List of top Questions asked in KEAM

The values of $\alpha$ so that $|\alpha\hat{i}+(\alpha+1)\hat{j}+2\hat{k}|=3$, are

If $\vec{u}=\hat{i}-3\hat{j}+2\hat{k}$ and $\vec{v}=2\hat{i}+4\hat{j}-5\hat{k}$, then $|\vec{u}\times\vec{v}|^{2}+|\vec{u}\cdot\vec{v}|^{2}=$

The value of $\lambda$ such that the vectors $2\hat{i}-\hat{j}+2\hat{k}$ and $3\hat{i}+2\lambda\hat{j}$ are perpendicular is

The latus rectum of the hyperbola $3x^{2}-2y^{2}=6$ is

The direction cosines of the vector $\hat{i}-5\hat{j}+8\hat{k}$ are

The equation of the circle whose radius is $\sqrt{7}$ and concentric with the circle $x^{2}+y^{2}-8x+6y-11=0$ is

The vertex of the parabola $y=(x-2)(x-8)+7$ is

The eccentricity of the ellipse $x^{2}+\frac{y^{2}}{4}=1$ is

The major and minor axis of the ellipse $400x^{2}+100y^{2}=40000$ respectively are

The vertex of the parabola $y=x^{2}-2x+4$ is shifted $p$ units to the right and then $q$ units up. If the resulting point is $(4,5)$, then the values of $p$ and $q$ respectively are

If (a,2) is the point of intersection of the straight lines $y=2x-4$ and $y=x+c$, then the value of c is equal to

If the straight lines $4x+6y=5$ and $6x+ky=3$ are parallel, then the value of k is equal to

If the points $P(7,5)$, $Q(a,2a)$ and $R(12,30)$ are collinear, then the value of a is equal to

The centre and radius of the circle $x^{2}+y^{2}-4x+2y=0$ are

A circle with centre at (3, 6) passes through (-1,1). Its equation is

The maximum value of $z=7x+5y$ subject to $2x+y\le100$, $4x+3y\le240$, $x\ge0$ $y\ge0$ is

The equation of the line passing through the point (-3,7) with slope zero is

$\frac{\sin 91^{\circ}+\sin 1^{\circ}}{\sin 91^{\circ}-\sin 1^{\circ}}=$

If $\tan x+\tan y=\frac{5}{6}$ and $\cot x+\cot y=5$ then $\tan(x+y)$ is

The line $y=mx+2$ intersects the parabola $y=ax^{2}+5x-2$ at $(1,5)$. Then the value of $a+m$ is equal to

The value of $\cos(\cos^{-1}\frac{1}{5}+2\sin^{-1}\frac{1}{5})$ is equal to

The value of $10 \tan(\cot^{-1}3+\cot^{-1}7)$ is equal to

Which of the following sentences is/are statement(s)?
(i) 10 is less than 5.
(ii) All rational numbers are real numbers.
(iii) Today is a sunny day.

The values of x in $0\le x\le\pi$ such that $\cos 2x=\cos x$ are

The value of $\sin(45^{\circ}+\theta)-\cos(45^{\circ}-\theta)$ is equal to