List of top Mathematics Questions asked in KEAM

The area of the plane region bounded by the curve $ x={{y}^{2}}-2 $ and the line $ y=-x $ is (in square units)

If $\begin{bmatrix}1&x&1\end{bmatrix} \begin{bmatrix}1&3&2\\ 2&5&1\\ 15&3&2\end{bmatrix}\begin{bmatrix}1\\ 2\\ x\end{bmatrix} = 0 $, then x can be

Two distinct numbers $x$ and $y$ are chosen from $1,2,3,4,5$. The probability that the arithmetic mean of $x$ and $y$ is an integer is

Equation of the plane passing through the intersection of the planes $ x+y+z=6 $ and $ 2x+3y+4z+5=0 $ and the point $(1, 1, 1)$ is

If $a = e^{i \theta}$ , then $\frac{1 + a}{1-a}$ is equal to

A man of $2\,m$ height walks at a uniform speed of $6 \,km/h$ away from a lamp post of $6 \,m$ height. The rate at which the length of his shadow increases is

If tan $\frac{\theta}{2}=\frac{1}{2}$,then the value of sin $\theta$ is

If $ y={{\sin }^{-1}}\sqrt{1-x}, $ then $ \frac{dy}{dx} $ is equal to

If $A = \begin{pmatrix}1&0\\ 1&1\end{pmatrix}$ , then $A^n + nI$ is equal to

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

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

If $A = \begin{pmatrix}1&5\\ 0&2\end{pmatrix}$ , then

$\int\frac{1}{\sin x\, \cos x}$ dx is equal to

If $|z + 1| < |z - 1|$ , then $z$ lies

If $a$ is positive and if $A$ and $G$ are the arithmetic mean and the geometric mean of the roots of $ {{x}^{2}}-2ax+{{a}^{2}}=0 $ respectively, then

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

If $C_{0}$, $C_{1}$, $C_{2}$, $C_{3}$, $\cdots$ are binomial coefficients in the expansion of $(1 + x)^n$, then $\frac{C_{0}}{3}- \frac{C_{1}}{4}+ \frac{C_{2}}{5}- \frac{C_{3}}{6}+ \cdots$ is equal to

If $a_1, a_2 , a_3 , a_4$ are in A.P., then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\frac{1}{\sqrt{a_{3}}+\sqrt{a_{4}}}=$

A die has four blank faces and two faces marked $3$. The chance of getting a total of $12$ in $5$ throws is

If $ \alpha $ and $ \beta $ are the roots of the equation $ a{{x}^{2}}+ $ $ bx+c=0,\text{ }\alpha \beta =3 $ and $a, b, c$ are in $A.P.$, then $ \alpha +\beta $ is equal to

The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is

The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to

Suppose $a, b$ and $c$ are real numbers such that $ \frac{a}{b}>1 $ and $ \frac{a}{c}<0 $ . Which one of the following is true?

$\int\left(\frac{x-a}{x}-\frac{x}{x+a}\right) dx$ is equal to