List of top Questions asked in KEAM- 2025

$\lim_{\theta\rightarrow 0}\frac{\theta \sin 2\theta}{1-\cos 2\theta} =$

An integer is chosen from the first 100 positive integers. Probability that the chosen number is a multiple of 11 is:

An unbiased die is thrown and B is an event showing an odd number on top. Then $P(B)$ is:

The standard deviation of 1, 2, 3, ..., 100 is:

The Cartesian equation of the line $\vec{r}=(2\hat{i}-7\hat{j}+11\hat{k})+\lambda(3\hat{i}+7\hat{j}-13\hat{k})$ is:

The point at which the line $\frac{x+3}{11}=\frac{y-2}{-1}=\frac{z+1}{3}$ meets the $zx$-plane is:

$\vec{a}, \vec{b}, \vec{c}, \vec{d}$ be non-zero vectors such that $\vec{a}\times\vec{b}=\vec{c}\times\vec{d}$ and $\vec{a}\times\vec{c}=\vec{b}\times\vec{d}$. Then:

Which one of the following is a point on the straight line $\vec{r}=(13\hat{i}-14\hat{j}+23\hat{k})+\lambda(5\hat{i}-7\hat{j}-9\hat{k})$?

Let $\vec{OP}=2\hat{j}$ be the position vector of a point $P$. Let $\vec{r}=\hat{j}+\lambda(\hat{i}+\hat{j})$ be a straight line. The distance of the point $P$ from the line is:

The mean deviation about the mean from the data 400, 410, 420, 430, 440 is:

Let $\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}-2\hat{k}$. Then $(\vec{a}+\vec{b}) \cdot (\vec{a}-\vec{b}) =$

If $\vec{a} \cdot \vec{b}=12$, then $(3\vec{a}) \cdot (3\vec{b})$ is equal to:

The eccentricity of the hyperbola $\frac{(x-1)^{2}}{25}-\frac{(y+2)^{2}}{11}=1$ is:

Let $\vec{a}, \vec{b}, \vec{c}$ be any three vectors and $m, n$ be scalars. Which one of the following is not true?

Let $P$ be any point on the ellipse $4(x+2)^{2}+9(y-4)^{2}=144$. If $F_{1}$ and $F_{2}$ are the foci of the ellipse, then $F_{1}P+F_{2}P=$

Let $y^{2}=8x$ be the equation of a parabola. Which one of the following is an arbitrary point on the parabola?

If $\tan^{-1}x = \tan^{-1}(3) - \frac{\pi}{4}$, then $x$ is equal to:

Let $ax+by+c=0$ be the equation of a straight line such that $3a+2b+4c=0$. Which one of the following points lies on the line?

If two diameters of a circle are along the lines $2x-3y=5$ and $3x-4y=7$, then the centre is at

If the distance of the line $4x-3y+k=0$ from the point (1, 2) is 5 units, then the values of k are

Two sides of a parallelogram are along the lines $x+y=5$ and $x-y=-5.$ If the diagonals of the parallelogram intersect at (3, 6) then one of its vertices is at

If $\sin^{-1}\left(\frac{x}{1+x}\right) = \frac{\pi}{2} - \cos^{-1}\left(\frac{1}{2}\right)$, then $x$ is equal to:

$\frac{(2 \sin \alpha)(1 + \sin \alpha)}{(1 + \sin \alpha + \cos \alpha)(1 + \sin \alpha - \cos \alpha)} =$

$\frac{\cos 75^{\circ} - \cos 15^{\circ}}{\cos 75^{\circ} + \cos 15^{\circ}} =$

$2^2 \sin(\frac{x}{2^2}) \cos(\frac{x}{2}) \cos(\frac{x}{2^2}) =$