List of top Questions asked in KEAM- 2025

Brewster's angle should lie between?
Find the rate constant at 310K if the initial concentration is 0.72 mol L$^{-1}$ and the final concentration is 1.44 mol L$^{-1}$ at 10 minutes.
What is the maximum wavelength to excite a hydrogen atom?
Arrange in the order of conductivity: \[ \text{Na, Ag, Fe, Cu} \]
Number of degrees of freedom for the monoatomic gas molecule is?
What technique is used to separate chloroform from aniline?
Common oxidation state of Cr?
In which of the following cases does manganese have a +7 oxidation state?
De Broglie wavelength of a quantum photon having energy \( E \)?
After a collision, two particles move together, then the collision is?
Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]
Relation between the drift velocity and an electric field is ----?
If the half-life of \( D \) is 1500 years and \( B \) is 2000 years, what is the mean lifetime?
The fundamental frequency of a string of length \( l \) is \( n \). The string is cut into 3 parts \( l_1, l_2, \) and \( l_3 \), each having fundamental frequency \( n_1, n_2, n_3 \). Then, what is the relationship between \( n_1, n_2, n_3 \)?
Given: \[ \sum_{k=0}^{5} \binom{10}{2k} = \alpha \quad \text{and} \quad \sum_{k=0}^{4} \binom{10}{2k+1} = \beta \] \text{Find the value of} \( \alpha - \beta \).
A planet revolves around the sun with a time period 27 times that of planet B. Planet A is at \( x \) times the distance of planet B from the sun. Find the value of \( x \).
Evaluate the integral: \[ \int_{\frac{\pi}{10}}^{\frac{2\pi}{5}} \frac{\cot^3 x}{1 + \cot^3 x} \, dx \]
If the frequency of the cyclotron is doubled, then the radius becomes?
The ratio of the angular speed of the minute hand to the second hand of a watch is?
Given the line equation \( Ax + By + C = 0 \), which passes through the point \( (-10, 7) \) and is perpendicular to the line \( 11x - 8y - 16 = 0 \), find \( C \).
Solve the system of equations: \[ \begin{bmatrix} 4 & 9 \\ 12 & -3 \\ 8 & -2 \end{bmatrix} \begin{bmatrix} 7 \\ 9 \end{bmatrix} = \begin{bmatrix} \alpha \\ \beta \end{bmatrix} \]
Evaluate the integral: \[ \int \frac{\sin^1 x}{\sqrt{1 - x^2}} \, dx \]
Find the equation of the circle touching the x-axis at \( (9, 0) \) and the line \( y = 14 \).
Evaluate the limit: \[ \lim_{x \to \infty} \frac{\sqrt{\cos^2 x + 3} - \sqrt{\cos^2 x + \sin x + 3}}{x} \]
If \(x + z = 2y\) and \(y = \frac{\pi}{4}\), what is \( \tan x \cdot \tan y \cdot \tan z \)?