List of top Mathematics Questions

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

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

If $z=\frac{1-i \sqrt{3}}{1+i \sqrt{3}}$, then $\arg (z)$ is

A lot of 12 bulbs contains 4 defective bulbs. Three bulbs are drawn at random from the lot, one after the other. The probability that all three are non-defective is

A train travels a distance of 300 km at a constant speed. If the speed of the train is increased by 5 km an hour the journey would have taken 2 h less. The original speed of the train was

In the binomial expansion of $(1+x)^{15}$ the coefficients of $x^r$ and $x^{r+3}$ are equal Then $r$ is _______

The roots of the quadratic equation $x^{2}-2\sqrt{3}x-22 = 0 $ are :

Prem invested a certain sum of money in a simple interest bond whose value grew to Rs 300 at the end of 3 years and to Rs 400 at the end of another 5 years. What was the rate of interest in which he invested his sum ?

If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15 students?

The value of $\begin{vmatrix}1&2&3\\ -4&3&6\\ 2&-7&9\end{vmatrix} $ is

If $a > b > 0, Sec^{-1} \left(\frac{a+b}{a-b} \right)= 2 \; Sin^{-1}x $ then $x = $ _____

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

If $a^x = b^{y} = c^{z} = d^{u}$ and $a, b,\, c,\, d$ are in $GP$, then $x,\, y,\, z,\, u$ are in

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

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

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

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

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.