List of top Questions asked in KEAM

Brewster's angle should lie between?
If \( -5<x \leq -1 \), then \( -21 \leq 5x + 4 \leq b \). Find \( b \).
The velocity is given as \( \mathbf{v} = 3\hat{i} + 3\hat{j} \). Find the acceleration \( \mathbf{a} \).
Work done on splitting a spherical drop into 8 droplets?
A cylindrical vessel contains 16 kg at 1 atm. A certain amount of substance is taken out so that pressure becomes 0.7 atm. Find the amount taken out (in kg).
Which among the following has the highest molar elevation constant?
De Broglie wavelength of a quantum photon having energy \( E \)?
If the frequency of the cyclotron is doubled, then the radius becomes?
Given the function \( F(x) = |\sin(3x)| - \cos(3x) \), for \( \frac{\pi}{6} \leq x \leq \frac{\pi}{3} \), find \( f' \left( \frac{\pi}{4} \right) \).
In an equilateral triangle with each side having resistance \( R \), what is the effective resistance between two sides?
Solve the system of equations: \[ \begin{bmatrix} 4 & 9 \\ 12 & -3 \\ 8 & -2 \end{bmatrix} \begin{bmatrix} 7 \\ 9 \end{bmatrix} = \begin{bmatrix} \alpha \\ \beta \end{bmatrix} \]
Given the function \( h(x) = f(g(x)) \), where \( f(x) = f'(x) = 3 \), and \( g(x) = 9 \), find \( g'(3) \), \( f'(3) \), and \( h'(3) \).
\( M^0 L T^{-1} \) is the dimension of ___________?
The ratio of the angular speed of the minute hand to the second hand of a watch is?
Number of sigma and pi bonds in methyl but-1-ene is:
What is the order of the SN2 reaction for the compounds: \[ \text{2-methyl-2-bromo-butene}, \quad \text{2-bromo-butene}, \quad \text{1-bromo-butane} \]
The reaction shown is: \[ \text{Phenol} + \text{CHCl}_3 + \text{NaOH} \rightarrow \text{Salicylaldehyde} \] What is the name of the above reaction?
When toluene is treated with chromium oxide and acetic anhydride, followed by hydrolysis, what is the product formed?
Layer's test is used for what purpose?
What is the IUPAC name of phenyl isopentylether?
Relation between the drift velocity and an electric field is ----?
If \( f(x) = \sqrt{x - 3} + 4 \sqrt{5 - x} \), find the domain of \( f(x) \).
The inward electric flux through a closed surface is \( 6 \times 10^{-5} \) and the outward flux is \( 3 \times 10^{-5} \). Then the total charge enclosed is?
Given the system of equations: \[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] Find \( |Z| \).
Find the equation of the circle touching the x-axis at \( (9, 0) \) and the line \( y = 14 \).