List of top Questions asked in KEAM

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?
If \( n \) cells of emf \( E \) and internal resistance \( r \) are connected in parallel, what is the equivalent emf and internal resistance of the combination?
Find the \( \Delta G \) during the reaction: \[ \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{O}(g) \quad \Delta S = +1 \, \text{kJ/mol} \, \text{at} \, 100^\circ C \]
Evaluate the derivative of the function: \[ f(x) = x |x|, \quad \text{find} \quad f'(-10) \]
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 \( a \):
Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]
Evaluate the integral: \[ \int \frac{\cos \theta}{2 - \sin^2 \theta} \, d\theta \]
Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]
Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]
If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]
Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]
The center of mass of a rod of length \( l \) is at a distance ______ from one end of the rod.
\( E^\circ_{\text{Cell}} = 1.1 \, \text{V}. \, \text{Find} \, E_{\text{Cell}} \, \text{for the reaction:} \, \text{Zn} + \text{Cu}^{2+} \, (0.1M) \rightleftharpoons \text{Zn}^{2+} \, (0.001M) + \text{Cu} \)
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 \( A_1 \)?
Alkali metal with highest first ionization enthalpy is:
Find the integral: \[ \int \left( \sin^{-1} \sqrt{x} + \cos^{-1} \sqrt{x} \right) \, dx \]
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 = \( R \))
What is the ratio of de Broglie wavelength of the particles if their kinetic energy are 0.002 eV and 2 eV respectively?
If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]
Solution set of \( -12x > 38 \text{ for } x \in \mathbb{N} \) \[ -12x > 38 \]
In which of the following \( K_c = K_p \)? a) \( \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \) b) \( \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g) \)
Integrating factor of \[ \frac{dy}{dx} - 2y = 2x - 3 \]
Find the range of \( f(x) = \log_e(4x^2 - 4x + 1) \)
Name of the reaction in which benzoyl chloride is converted to benzaldehyde is