List of top Mathematics Questions asked in KEAM

If $tan \left(\frac{\theta}{2}\right)=\frac{2}{3}$, then $sec\,\theta $ is equal to

The area of the circle $x^2 - 2x + y^2 - 10\,y + k = 0$ is $25 \pi $ . The value of k is equal to

The angle between the planes $3x + 4y + 5z = 3$ and $4 x-3 y + 5z = 9$ is equal to

If $p : 2$ plus $3$ is five and $q $ : Delhi is the capital of India < are two statements, then the statement "Delhi is the capital of India and it is not that $2$ plus $3$ is five" is

If $ A= \begin{bmatrix} 1 & 0 & 0 \\ x & 1 & 0 \\ x & x & 1 \\ \end{bmatrix} $ and $ I= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} , $ then $ {{A}^{3}}-4{{A}^{2}}+3A+I $ is equal to

If the combined mean of two groups is $\frac{40}{3}$ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is equal to

The position of a particle is given by $ r =\hat{i}+2\hat{j}-\hat{k} $ and its linear momentum is given by $ p = 3\hat{i}+4\hat{j}-2\hat{k} $ . Then its angular momentum, about the origin is perpendicular to

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

A plane makes intercepts $a, b, c$ at $A, B, C$ on the coordinate axes respectively. If the centroid of the $ \Delta ABC $ is at $(3, 2, 1)$, then the equation of the plane is

How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?

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

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 $\begin{pmatrix}2x+y&x+y\\ p-q&p+q\end{pmatrix}=\begin{pmatrix}1&1\\ 0&0\end{pmatrix}$ , then $(x, y, p, q) $ equals

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

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

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

If $y^{2}=100 \tan^{-1}x+45 sec^{-1}x ,$ then $\frac{dy}{dx}=$

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

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

If the plane $ 3x+y+2z+6=0 $ is parallel to the line $ \frac{3x-1}{2b}=3-y=\frac{z-1}{a}, $ then the value of $ 3a+3b $ 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: