List of top Mathematics Questions asked in KEAM

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

Which one of the following functions is one-to-one?

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

$\int\frac{dx}{x-\sqrt{x}}$ 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

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 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

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

The solution set of the in equation $ \frac{x+11}{x-3}>0 $ is

There are $10$ persons including $3$ ladies. A committee of $4$ persons including at least one lady is to be formed. The number of ways of forming such a committee is

Which one of the following is not a statement?

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

If $a , \,b$ and $c$ are three non-zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of $| a + b + c |^{2}$ 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 $a$ and $b$ are positive numbers such that $ a>b, $ then the minimum value of $ a\sec \theta -b\tan \theta \left( 0

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