List of top Questions asked in KEAM

Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)
Evaluate: \[ \sec \left( \cos^{-1} \left( \frac{2024}{2025} \right) \right) \]
When a rotating disc suddenly shrinks in radius, what happens to the angular velocity \( \omega \)?
Which of the following is an ambidentate ligand? a) \( \text{C}_2 \text{O}_4^{2-} \) b) \( \text{CN}^- \) c) \( \text{NH}_3 \)
Maximum magnetic moment shown by:
A guitar string is vibrating in the third harmonic. The number of nodes and antinodes present are:
Given that \( a, \frac{3}{4} a r^2, a r^3 \) are in G.P. Product of first four terms = \( \frac{3^6}{4^3} \), then find \( a \):
A rod of length 0.5 m moves with a velocity of 3 m/s in a perpendicular magnetic field of strength 2 T. Find the emf induced across its ends.
The tennis ball of mass 120 g moving with a velocity of 20 m/s towards gets by a rocket of velocity and the final speed becomes 30 m/s with direction reversed. If the time of contact is 0.01 s, what is the average force acting on the ball?
Which of the following contains 2 primary –OH groups in its structure?
Find the limit: \[ \lim_{x \to 0} \frac{\sin[x]}{[x]}, \text{ where } [x] \text{ represents greatest integer function} \]
What is the potential energy of an object of mass \( m \) placed on the surface of the Earth? (Mass of Earth = \( M \), radius of Earth = \( R \))
Molecule with 2\( \sigma \) and 2\( \pi \) bonds:
10 g of (90 percent pure) \( \text{CaCO}_3 \), treated with excess of HCl, gives what mass of \( \text{CO}_2 \)?
The center of mass of a rod of length \( l \) is at a distance ______ from one end of the rod.
The temperature of the source and sink of a heat engine are 127°C and 27°C respectively. By how much should the temperature of the source be increased so as to double the efficiency?
The most basic oxide
Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]
Water flows through a pipe with velocity \( V_1 = 3 \, \text{m/s} \) where the area of the pipe is \( A_1 \). What is the velocity \( V_2 \), where the diameter of the pipe is half of that at area \( A_1 \)?
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?
Friedel Craft's reaction is an example of:
Benzene when treated with Br\(_2\) in the presence of FeBr\(_3\), gives 1,4-dibromobenzene and 1,2-dibromobenzene. Which type of reaction is this?
Equation of line through (0, 0, 1) and (1, 1, 0)
Electric field lines around a positive charge are directed:
The acceleration of a particle varies with time as \( a = 6t \). What is the displacement and velocity of the particle at \( t = 4s \)?