List of top Mathematics Questions

From the salary of an officer, 10% is deducted as house rent, 15% of the rest he spends on children's education and 10% of the balance he spends on clothes. After this expenditure he is left with Rs 1377. His salary is

At a college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidates who are really capable, 80% pass the tests and of the incapable, 25% pass the tests. Given that 40% of the candidates are really capable, then the proportion of capable college students is about

In an examination, there were 2000 candidates, out of which 900 candidates were boys and the rest were girls. If 32% of the boys and 38% of the girls passed, then the total percentage of failed candidates is

A mixture of 40 litres of milk and water contains 10% water. How much water should be added to this so that water may be 20% in the new mixture?

If $ x\ne 0,\,\left| \begin{matrix} x+1 & 2x+1 & 3x+1 \\ 2x & 4x+3 & 6x+3 \\ 4x+4 & 6x+4 & 8x+4 \\ \end{matrix} \right|=0, $ then $2x+1 $ is equal to

The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is

The coefficient of $ {{x}^{r}} $ in the expansion of $ {{(1-x)}^{-2}} $ is

$ 3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx $ is equal to

The number of solutions of $ \sin x=\sin 2x $ between $ \frac{-\pi }{2} $ and $ \frac{\pi }{2} $ is

If $A$ is a square matrix. $A'$ its transpose, then $ \frac{1}{2}(A-A') $ is

The foot of the perpendicular from $ (2,4,-1) $ to the line $ x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6) $

If $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$, then $10^{th}$ term is

If $ y={{\sec }^{-1}}\left( \frac{1}{\sqrt{1-{{x}^{2}}}} \right), $ then $ \frac{dy}{dx} $ is equal to

If $ \alpha ,\beta $ are the roots of the equation $ {{x}^{2}}+ax+b=0, $ then $ \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}} $ is equal to

The distance between the planes $ 2x-2y+z+3=0 $ and $ 4x-4y+2z+5=0 $ is

If $ |a|<1, $ then $ 1+2a+3{{a}^{2}}+4{{a}^{3}}+..... $ is equal to

$ \left| \begin{matrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \\ \end{matrix} \right| $ is equal to

The standard deviation of the first n natural numbers is

$ \frac{1}{3!}+\frac{2}{5!}+\frac{3}{7!}+... $ is equal to

The standard deviation for the scores $1, 2, 3, 4, 5, 6$ and $7$ is $2$. Then, the standard deviation of $12, 23, 34, 45, 56, 67$ and $78$ is

The maximum value of $\frac{Log \, x}{x} $ in $(2, \infty)$ is

If $Log_{10}7=0.8451$ then the position of the first significant figure of $7^{-20}$ is

A unit vector perpendicular to both the vectors $\hat {i} +\hat { j} $ and $ \hat {j} +\hat {k}$ is

If $\vec{a} $ and $\vec{b}$ are unit vectors and $|\vec{a} + \vec{b}|=1$ then $|\vec{a} -\vec{b}|$ is equal to