List of top Mathematics Questions

The numerically greatest term in the expansion of $(3-5x)^{11}$ when $x = \frac{1}{5},$ is

If $F$ is function such that $F (0) = 2, F (1) = 3, F (x+2) = 2F (x) - F (x+1)$ for $x \ge 0$, then $F (5)$ is equal to

Let $S$ be a set containing $n$ elements. Then, number of binary operations on $S$ is

The number of solutions of the equation $\sin \; (e^{x}) = 5^x + 5^{-x}$, is

The principal value of $\sin^{-1} \left\{\sin \frac{5\pi}{6}\right\} $ is

The value of $\frac{\cos\theta}{1+ \sin\theta}$ is equal to

Domain of the function $f (x) = \log_x \; \cos \; x$, is

If $f(x) = \sqrt{\log_{10} x^2} $ . The set of all values of $x$ for which $f(x)$ is real , is

$\displaystyle\lim_{n\to\infty} \left[\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + .... + \frac{1}{n\left(n+1\right)}\right] $ is equal to

Range of the function $y =\sin^{-1} \left(\frac{x^{2}}{1+x^{2}}\right) $ is

Which one of the following is the unit vector perpendicular to both $\vec{a}=-\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ ?

If $f(x)=\frac{x}{\sqrt{1+x^{2}}}$, then (fof of) ( $x$ ) is

If $A = \begin{bmatrix}1&3\\ 3&2\\ 2&5\end{bmatrix}$ and $ B = \begin{bmatrix}-1&-2\\ 0&5\\ 3&1\end{bmatrix} $ and $A + B - D = 0$ (zero matrix), then $D$ matrix will be -

The area of the region bounded by the curve $y=x |x|, x$-axis and the ordinates $x=1, x=$ $-1$ is given by:

The value of $\cos^{-1}x + \cos^{-1} \left(\frac{x}{2} + \frac{1}{2} \sqrt{3-3x^{2}}\right) ; \frac{1}{2} \le x \le 1 $ is

The slope of the tangent to the hyperbola $2x^2 - 3y^2 = 6$ at $(3, 2)$ is

With $17$ consonants and $5$ vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

If $m$ arithmetic means are inserted between $1$ and $31$ so that the ratio of the $7^{th}$ and $(m - 1)^{th}$ means is $5 : 9$, then find the value of m.

If $I_{m}=\int\limits_{1}^{e}(\ln x)^{m} d x$, where $m \in N$, then $I_{10}+10 I_{9}$ is equal to -

Mean of $25$ observations was found to be $78.4$. But later on it was found that $96$ was misread $69$. The correct mean is

The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

The function $f(x) = \tan x - 4x$ is strictly decreasing on

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be $70$ then the number of diagonals of the polygon is

A plane left 30 min later than its scheduled time to reach its destination 1500 km away. In order to reach in time it increases its speed by 250 km/h. What is its original speed