List of top Questions asked in KEAM- 2025

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

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

$\sec^{2}x + \csc^{2}x - \sec^{2}x \csc^{2}x =$

Let $x$ be a real number such that $7x+4 < 9x+8$. Then the solution set of the inequality is:

Let $P=\begin{pmatrix}1 & 1 & 1 \\ 0 & 2 & 2 \\ 0 & 0 & 3\end{pmatrix}$ and $Q=\begin{pmatrix}2 & 1 & \frac{2}{3} \\ 0 & 4 & \frac{4}{3} \\ 0 & 0 & 6\end{pmatrix}$. Then $\det(QPQ^{-1})$ is equal to:

Let $A=\begin{pmatrix}1 & 3 & 5 \\ -6 & 8 & 3 \\ -4 & 6 & 5\end{pmatrix}$ and $P=\frac{1}{2}(A + A^T)$. Then:

Let $x$ be a real number such that $\frac{3(x+3)}{7} \le \frac{6(x-1)}{5}$. Then the solution set of the inequality is:

Let $B$ be a matrix of order $3 \times 2$ and $C$ be a matrix of order $3 \times 3$. If $A$ is a matrix such that $BA = C$, then the order of $A$ is

The constant term in $\left(\frac{\sqrt{x}}{2} + \frac{1}{3x^2}\right)^{10}$ is:

${}^{21}C_1 + {}^{21}C_2 + \dots + {}^{21}C_{10} =$

25 distinct objects are divided into 5 groups and each group consists of exactly 5 objects. Then the number of ways of forming such groups, is

The coefficient of $x^{10}$ in $(1-x^2)(1-x^3)^9$ is:

Let $G_1, G_2, G_3$ be geometric means between $l$ and $n$, where $l$ and $n$ are positive real numbers. Then the common ratio is

The sum of first $n$ terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2, then the value of $n$ is

$1 + {}^{100}C_1 + {}^{100}C_2 + \dots + {}^{100}C_{99} + 1 =$

The 25th term of $9, 3, 1, \frac{1}{3}, \frac{1}{9}, \ldots$ is:

The first three terms in a G.P. are $a, b$ and $c$ where $a \neq b$. Then the fifth term is:

Real part of $\frac{1+\sin\frac{2\pi}{27}-i\cos\frac{2\pi}{27}}{1+\sin\frac{2\pi}{27}+i\cos\frac{2\pi}{27}}$ is equal to:

Let $z$ be a complex number such that $z^{3}+iz^{2}-iz+1=0$ where $i^{2}=-1$. Then $|z|=$

Let $z=x+iy$ be a complex number, where $i=\sqrt{-1}$ is the complex unit. Then $|z-1+i|=5$ is a circle with:

The domain of the function $f(x)=\sqrt{x^{2}+x-2}$ is:

The range of the function $f(x)=\sqrt{x^{2}+4x+4}$ is:

Let $s, t, r$ be non-zero distinct positive real numbers. If the complex number $z=x+iy$ satisfies $sz+t\overline{z}+r=0$, then $z$ lies on:

If two sets A and B are having 11 elements in common, then the number of elements common to $A\times B$ and $B\times A$ is:

The relation \( R = \{(1,3), (2,3), (2,4), (3,1), (4,4), (4,1)\} \) on the set \( X = \{1,2,3,4\} \) is: