \begin{cases} x , \text{if } x \text{ is rational}\\ 0, \text{if } x \text{ is rational} \end{cases}$ then $f$ is
If sin $\theta$ , cos $\theta$ , tan $\theta$ are in G.P. then $cos^{9} \theta + cos^{6}\theta + 3cos^{5}\theta- 1$ is equal to
A plane passes through $ (1 ,-2 ,1 )$ and is perpendicular to two planes $2x - 2y + z = 0$ and $x - y + 2z = 4, $ then the distance of the plane from the point $ (1, 2, 2)$ is
For x > 0, $ lim_{ x \to 0} \Bigg [ (sin \, x)^{1/x} + \bigg( \frac{1}{x}\bigg)^{sin \, x} \Bigg ] $ is
Let, $\overrightarrow{a}=\widehat{i}+2\widehat{j}+\widehat{k}, \overrightarrow{c}=\widehat{i}+\widehat{j}+\widehat{k}.$ A vector coplanar to $\overrightarrow{a}$ and $\overrightarrow{c}$ of magnitude $\frac{1}{\sqrt{3}},$ then the vector is
If a, b,c are the sides of a triangle ABC such that $x^2 - 2(a+b+c)x+3\lambda(ab+bc+ca)=0$ has real roots, then
If $r, s, t$ are prime numbers and p , q are the positive integers such th a t LCM of p , q is $r^2 s^4 t^2$ then the number of ordered pairs (p, q) is
If $e_1$ is the eccentricity of the ellipse $\frac {x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e_1e_2=1$ then equation of the hyperbola is
If $a, b$ and $c \in N$ which one of the following is not true ?
If $2A+3B =\begin{bmatrix} {2}&{-1} &{4}\\ {3}&{2}& {5} \\ \end{bmatrix} $ and $A+2B \begin{bmatrix} {5}&{0} &{3}\\ {1}&{6}& {2} \\ \end{bmatrix} $then $B =$
The tangents from a point $(2 \sqrt{2}, 1)$ to the hyperbola $16 x ^{2}-25 y ^{2}=400$ include an angle equal to.
The degree of the differential equation $y(x)=1 +\frac{dy}{dx}+\frac{1}{1.2}\left(\frac{dy}{dx}\right)^2+\frac{1}{1.2.3}\left(\frac{dy}{dx}\right)^3+.........$ is
The number of common tangents to circle $x^{2}+y^{2}+2 x+8 y-23=0$ and $x^{2}+y^{2}-4 x-10 y+9=0$, is.
The largest value of $2x^3 - 3x^2 - 12x + 5$ for $-2 \leq x \leq 4$ occurs at $x$ is equal to :
The equation of plane passing through a point $A (2,-1,3)$ and parallel to the vectors $a =(3,0,-1)$ and $b =(-3,2,2)$ is:
Let $\alpha, \beta, \gamma$ and $\delta$ are four positive real number such that their product is unity, then the least value of $(1+\alpha)(1+\beta)(1+\gamma)(1+\delta)$ is:
Total number of books is $2n + 1$. One is allowed to select a minimum of the one book and a maximum of $n$ books. If total number of selections if $63$, then value of $n$ is :
Given function $f(x)=\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right)$ is.
Value of $\displaystyle\sum_{ k =1}^{6}\left(\frac{2 k \pi}{7}\right)- i \cos \left(\frac{2 k \pi}{7}\right)$ is equal to.
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from the opposite direction in 6 seconds. The speed of the second train is
Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs. travelling at speed of 80 kmph. How far away from Delhi will the two trains meet?
If \(log2\) = 0.30103, find number of digits in 256