List of top Mathematics Questions asked in KEAM

Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals

If $n\left(A\right)=43, n\left(B\right)=51\quad and \quad n\left(A\cup B\right)=75, then\quad n\left(A-B\right)\cup\left(B-A\right)$ is equal to

If t$_5$, t$_{10}$ and t$_{25}$ are 5$^{th}$, 10$^{th}$, and 25$^{th}$ terms of an A.P. respectively, then the value of $\begin{vmatrix}t_{5}&t_{10}&t_{25}\\ 5&10&25\\ 1&1&1\end{vmatrix}$ is equal to

If $\left(1+ax\right)^{n} =1+6x+\frac{27}{2}x^{2}+\cdots+a^{n}\, x^{n}$, then the values of $a$ and $n$ are respectively

If $|x - 3| < 2x + 9$ then $x$ lies in the interval

Let $s_n = \cos \left(\frac{n\pi}{10}\right), n=1,2,3,\ldots$ Then the value of $\frac{s_{1}s_{2}\ldots s_{10}}{s_{1}+s_{2}+\ldots+s_{10}}$ is equal to

If $cos x = -\frac{4}{5}$, where $x\in\left[0, \pi\right]$, then the value of $cos \left(\frac{x}{2}\right)$ is equal to

If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to

If $log_e\,5$, $log_e(5^x-1)$ and $log_e$ $\left(5^{x}-\frac{11}{5}\right)$ are in $A.P.$, then the values of $x$ are

If $f(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}}$ , then $f'(2) $ is equal to

If $X=\{1,2,3, \ldots, 10\}$ and $A=\{1,2,3,4,5\}$. Then, the number of subsets $B$ of $X$ such that $A-B=\{4\}$ is

$\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} \,dx$ is equal to

Let $a, b, c$ be in $AP$. If $ 0 < a,b,c < 1 ,x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}}, $ $ y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}} $ and $ z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}}, $ then

If $^{n}C_{r-1}=28$, $^{n}C_{r}=56$ and $^{n}C_{r+1}=70$, then the value of $r$ is equal to

If $A = \begin{bmatrix}log\,x&-1\\ -log\,x&2\end{bmatrix}$ and if $det (A) = 2$, then the value of $x$ is equal to

The remainder when $2^{2016}$ is divided by $63$, is

Let $ A(1,-1,2) $ and $ B(2,3,-1) $ be two points. If a point $P$ divides $AB$ internally in the ratio $ 2:3, $ then the position vector of $P$ is

If $f \left(z\right)=\frac{1-z^{3}}{1-z} ,$ where $z=x+iy$ with $z\ne1,$ then $Re\left\{\overline{f \left(z\right)}\right\}=0$ reduces to

If $ {{(\sqrt{5}+\sqrt{3}i)}^{33}}={{2}^{49}}z, $ then modulus of the complex number $z$ is equal to

If $r$ is a real number such that $ |r| < 1 $ and if $ a=5(1-r), $ then

The value of $\frac{1}{i}+\frac{1}{i^{2}}+\frac{1}{i^{3}}+\cdots+\frac{1}{i^{102}}$ is

$\int\limits_{0}^{1} x e^{-5x} \, dx$ is equal to

If $ A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right], $ then the value of the determinant $ |{{A}^{2009}}-5{{A}^{2008}}| $ is

The number of ways in which $5$ ladies and $7$ gentlemen can be seated in a round table so that no two ladies sit together, is

If $ f(x)=(x-2)(x-4)(x-6)....(x-2n), $ then $ f'(2) $ is