List of top Questions asked in KEAM

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:
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:
A bullet of 10 g, moving at 250 m/s, penetrates 5 cm into a tree limb before coming to rest. Assuming uniform force being exerted by the tree limb, the magnitude of the force is:
A narrow single slit of width \( d \) is illuminated by white light. If the first minimum for violet light (\( \lambda = 4500 \, {Å} \)) falls at \( \theta = 30^\circ \), the width of the slit \( d \) in microns is (1 micron = \( 10^{-6} \) m):
Four hydrogen atoms combine to form an \( ^4_2He \) atom with a release of 26.7 MeV of energy. This is:
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:
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:
Threshold frequency for photoelectric effect from a metallic surface corresponds to a wavelength of 6000 \({Å}\). The photoelectric work function for the metal is \( h = 6.6 \times 10^{-34} \, {Js} \):
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:
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:
Let \( z \) be a complex number satisfying \( |z + 16| = 4|z + 1| \). Then:
Let \( X \) and \( Y \) be subsets of \( \mathbb{R} \). If \( f : X \rightarrow Y \) given by \( f(x) = -8(x + 5)^2 \) is one-to-one, then the codomain \( Y \) is:
If \( f(x) = \begin{cases} x^2 & \text{for } x < 0 \\ 5x - 3 & \text{for } 0 \leq x \leq 2 \\ x^2 + 1 & \text{for } x > 2 \end{cases} \), then the positive value of \( x \) for which \( f(x) = 2 \) is:
If A and B are two sets, such that A has 20 elements, \( A \cup B \) has 32 elements, and \( A \cap B \) has 10 elements, the number of elements in the set B is: