List of top Mathematics Questions asked in KEAM

If $f\left(x\right) = \int\limits^{sin\,x}_{2x}cos\left(t^{3}\right)dt$, then $f'{x}$ is equal to

The plane $ \overrightarrow{r}=s(\hat{i}+2\hat{j}-4\hat{k})+t(3\hat{i}+4\hat{j}-4\hat{k}) $ $ +(1-t)(2\hat{i}-7\hat{j}-3\hat{k}) $ is parallel to the line

$\int \frac{e^{x}}{x}\left(x\,log\,x+1\right)dx$ is equal to

If $A$ and $B$ are mutually exclusive events and if $ p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21}, $ then $P(A)$ is equal to

Out of $15$ persons $10$ can speak Hindi and $8$ can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

If $ \alpha ,\beta ,\gamma $ are the cube roots of a negative number $p$, then for any three real numbers, $ x,y,z $ the value of $ \frac{x\alpha +y\beta +z\gamma }{x\beta +y\gamma +z\alpha } $ is

If one of the roots of the quadratic equation $ax^2 - bx + a = 0$ is $6$, then value of $\frac{ b}{ a}$ is equal to

If $ {{x}^{2}}-px+q=0 $ has the roots $ \alpha $ and $ \beta $ then the value of $ {{(\alpha -\beta )}^{2}} $ is equal to

Let $x_{1},x_{2},\cdots,x_{n}$ be in an $A.P$. If $x_{1}+x_{4}+x_{9}+x_{11}+x_{20}+x_{22}+x_{27}+x_{30}=272, $ then $x_{1}+x_{2}+x_{3}+\cdots+x_{30}$ is equal to

If $a + 1, 2a + 1, 4a - 1$ are in arithmetic progression, then the value of $a$ is

If $ {{a}_{1}},{{a}_{2}},.....,{{a}_{n}} $ are in AP with common difference $ d\ne 0, $ then $ (\sin d) $ $ [\sec {{a}_{1}}\sec {{a}_{2}}+ $ $ \sec {{a}_{2}}\sec {{a}_{3}}+...+\sec {{a}_{n-1}}\sec {{a}_{n}}] $ is equal to

$\displaystyle \int^{\sqrt{\pi}/2}_0$ $2x^{3} sin\left(x^{2}\right) dx =$dx is equal to

$\int\frac{3 ^{x}}{\sqrt{1-9 ^{x}}}dx\quad$is equal to

If one root of the equation $ l{{x}^{2}}+mx+n=0 $ is $ \frac{9}{2} $ $ (l,m $ and n are positive integers) and $ \frac{m}{4n}=\frac{l}{m}, $ then $ \frac{1}{x}+\frac{1}{y} $ is equal to

If the sum to first $n$ terms of the $A.P. 2,4,6,...$ is $240$, then the value of $n$ is

Let $A$ and $B$ be two events such that $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right).$ If $0 < P\left(A\right)< 1$ and $0 < P\left(B\right)< 1$ , then $P\left(A\cup B\right)^{'}=$

The solution set of $\frac{x+3}{x-2} \le\,2$ is

The coefficient of $x^5$ in the expansion of $(1 + x^2)^5(1 + x)^4$ is

Which one of the following is not a statement?

If $a =\hat{ i }+2 \hat{ j }+2 \hat{ k },| b |=5$ and the angle between $a$ and $b$ is $\pi / 6$, then the area of the triangle formed by these two vectors as two sides is

The value of The value of $\frac{2(\cos \, 75^{\circ} + i \, \sin \, 75^{\circ})}{0.2(\cos \, 30^{\circ} + i \, \sin \, 30^{\circ})}$ is

The value of the determinant $ \left| \begin{matrix} 15! & 16! & 17! \\ 16! & 17! & 18! \\ 17! & 18! & 19! \\ \end{matrix} \right| $ is equal to

The value of $ \frac{\cos 30{}^\circ +i\sin 30{}^\circ }{\cos 60{}^\circ -i\sin 60{}^\circ } $ is equal to

Let $S(n)$ denote the sum of the digits of a positive integer n. e.g. $S(178)=1+$ $7+8=16 .$ Then, the value of $S(1)+S(2)+S(3)+\ldots+S(99)$ is

$ \int{(x+1){{(x+2)}^{7}}}(x+3)dx $ is equal to