List of top Questions asked in KEAM- 2025

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

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

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

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

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

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

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

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

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

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

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

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

The sum of the geometric series \(\sqrt{3}+\sqrt{12}+\sqrt{48}+\dots\) up to \(10\) terms is

The sum and difference of the arithmetic mean and the geometric mean of two positive integers are respectively, \(18\) and \(8\). Then the values of the two numbers are

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 \( z = \frac{3+i}{2-i} \), then \( z^{-1} \) is equal to

If \( z = 1 + i \tan \theta \), where \( \pi < \theta < \dfrac{3\pi}{2} \), then \( |z| \) is equal to

If \( f(x) = ax + bx^2 \), then the coefficient of \( x^3 \) in \( f(f(x)) \) is

If \(z\) is a complex number, then the minimum value of \(|z-2|+|z-4|\) is

Let \( A = \{x : x \text{ is a positive multiple of } 2 \text{ less than } 36\},\)
\(B = \{x : x \text{ is a positive multiple of } 3 \text{ greater than } 16\}, \text{ and }\)
\(C = \{x : x \text{ is a positive multiple of } 4 \text{ less than } 42\}. \text{ Then } (A \cap B) \cap C =\)

If \(f(x) = [2x]\), where \([x]\) denotes the greatest integer function in \(x\), then the image of \(\{-2.3, 2.9\}\) is

If \(n(A) = 8\), then the number of subsets of \(A\) which contain \(2\) or \(6\) elements is