List of top Mathematics Questions asked in KEAM

If the length of the latus rectum of an ellipse is one-fourth of the major axis, then the eccentricity of the ellipse is

If the normal form of the equation of a straight line \( x+\sqrt{3}y=2\sqrt{3} \) is \( x\cos\alpha+y\sin\alpha=p \), then the values of \( \alpha \) and \( p \) are respectively

If the line joining of two points \((1,0)\) and \((4,3)\) is rotated about the point \((1,0)\) in counter clockwise direction through an angle \(15^\circ\), then the equation of the line in the new position is

The point with integral coordinates on the line \(x+y=1\), that lie at a distance \(2\) units from the line \(5x+12y=0\), is

If \( \sin^{-1}x+\sin^{-1}y=\dfrac{2\pi}{3} \), then \( \cos^{-1}x+\cos^{-1}y \) is equal to

If the two circles \( (x-2)^2+(y-3)^2=9 \) and \( (x-2)^2+(y+3)^2=a^2 \) intersect in two distinct points, then

If \( \cos^{-1}x+\cos^{-1}y+\cos^{-1}z=3\pi \), then \( (x+y+z) \) is equal to

If \( \theta \in \left[\dfrac{\pi}{2}, \dfrac{3\pi}{2}\right] \), then \( \sin^{-1}(\sin\theta) \) is equal to

\(\frac{1-\cos 2x}{1+\cos 2x}-\sec^2 x=\)

The period of the function \(f(x)=2\sin 4x+3\cos 2x\) is

The value of \( \tan \dfrac{\pi}{12}+\tan \dfrac{\pi}{6}+\left(\tan \dfrac{\pi}{12}\tan \dfrac{\pi}{6}\right) \) is equal to

If $\tan(x-y)=\frac{4}{5}$, $\tan(x+y)=\frac{6}{5}$ and $0<x,y<\frac{\pi}{4}$, then $\tan 2x$ is:

The solution set of inequality \( |x+2|<3 \) is

If the following system of linear equations
\[ x-2y+z=5 \] \[ 2x-y+2z=7 \] \[ x+2y+\lambda z=5 \] has a unique solution, then \(\lambda \ne\)

If \(\frac{x+1}{x-1}<2\), then \(x\) lies in the interval

If \(\begin{vmatrix} a & 1 & 1 1 & b & 1 1 & 1 & c \end{vmatrix}=2\), where \(a,b\) and \(c\) are positive integers, then \(a+b+c\) is equal to

Let \( \Delta = \begin{vmatrix} x & y & 1 x+y & y+1 & x+1 1 & x & y \end{vmatrix} \). If \( x+y=-1 \), then the value of \( \Delta \) is equal to

A bag contains \( 5 \) red balls, \( 4 \) black balls, and \( 3 \) white balls. Then the number of ways of selecting three balls at random that contains at least one white ball is

Four fair dice are rolled. Then the number of ways in which the sum of upper faces of four dices can be six, is

\(2+{}^{15}C_{1}+{}^{15}C_{2}+\dots+{}^{15}C_{14}=\)

Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is

The coefficient of $x^{1}$ in the binomial expansion of $\left(\sqrt{x}+\frac{1}{x}\right)^{10}$ is:

If the numbers \( x, 6, y, 54, 162 \) are in geometric progression, then \( \dfrac{y}{x} \) is equal to

The point \(z=\frac{1}{\sqrt{2}}(1+i)\) in the complex plane is rotated about the origin through an angle \(\frac{\pi}{4}\) in the clockwise direction, then the new position of \(z\) is

If \( 1, a, b, c, 16 \) are in geometric progression, then \( \sqrt[3]{abc} \) is equal to