List of top Questions asked in KEAM- 2025

Find the integral: \[ \int \left( \sin^{-1} \sqrt{x} + \cos^{-1} \sqrt{x} \right) \, dx \]
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 \( A_1 \)?
The most basic oxide
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?
Galvanometer can be converted into a voltmeter by connecting...
Given: \[ \frac{197}{96} X \to \frac{197}{95} Y + Z + V \quad \text{what is Z?} \]
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.
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?
Alkali metal with highest first ionization enthalpy is:
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?
Number of valence electrons in Germanium?
Relation between Azimuthal quantum number and magnetic quantum number
The center of mass of a rod of length \( l \) is at a distance ______ from one end of the rod.
The acceleration of a particle varies with time as \( a = 6t \). What is the displacement and velocity of the particle at \( t = 4s \)?
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?
When a rotating disc suddenly shrinks in radius, what happens to the angular velocity \( \omega \)?
Equation of line through (0, 0, 1) and (1, 1, 0)
Equation of line through (0, 0, 1) and (1, 1, 0)
Evaluate: \[ \sec \left( \cos^{-1} \left( \frac{2024}{2025} \right) \right) \]
Find the center of the ellipse given by the equation \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]
Find the minimum of the function \[ f(x) = |x+2| \]
For an ideal gas of molar mass \( M \), the slope of the graph between the rms speed \( V \) and \( \sqrt{T} \) where \( T \) represents the temperature is...
Electric field lines around a positive charge are directed:
Axis of parabola is \( x = 0 \). If the vertex is at a distance of 3 from the origin above the x-axis, find the vertex.