List of top Questions asked in KEAM

Given: \[ \sum_{k=0}^{5} \binom{10}{2k} = \alpha \quad \text{and} \quad \sum_{k=0}^{4} \binom{10}{2k+1} = \beta \] \text{Find the value of} $ \alpha - \beta $.

Given the line equation $ Ax + By + C = 0 $, which passes through the point $ (-10, 7) $ and is perpendicular to the line $ 11x - 8y - 16 = 0 $, find $ C $.

Find the domain of the composite function $ f \circ g(x) $ where $ f(x) = \log(5x) $ and $ g(x) = \cos(x) $.

Which of the following substitution reaction with methane requires HIO$_3$ as an oxidising agent?

Which of the following statement is incorrect?

Which of the following pair exhibits diagonal relationship?

The values of X, Y, and Z in the following chemical equation are respectively:
$ S_8 + X HNO_3 ({conc.}) \rightarrow Y H_2SO_4 + X NO_2 + Z H_2O $

The instantaneous displacement of a particle executing simple harmonic motion is given by $x = 2(\cos(\pi t) + \sin(\pi t))$.
The amplitude of oscillation is

The ratio of the maximum kinetic energy to the maximum potential energy of a bob of a simple pendulum executing small oscillations is

A block of mass 3 kg executes simple harmonic motion under the restoring force of a spring. The amplitude and the time period of the motion are 0.1 m and 3.14 s respectively. The maximum force exerted by the spring on the block is

A particle executes a linear SHM with an amplitude $a$ and angular velocity $\omega$. The ratio between its acceleration amplitude and displacement amplitude is

A particle is executing linear simple harmonic oscillation with an amplitude of $ A $. If the total energy of oscillation is $ E $, then its kinetic energy at a distance of $ 0.707A $ from the mean position is:

Radius of gyration $ K $ of a hollow cylinder of mass $ M $ and radius $ R $ about its long axis of symmetry is:

A projectile is given an initial velocity of $(\hat{i} + \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical direction. The equation of its trajectory is $(g = 10 \, \text{m/s}^2)$.

A projectile is projected with a velocity of $ 20 \, {ms}^{-1} $ at an angle of 45° to the horizontal. After some time its velocity vector makes an angle of 30° to the horizontal. Its speed at this instant (in $ {ms}^{-1} $) is:

Let $ x \text{ and } y $ be two positive real numbers. Then
\[ \left( x + \frac{1}{x} \right) \left( y + \frac{1}{y} \right) \] is greater than or equal to:

The type of processes represented by the curves X and Y are:

The work done by a source in taking unit charge from lower to higher potential energy is called the source's: