List of top Questions asked in KEAM

Electrostatic force is maximum when charge \( Q \) is placed at ------?
Find the standard deviation of the numbers: -3, 0, 3, 8.
What is the maximum wavelength to excite a hydrogen atom?
Which among the following acts as a Lewis acid? \[ A) \text{AlCl}_3, \quad B) \text{NH}_3, \quad C) \text{OH}^-, \quad D) \text{H}_2\text{O} \]
Given that \( \vec{a} \parallel \vec{b} \), \( \vec{a} \cdot \vec{b} = \frac{49}{2} \), and \( |\vec{a}| = 7 \), find \( |\vec{b}| \).
Which of the following has the highest \( K_b \) value?
What is the formula of lanthanoids with sulfur?
Fehling's solution is a mixture of:
A body of mass 0.8kg moves with velocity \( v = 2x^2 + 2 \, \text{m/s} \). What is the work done during its motion from \( x = 0 \) to \( x = 2 \, \text{m} \)?
The ratio of the angular speed of the minute hand to the second hand of a watch is?
A solid sphere, hollow sphere, and solid cylinder start sliding from an inclined plane without rolling. Then the ratio of time taken by them to reach the ground is?
If the half-life of \( D \) is 1500 years and \( B \) is 2000 years, what is the mean lifetime?
A body of mass 0.8kg moves with velocity \( v = 2x^2 + 2 \, \text{m/s} \). What is the work done during its motion from \( x = 0 \) to \( x = 2 \, \text{m} \)?
If the frequency of the cyclotron is doubled, then the radius becomes?
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 \( x \).
How can we decrease the effective capacitance of a parallel plate capacitor?
De Broglie wavelength of a quantum photon having energy \( E \)?
Given the system of equations: \[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] Find \( |Z| \).
If \( Z = \frac{2 - i}{\alpha + i} \) and \( 4 \, \text{Re}(Z) = 3 \, \text{Im}( \overline{Z} ) \), find \( \alpha \).
Find the value of \( Z^2 \) if \( Z = \left( 1 + \frac{1}{i} \right) \).
Find the equation of the circle touching the x-axis at \( (9, 0) \) and the line \( y = 14 \).
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 limit: \[ \lim_{x \to \infty} \frac{\sqrt{\cos^2 x + 3} - \sqrt{\cos^2 x + \sin x + 3}}{x} \]
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).