List of top Questions asked in KEAM

The most basic oxide
Pressure of pure benzene is 0.75. When 0.2g of a non-volatile solute is added to 39g of benzene, pressure changes to 0.745. The molar mass of solute is?
Find the range of \( f(x) = \log_e(4x^2 - 4x + 1) \)
If \( 5 \sin^{-1} \alpha + 3 \cos^{-1} \alpha = \pi \), then \( \alpha = ? \)
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?
Work done on splitting a spherical drop into 8 droplets?
If \( f(x) = \cos x \), find the following expression: \[ \frac{1}{2} \left[ f(x + y) + f(y - x) - f(x) \cdot f(y) \right] \]
What is the maximum wavelength to excite a hydrogen atom?
\( M^0 L T^{-1} \) is the dimension of ___________?
Find the focus of the parabola \( x^2 - 4x + 8y + 4 = 0 \).
Find the resistance required to be connected to a galvanometer of resistance \(100 \, \Omega\) with a full scale deflection of 1mA into a voltmeter of range 1V.
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 \( n_1, n_2, n_3 \)?
Find the domain of the composite function \( f \circ g(x) \) where \( f(x) = \log(5x) \) and \( g(x) = \cos(x) \).
Wave nature of light can be used to explain which phenomenon?
Relation between the drift velocity and an electric field is ----?
In a Carnot engine, efficiency is dependent on ________?
How can we decrease the effective capacitance of a parallel plate capacitor?
If \( Z = \frac{2 - i}{\alpha + i} \) and \( 4 \, \text{Re}(Z) = 3 \, \text{Im}( \overline{Z} ) \), find \( \alpha \).
If \(x + z = 2y\) and \(y = \frac{\pi}{4}\), what is \( \tan x \cdot \tan y \cdot \tan z \)?
If the half-life of \( D \) is 1500 years and \( B \) is 2000 years, what is the mean lifetime?
Given the system of equations: \[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] Find \( |Z| \).
Find the value of \( Z^2 \) if \( Z = \left( 1 + \frac{1}{i} \right) \).
Which among the following acts as a Lewis acid? \[ A) \text{AlCl}_3, \quad B) \text{NH}_3, \quad C) \text{OH}^-, \quad D) \text{H}_2\text{O} \]