List of top Mathematics Questions

Let T > 0 be a fixed real number. Suppose, f is a continuous function such that for all $x \in R. f(x+T)=f(x). \, If \, I = \int_0^T f(x)dx$ then the value of $\int_3^{3+3T} f(2x)dx$

The sum $\displaystyle \sum_{i-0}^{m} \binom{10}{i} \binom{20}{m-i},$ where $ \binom{p}{q}=0 \, if \, p>q,$ is maximum when m is equal to

The area (in sq units) bounded by the curves $y=|x|-1$ and $y=-|x|+1$ is

The set of all real numbers x for which $x^2-|x+2|+x>0$ is

If $a > 0$ and discriminant of $ax^2 + 2bx +c $ is -ve then $\begin{vmatrix}a&b&ax+b\\ b &c&bx+c\\ ax+b &bx+c&0\end{vmatrix} $ is equal to

The domain of $\sin^{-1}\left[\log_3\left(\frac{x}{3}\right)\right]$ is

If $(\omega\,\neq\,1)$ is a cube root of unity , then $ \begin{vmatrix} 1 &1+i+\omega^2 &\omega^2 \\[0.3em] 1-i&-1 & \omega^2-1 \\[0.3em] -i & -1+\omega-i& -1 \end{vmatrix}=$

If the vectors $\vec{ a }=x \hat{ i }+y \hat{ j }+z \hat{ k }$ and such that $\vec{ a }, \vec{ c }$ and $\vec{ b }$ form a right handed system, then $\vec{ c }$ is :

The direction ratios of a normal to the plane through $ (1, 0, 0), (0, 1, 0)$ which makes angles of $\frac{\pi}{4}$ with the plane $x + y = 3$ are

The positive integer just greater than $(1 + 0.0001)^{10000}$ is

If the sum of the coefficients in the expansion of $(a + b)^n$ is 4096, then the greatest coefficient in the expansion is

r and n are positive integers $r > 1, n > 2$ and coefficient of $(r+2)^{th}$ term and $3r^{th}$ term in the expansion of $(1 + x)^{2n }$ are equal, then n equals

The coefficients of $x^p$ and $x^q$ (p and q are positive integers) in the expansion of $(1+ x )^{p+q}$ are

If $a, b, c$ are distinct +ve real numbers and $a^2 + b^2 + c^2 = 1$ then $ab + bc + ca$ is

$\displaystyle\lim_{x \to 0} \frac{ \sqrt{1 -\cos \, 2x}}{\sqrt{2} x}$ is

A biased coin with probability p, $0

Let f(x) =$\int_1^x \sqrt{2-t^2}dt $ Then, the real roots of the equation $x^2-f'(x)=0$ are

If $a_1,a_2,...,a_n$ are positive real numbers whose product is a fixed number c, then the minimum value of $ a_1 + a_2 +...+ a_{n-1}+2a_n$ is

Let $\omega=-\frac{1}{2}+i\frac{\sqrt 3}{2},$ then value of the determinant $\begin {vmatrix} 1 & 1& 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega \\ \end {vmatrix} is $

If $0 < \alpha

Let $a, b, c$ be in an AP and $a^2,b^2,c^2$ be in GP, if $a < b < c$ and $a+b+c= \frac{3}{2}$, then the value of a is

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is

The integral $ \int\limits^{1/2}_{-1/2} \bigg ([x] + \log \bigg ( \frac{1+ x}{1 - x} \bigg ) \bigg ) \, dx $ equals

If Sin A : Cos A = 4 : 7 , then the value of \(\frac{(7sinA−3cosA)}{(7sinA+2cosA)}\) is 

Probability of four sons to a couple is