List of top Mathematics Questions asked in KEAM

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 $^{n}C_{r-1}=28$, $^{n}C_{r}=56$ and $^{n}C_{r+1}=70$, then the value of $r$ is equal to

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

The remainder when $2^{2016}$ is divided by $63$, is

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 $f \left(z\right)=\frac{1-z^{3}}{1-z} ,$ where $z=x+iy$ with $z\ne1,$ then $Re\left\{\overline{f \left(z\right)}\right\}=0$ reduces to

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

$\int\limits_{0}^{1} x e^{-5x} \, dx$ is equal to

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

The total revenue in rupees received from the sale of x units of a product is given by $ R(x)=13{{x}^{2}}+26x+15 $ . Then, the marginal revolution rupees, when $ x=15 $ 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

The order of the differential equation $\left(\frac{d^{3}\, y }{dx^{3}}\right)^{2} + \left(\frac{d^{2}\,y}{dx}\right)^{2} + \left(\frac{dy}{dx}\right)^{5} = 0 $ 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

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 $ \overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c} $ are non-coplanar and $ (\overrightarrow{a}+\lambda \overrightarrow{b}).[(\overrightarrow{b}+3\overrightarrow{c})\times (\overrightarrow{c}\times 4\overrightarrow{a})]=0, $ then the value of $ \lambda $ is equal to

The image of the interval [-1, 3] under the mapping $f : R\rightarrow R$ given by $f \left(x\right)=4x^{3}-12x$ is

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

If $A$ and $B$ are square matrices of the same order and if $A=A^{T},B=B^{T},$ then $\left(ABA\right)^{T}=$

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

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

The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents

In the expansion of $ {{(1+x+{{x}^{2}}+{{x}^{3}})}^{6}}, $ the coefficient of $ {{x}^{14}} $ is

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