List of top Mathematics Questions

A person pays Rs. 975 in monthly instalments, each monthly instalment being less than the former by Rs. 5. The amount of the first instalment is Rs. 100. In what time, will the entire amount be paid?

Which of the following is not a proposition.

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