List of top Mathematics Questions asked in KEAM

An integrating factor of the differential equation $xdy - ydx + x^2e^xdx = 0$ is

$ \tan\left(\frac{\pi}{4} +\frac{\theta}{2}\right) + \tan\left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is equal to

If $\tan^{-1} x$ + $\tan^{-1} y$ = $\frac{2\pi}{3 }$ , then $\cot^{-1} x$ + $\cot^{-1} y$ is equal to

In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is

The distance between the line $ \overrightarrow{r}=(2\hat{i}+2\hat{j}-\hat{k})+\lambda (2\hat{i}+\hat{j}-2\hat{k}) $ and the plane $ \overrightarrow{r}.(\hat{i}+2\hat{j}+2\hat{k})=10 $ is equal to

Suppose that two persons $A$ and $B$ solve the equation $ {{x}^{2}}+ax+b=0 $ . While solving $A$ commits a mistake in the coefficient of $ x $ was taken as $15$ in place of $-9$ and finds the roots as $ -7 $ and $ -2 $ . Then, the equation is

If the set $A$ contains $5$ elements, then the number of elements in the power set $ P(A) $ is equal to

If $\frac{|x-3|}{x-3}$ > 0 , then

If the direction cosines of a vector of magnitude $3$ are $\frac{2}{3},\frac{-a}{3},\frac{2}{3}, a>0, $ then the vector is

If the scalar product of the vector $ \hat{i}+\hat{j}+2\hat{k} $ with the unit vector along $ m\hat{i}+2\hat{j}+3\hat{k} $ is equal to $2$, then one of the values of $m$ is

If the straight line $y = 4x + c$ touches the ellipse $\frac{x^2}{4} + y^2 = 1 $ then c is equal to

The solution of $\frac{dy}{dx} + y \, \tan \, x = \sec \, x, y (0) = 0$ is

If \(\begin{bmatrix}e^{x}&e^{y}\\ e^{y}&e^{x}\end{bmatrix} = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}\), then the values of \(x\) and \(y\) are respectively:

The parametric form of the ellipse $4\left(x+1\right)^{2}+\left(y-1\right)^{2}=4$ is

Let $P$ be the statement Ravi races and let $Q$ be the statement Ravi wins. Then, the verbal translation of $ \tilde{\ }(p\vee (\tilde{\ }q)) $ is

The value of $\displaystyle \lim_{x \to 3} \frac{x^{5}-3^{5}}{x^{8}-3^{8}}$ is equal to

If $\displaystyle\sum^{9}_{i-1}\left(x_{i}-5\right)=9$ and $\displaystyle\sum^{9}_{i-1}\left(x_{i}-5\right)^{2}=45$ , then the standard deviation of the $9$ items $x_{1}, x_{2} ,\cdots, x_{9}$ is

The vector equation of the straight line $ \frac{1-x}{3}=\frac{y+1}{-2}\,=\frac{3-z}{-1} $

If $\lambda\left(3\hat{i}+2\hat{j}-6\hat{k}\right)$ is a unit vector, then the values of $\lambda$ are

Let $a =\hat{ i }-2 \hat{ j }+3 \hat{ k }$. If $b$ is a vector such that $a \cdot b =| b |^{2}$ and $| a - b |=\sqrt{7}$, then $| b |$ is equal to

The perpendicular distance from the point $(1, -1)$ to the line $x + 5y - 9 = 0$ is equal to

The number of functions that can be defined from the set $A \,= \{a, b, c, d\}$ into the set $B\, =\{1,2,3\}$ is equal to

Let $ {{a}_{n}}={{i}^{{{(n+1)}^{2}}}}, $ where $ i=\sqrt{-1} $ and $ n=1,2,3..... $ . Then the value of $ {{a}_{1}}+{{a}_{3}}+{{a}_{5}}+...+{{a}_{25}} $ is