List of top Mathematics Questions

The cartesian product $ A\times A $ has $9$ elements among which are found $ (-1,0) $ and $ (0,1), $ then set $A$ = ?

A survey shows that $63\%$ of the Americans like cheese where as $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples, then the value of $x$ is

The value of $ \int_{0}^{\pi /2}{\frac{dx}{1+\tan x}} $ is

If $ A=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right], $ then $ (A-A') $ is equal to (where, $A'$ is transpose of matrix $A$)

Which of the following is not a function?

The value of $ \left| \begin{matrix} {{a}^{2}} & 2ab & {{b}^{2}} \\ {{b}^{2}} & {{a}^{2}} & 2ab \\ 2ab & {{b}^{2}} & {{a}^{2}} \\ \end{matrix} \right| $ is

If $ \theta =\frac{\pi }{{{2}^{n}}+1}, $ then the value of $ {{2}^{n}}\cos \theta \,\cos \,2\theta \,\cos \,{{2}^{2}}\theta .....\cos {{2}^{n-1}}\theta $ is

The value of $ \frac{d}{dx}[{{x}^{n}}\,{{\log }_{a}}\,x{{e}^{x}}] $ is

Using the principal values, the value of $ {{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}+{{\tan }^{-1}}\left\{ \tan \frac{\pi }{6} \right\} $ = ?

If $ {{S}_{n}} $ denotes the sum of first $n$ terms of $A.P.$ $ , $ such that $ \frac{{{S}_{m}}}{{{S}_{n}}}=\frac{{{m}^{2}}}{{{n}^{2}}}, $ then $ \frac{{{a}_{m}}}{{{a}_{n}}} $ is equal to

$ \underset{x\to 0}{\mathop{\lim }}\,\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}} $ is equal to

If the determinant of the adjoint of a (real) matrix of order $3$ is $25$, then the determinant of the inverse of the matrix is

How many numbers with no more than three digits can be formed using only the digits $1$ through $7$ with no digit used more than once in a given number?

If the area of the auxiliary circle of the ellipse $\frac {x^2}{a^2}+\frac {y^2}{b^2}=1 (a >\, b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is

Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all $5$ persons leaving at different floors is

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is

The area of the region enclosed between parabola $y^2 = x$ and the line $y = mx$ is $\frac{1}{48}. $

If the distance between the foci of an ellipse is equal to the length of the latus rectum, then its eccentricity is

Let $f(?) = (1+sin^2?)(2-sin^2?)$. Then for all values of $?$

There are two coins, one unbiased with probability $\frac{1}{2}$ of getting heads and the other one is biased with probability $\frac{3}{4}$ of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiased coin was selected is

The limit of $ \sum\limits^{1000}_{ n-1} (-1)^n \, x^n $ as $x?8$