List of top Mathematics Questions asked in KEAM

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

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 $a_1, a_2 , a_3 , a_4$ 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

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

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 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

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

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

$ \int{\frac{dx}{\sqrt{1-{{e}^{2x}}}}} $ is equal to

If $z^2 + z + 1 = 0$ where $z$ is a complex number, then the value of $\left(z+ \frac{1}{z}\right)^{2} + \left(z^{2} + \frac{1}{z^{2}}\right)^{2} + \left(z^{3} + \frac{1}{z^{3}}\right)^{2} $ equals

Let $S_n$ denote the sum of first n terms of an $A.P.$ If $S_4 = -3 4 , S_5 = -60$ and $S_6 = -93$, then the common difference and the first term of the $A.P.$ are respectively

Let $a, a + r$ and $a + 2r$ be positive real numbers such that their product is $64$. Then the minimum value of $a + 2r$ is equal to

$\displaystyle \lim_{x \to 2} $ $\frac{x^{100}-2^{100}}{x^{77}-2^{77}}$ is equal to

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

If the vectors $ \overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k} $ and $ \overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k} $ are coplanar, then the value of $\lambda$ is equal to

If $\int \frac{f\left(x\right)}{log\,cos\,x}dx=-log\left(log\,cos\,x\right)+C$, then $f\left(x\right)$ is equal to

The roots of the equation $\begin{vmatrix}x-1&1&1\\ 1&x-1&1\\ 1&1&x-1\end{vmatrix} = 0 $ are

The coefficient of $x^2$ in the expansion of the determinant $\begin{vmatrix}x^{2}&x^{3}+1&x^{5}+2\\ x^{2}+3&x^{3}+x&x^{3}+x^{4}\\ x+4&x^{3}+x^{5}&2^{3}\end{vmatrix}$ is