List of top Mathematics Questions asked in KEAM

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

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

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

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

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

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

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

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

Three numbers $x, y$ and $z $ are in arithmetic progression. If $x + y + z = - 3$ and $xyz= 8$, then $x^2 + y^2 + z^2$ is equal to

The output of the circuit is

Let $ z=\frac{11-3i}{1+i}. $ If a is a real number such that $ z-i\alpha $ is real, then the value of $ \alpha $ is

Let $S_{n}$ denote the sum of first $n$ terms of an $A.P$. and $S_{2n} = 3S_{n}$. If $S_{3n} =k S_{n}$, then the value of $k$ is equal to

The coefficient of $x$ in the expansion of $ (14+x)(1+2x)(1+3x)....(1+100x) $ is

The coefficient of $ {{a}^{5}}{{b}^{6}}{{c}^{7}} $ in the expansion of $ {{(bc+ca+ab)}^{9}} $ is

The statement $p \rightarrow \left(\sim q\right)$ is equivalent to

The $100^{th}$ term of the sequence $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \dots$, is