List of top Questions asked in KEAM

The coefficient of $x ^{49}$ in the product $\left(x-1\right)\left(x-2\right)\cdots\left(x-50\right)$ is

If $ \tan \alpha =\frac{b}{a},a>b>0 $ and if $ 0

$\int \limits^{2017}_{2016} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{4033 - x}} dx $ is equal to

The negation of $\left(p\vee\sim q\right)\wedge q$ is

$\int\frac{dx}{x-\sqrt{x}}$ is equal to

$\int\frac{2x+\sin2x}{1+\cos2x}\, dx$ is equal to

If $y = x + \frac{1}{x}, x \ne 0$, then the equation $\left(x^{2}-3x+1\right)\left(x^{2}-5x+1\right)=6x^{2}$ reduces to

$ \displaystyle\lim_{x\rightarrow0} \frac{1}{3-2^{\frac{1}{x}}}$ is equal to

Let $ {{(1+x)}^{n}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}} $ .If $ {{a}_{1}},{{a}_{2}} $ and $ {{a}_{3}} $ are in $AP$, then the value of $n$ is

Let $p$ : roses are red and q : the sun is a star. Then, the verbal translation of $ (-\text{ }p) \vee q $ is

Let $t_n$ denote the $n^{th}$ term in a binomial expansion. If $ \frac{t_{6}}{t_{5}}$ in the expansion of $(a+ b)^{n+4}$ and $ \frac{t_{5}}{t_{4}}$ in the expansion of $(a + b)^n$ are equal, then $n$ is

Let $u , v$ and $w$ be vectors such that $u + v + w = 0 .$ If $| u |=3,| v |=4$ and $| w |=5$ then $u \cdot v + v \cdot w + w \cdot u$ is equal to

The value of $\sum\limits^{n}_{k=0}\left(i^{k}+i^{k+1}\right)$, where $i^2 = -1$, is equal to

Number of integral solutions of $ \frac{x+2}{{{x}^{2}}+1}>\frac{1}{2} $ is

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

If the equation $2x^2 - (a+3)x + 8 = 0$ has equal roots, then one of the values of $a$ is

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

If $ {{x}^{2}}+4ax+2>0 $ for all values of $ x, $ then $a$ lies in the interval

If z =$\frac{2-i}{i}$ = , then Re(z$^2$) + lm(z$^2$) is equal to

If $z = \cos\left(\frac{\pi}{3} \right) - i \sin \left(\frac{\pi }{3}\right),$ the $z^{2} - z +1 $ is equal to

If $z = i^9 + i^{19}$ , then $z$ is equal to

Let $S_{1}$ be a square of side $5\,cm$. Another square $S_{2}$ is drawn by joining the midpoints of the sides of $S_{1}$ Square $S_{3}$ is drawn by joining the midpoints of the sides of $S_{2}$ and so on. Then (area of $S_{1}$ + area of $S_{2}$ + area of $S_{3}$ $+\ldots+$ area of $S_{10}$) =

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 $A$ 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