List of top Mathematics Questions asked in KEAM

If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to

If $log_e\,5$, $log_e(5^x-1)$ and $log_e$ $\left(5^{x}-\frac{11}{5}\right)$ are in $A.P.$, then the values of $x$ are

If $f(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}}$ , then $f'(2) $ is equal to

If $X=\{1,2,3, \ldots, 10\}$ and $A=\{1,2,3,4,5\}$. Then, the number of subsets $B$ of $X$ such that $A-B=\{4\}$ is

Let $a, b, c$ be in $AP$. If $ 0 < a,b,c < 1 ,x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}}, $ $ y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}} $ and $ z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}}, $ then

If $A = \begin{bmatrix}log\,x&-1\\ -log\,x&2\end{bmatrix}$ and if $det (A) = 2$, then the value of $x$ is equal to

Let $ A(1,-1,2) $ and $ B(2,3,-1) $ be two points. If a point $P$ divides $AB$ internally in the ratio $ 2:3, $ then the position vector of $P$ is

If $ {{(\sqrt{5}+\sqrt{3}i)}^{33}}={{2}^{49}}z, $ then modulus of the complex number $z$ is equal to

The value of $\frac{1}{i}+\frac{1}{i^{2}}+\frac{1}{i^{3}}+\cdots+\frac{1}{i^{102}}$ is

The number of ways in which $5$ ladies and $7$ gentlemen can be seated in a round table so that no two ladies sit together, is

If $ f(x)=(x-2)(x-4)(x-6)....(x-2n), $ then $ f'(2) $ is

Let $O$ be the origin and $A$ be the point $(64, 0).$ If $P$, $Q$ divide $OA$ in the ratio $1 : 2 : 3$ , then the point $P$ is

If $x=5+2$ sec $\theta$ and $y=5+2\, \tan \, \theta ,$ then $\left(x-5\right)^{2}-\left(y-5\right)^{2}$ is equal to

If $ y={{\sin }^{2}}{{\cot }^{-1}}\sqrt{\frac{1+x}{1-x}}, $ then $ \frac{dy}{dx} $ is equal to

If the projection of the vector $\vec {a}$ on $\vec{b}$ is $ \overrightarrow{a} $ on $ \overrightarrow{b} $ is $ |\overrightarrow{a}\times \overrightarrow{b}| $ and if $ 3\overrightarrow{b}=\vec{i}+\vec{j}+\vec{k}, $ then the angle between $ \vec{a} $ and $ \vec{b} $ is

The value of $\frac{\sqrt{3}}{\sin15^{\circ}} - \frac{\sqrt{1}}{\cos15^{\circ}}$ is equal to

The general solution of the differential equation $(x + y + 3) \,\frac{dy}{dx}\, =\,1$ is

If $\begin{vmatrix}3i&-9i&1\\ 2&9i&-1\\ 10&9&i\end{vmatrix} = x + iy $, then

The principal argument of the complex numb $Z=\frac{1+\sin \frac{\pi}{3}+i \cos\frac{\pi}{3} }{1+\sin \frac{\pi}{3} - i \cos\frac{\pi}{3} }$ is

If sin $\left(\theta-\phi\right) = n \, sin (\theta - \phi),n \ne1,$ then the value of $\frac{\tan\theta}{\tan\phi}$ is equal to

The domain of the function $f\left(x\right) = sin^{-1}\left(\frac{x+5}{2}\right)$ is

The angle between the straight lines $x-1=\frac{2y+3}{3}=\frac{z+5}{2}$ and $x-3r+2; y=-2r-1; z=2,$ where $r$ is a parameter, is

If the position vectors of three consecutive vertices, of a parallelogram are $ \vec{i}+\vec{j}+\vec{k}, $ $ \vec{i}+3\vec{j}+5\vec{k} $ and $ 7\vec{i}+9\vec{j}+11\vec{k}, $ then the coordinates of the fourth vertex are

Let $ \alpha $ and $ \beta $ be the roots of $ a{{x}^{2}}+bx+c=0 $ . Then, $ \underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}} $ is equal to

The $A$.$M$. of $9$ terms is $15$. If one more term is added to this series, then the $A$.$M$. becomes $16$. The value of the added term is