List of top Questions asked in KEAM

In an LCR circuit, at resonance, the value of the power factor is:
Focal length of a convex lens of refractive index 1.5 is 3 cm. When the lens is immersed in water of refractive index \( \frac{4}{3} \), its focal length will be:
An electromagnetic wave is propagating in a medium with velocity \( \vec{v} = v \hat{i} \). The instantaneous oscillating magnetic field of this electromagnetic wave is along positive \( z \)-direction. Then the direction of the oscillating electric field is in the:
The magnetic field at the centre of a circular coil having a single turn of the wire carrying current \( I \) is \( B \). The magnetic field at the centre of the same coil with 4 turns carrying the same current is:
Four hydrogen atoms combine to form an \( ^4_2He \) atom with a release of 26.7 MeV of energy. This is:
A particle is projected at an angle \( \theta \) with the x-axis in the xy-plane with a velocity \( \mathbf{v} = 6\hat{i} - 4\hat{j} \). The velocity of the body on reaching the x-axis again is:
A particle of mass 40 g executes simple harmonic motion with an amplitude of 2.0 cm. If the time period of oscillation is \( \frac{\pi}{20} \) s, the total mechanical energy of the system is:
When light is reflected from an optically rarer medium:
Threshold frequency for photoelectric effect from a metallic surface corresponds to a wavelength of 6000 \({Å}\). The photoelectric work function for the metal is \( h = 6.6 \times 10^{-34} \, {Js} \):
The dimensions of torque are:
A proton and a photon have the same energy. Then the de-Broglie wavelength of proton \( \lambda_p \) and wavelength of photon \( \lambda_0 \) are related by:
A current carrying square loop is suspended in a uniform magnetic field acting in the plane of the loop. If \( \vec{F} \) is the force acting on one arm of the loop, then the net force acting on the remaining three arms of the loop is:
A ball is thrown up vertically at a speed of 6.0 m/s. The maximum height reached by the ball (Take \( g = 10 { m/s}^2 \)) is:
If the displacement of a body moving on a horizontal surface is 151.25 cm in a time interval of 2.25 s, then the velocity of the body in the correct number of significant figures in cm s\(^{-1}\) is:
If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:
If \( B = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then the value of \( \alpha \) is:

If 

then the value of \( x - y \) is:

The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The numbers \( a, b, c, d \) are in G.P. with common ratio \( r \). If \( \frac{1}{a^3 + b^3} + \frac{1}{b^3 + c^3} + \frac{1}{c^3 + d^3} \) are also in G.P., then the common ratio is:
The second term of a G.P. is 4, then the product of the first three terms is:
If \( z_1 \) and \( z_2 \) are two complex numbers with \( |z_1| = 1 \), then \( \left| \frac{z_1 - z_2}{1 - z_1 \overline{z_2}} \right| \) is equal to:
If \( \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib \), then the values of \( a \) and \( b \) are, respectively: