List of top Questions asked in KEAM- 2026

Let $f(x) = \frac{(\sqrt{x}+3)(\sqrt{x}-1)}{x - 1}$ for $x \neq 1$. Then $\lim_{x \to 1} f(x)$ is equal to

Let $f(x) = \frac{1}{1 + \tan x}, 0 < x < \frac{\pi}{2}$. Then $f^{-1}(x) =$}

Let $f(x) = \begin{cases} \frac{1-\sec^2(\alpha x)}{\alpha x^2}, & \text{for } x \neq 0 \\ -3, & \text{for } x = 0 \end{cases}$ be continuous at $x = 0$. Then the value of $\alpha$ is equal to

The value of $\lim_{x \to 0} \frac{x - \tan(3x)}{\sin(2x)}$ is equal to

The mean of the data : 4, 7, $x$, 13, 16 is 10. Then the mean deviation of the data is

Given the data: 5, 7, 9, 11, 13. The variance of the data, is

A die is rolled twice. Let $A$ be an event of getting 1 in the first roll and let $B$ be an event of getting 4 in the second roll. Then $P(A|B)$ is equal to

There are 20 boys and 5 girls in a class. Three students are selected at random. If $E$ is an event of selecting one boy and two girls, then $P(E)$ is equal to

The straight line passing through the points $(3,2,3)$ and $(5,-1,-2)$ is perpendicular to the straight line passing through the points $(1,3,1)$ and $(\alpha, \alpha, \alpha)$. Then the value of $\alpha$ is equal to

The shortest distance from the point $(-10, 10, -10)$ to the $z$-axis, is

A unit vector parallel to the straight line $\vec{r} = -(5 + 4s)\hat{i} + (7 - 2s)\hat{j} + (3 + 4s)\hat{k}$, where $s$ is the parameter of the line, is

If the straight line passing through the points $(1,-1,2)$ and $(3,2,8)$ makes angle $\beta$ with the $y$-axis, then the value of $\cos \beta$ is equal to

Let $P(2, 1, -3)$ be a given point. If the point $Q$ is such that $\vec{PQ} = 3\hat{i} - \hat{j} + 5\hat{k}$, then the distance of $Q$ from the origin $O$ is

If $\vec{a} = 4\hat{i} + \lambda \hat{j} - 6\hat{k}$ and $\vec{b} = -6\hat{i} + 12\hat{j} + 9\hat{k}$ are collinear, then the value of $\lambda$ is equal to

Let $\theta$ be the angle between the unit vectors $\hat{a}$ and $\hat{b}$. If $|\hat{a} - \hat{b}| = \frac{\sqrt{3}}{2}$, then the value of $\cos \theta$ is

The position vectors of the points $A$ and $B$ are $\vec{a} = 2\hat{i} - \lambda \hat{j} + 5\hat{k}$ and $\vec{b} = \mu \hat{i} + 7\hat{j} + 3\hat{k}$ respectively. If the position vector of the mid-point of the line segment $AB$ is $\vec{c} = 3\hat{i} + 2\hat{j} + 4\hat{k}$, then the value of $\lambda + \mu$ is equal to

If the distance between the foci of an ellipse is 4 and its eccentricity is $\frac{1}{2}$, then the length of its latus rectum is

The vertex of the parabola $2y = -3x^2 + 48x - 200$, is

If the foci of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ coincide with the foci of the ellipse $\frac{x^2}{49} + \frac{y^2}{36} = 1$, then the value of $a^2 + b^2$ is equal to

The area of the circle $x^2 + y^2 + 8x - 6y + c = 0$ is $75\pi$. Then the value of $c$ is equal to

The straight line passing through the points $(1, 5)$ and $(3, -5)$ meets the coordinate axes at the points $A$ and $B$. Then the area of the triangle $\triangle OAB$, where $O$ is the origin, is

If the equation of the straight line passing through the points $(3, -4)$ and $(4, a)$ is $x - y = 7$, then the value of $a$ is equal to

Let $O$ be the origin and $P$ be a point on a line such that $OP$ is perpendicular to that line. If $OP$ makes an obtuse angle $\alpha$ with the $x$-axis, $OP = 5$ and $\sin \alpha = \frac{3}{5}$, then the equation of the line is

The point $P(\frac{1}{6}, \alpha)$, where $\alpha$ is a constant, lies on the curve with equation $\sin^{-1}(3x) + 2\sin^{-1}(y) = \frac{\pi}{2}, |x| \leq \frac{1}{3}, |y| \leq 1$, then the value of $\alpha$ is equal to

If $2\cot^{-1}(\frac{4}{3}) = \cos^{-1}(\frac{x}{5})$, then the value of $x$ is equal to