List of top Mathematics Questions

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

If $0 < \alpha

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 $

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

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

The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the two trees is

\(\frac{{3}\pi}{5}\) radians is equal to

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

A tree breaks due to storm and the broken part bends so that the top of the tree first touches the ground, making an angle of 30 with the horizontal. The distance from the foot of the tree to the point where the top touches the ground is 10 m. The height of the tree is

Probability of four sons to a couple is