List of top Questions asked in KEAM

$\left(\frac{1+\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)}{1+\cos \left(\frac{\pi}{12}\right) - i \sin\left(\frac{\pi}{12}\right)}\right)^{72}$ is equal to

The locus of a point which is equidistant from the points $(1,1)$ and $(3, 3)$ is

If $A$ and $B$ are non-empty sets such that $A \supset B$, then

The angle between the line $ \frac{3x-1}{3}=\frac{y+3}{-1} $ $ =\frac{5-2z}{4} $ and the plane $ 3x-3y-6z=10 $ is equal to

The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents

The area bounded by $y =x^{2} +3$ and $y =2x+3$ is

If $ |2x-3|

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

If a$_1$ = 4 and $a_{n+1}=a_{n}+4n\quad for\quad n\ge1. $ then the value of a$_{100}$ is

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

The term independent of $x$ in the expansion of $\left(x+\frac{1}{x^{2}}\right)^{6}$ is

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

A complete cycle of a traffic light takes $60\, seconds$. During each cycle the light is green for $25\, seconds$, yellow for $5 \,seconds$ and red for $30\, seconds$. At a randomly chosen time, the probability that the light will not be green, is

If $p : 2$ plus $3$ is five and $q $ : Delhi is the capital of India < are two statements, then the statement "Delhi is the capital of India and it is not that $2$ plus $3$ is five" is

If the standard deviation of $3$, $8$, $6$, $10$, $12$, $9$, $11$, $10$, $12$, $7$ is $2.71$, then the standard deviation of $30$, $80$, $60$, $100$, $120$, $90$, $110$, $100$, $120$, $70$ is

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

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

If $ 3\le 3t-18\le 18, $ then which one of the following is true?

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

If the semi-major axis of an ellipse is 3 and the latus rectum is $\frac{16}{9},$ then the standard equation of the ellipse is

If $y^{2}=100 \tan^{-1}x+45 sec^{-1}x ,$ then $\frac{dy}{dx}=$

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

If $a$ and $b$ are positive numbers such that $ a>b, $ then the minimum value of $ a\sec \theta -b\tan \theta \left( 0

If $6^{th}$ term of $G.P.$ is $2$, then the product of first $11$ terms of the $G.P.$ is equal to

If $ A= \begin{bmatrix} 1 & 0 & 0 \\ x & 1 & 0 \\ x & x & 1 \\ \end{bmatrix} $ and $ I= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} , $ then $ {{A}^{3}}-4{{A}^{2}}+3A+I $ is equal to