List of top Mathematics Questions asked in KEAM

The first term of an infinite $GP$ is $1$ and each term is twice the sum of the succeeding terms, then the sum of the series is

$ \int_{-1}^{1}{\frac{17{{x}^{5}}-{{x}^{4}}+29{{x}^{3}}-31x+1}{{{x}^{2}}+1}}dx $ is

Let $x = 2$ be a root of $y = 4x^2 - 14x + q = 0$. Then $y$ is equal to

$\displaystyle \lim_{x \to 0} \left(\frac{10}{9}\frac{sin \, 9x}{sin \, 10x}\right) \left(\frac{8}{7}\frac{sin \, 7x}{sin \, 8x}\right) \left(\frac{6}{5}\frac{sin \, 5x}{sin \, 6x}\right) \left(\frac{4}{3}\frac{sin \, 3x}{sin \, 4x}\right) \left(\frac{sin \, x}{sin \, 2x}\right) $ =

$ \underset{x\to 2}{\mathop{\lim }}\,\frac{{{x}^{100}}-{{2}^{100}}}{{{x}^{77}}-{{2}^{77}}} $ is equal to

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

Number of integral solutions of $ \frac{x+2}{{{x}^{2}}+1}>\frac{1}{2} $ 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 negation of $\left(p\vee\sim q\right)\wedge q$ is

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

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

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

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

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

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

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

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

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

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

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

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

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 $S_{10}$) =