List of top Mathematics Questions asked in KEAM

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

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

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

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

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

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 $\left(ABA\right)^{T}=$

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

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

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

If $ l,m $ and $ n $ are real numbers such that $ {{l}^{2}}+{{m}^{2}} $ $ +{{n}^{2}}=0, $ then $ \left| \begin{matrix} 1+{{l}^{2}} & lm & ln \\ lm & 1+{{m}^{2}} & mn \\ ln & mn & 1+{{n}^{2}} \\ \end{matrix} \right| $ 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

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

If $xy\, = \,A \,sinx \,+ \,B \,cos \,x$ is the solution of the differential equation $x\frac{d^{2}y}{dx^{2}}-5a\frac{dy}{dx}+xy=0$ then the value of $a$ is equal to

Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are

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

In a certain town $25\%$ families own a cell phone, $15\%$ families own a scooter and $65\%$ families own neither a cell phone nor a scooter. If $1500$ families own both a cell phone and a scooter, then the total number of families in the town is

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

If $p :$ It is snowing, $q :$ I am cold, then the compound statement "It is snowing and it is not that I am cold" is given by

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