List of top Questions asked in KEAM

When \( y = vx \), the differential equation \[ \frac{dy}{dx} = \frac{y}{x} + \frac{f\left( \frac{y}{x} \right)}{f'\left( \frac{y}{x} \right)} \] reduces to:
If \[ \begin{vmatrix} x & 2 & -1 \\ 1 & x & 5 \\ 3 & 2 & x \end{vmatrix} = 0, \quad \text{then the real value of} \quad x \quad \text{is:} \]
The electric field intensity due to an ideal dipole at a distance \( r \) from its center on the axial point is directly proportional to:
The ratio of the respective rms velocities of the gas molecules of an ideal gas at 327°C and at 627°C is:
Simplify the following expression: \[ \frac{\sin 7x + \sin 5x}{\cos 7x + \cos 5x} \] The simplified form is:
If a body is taken above the surface of the Earth, it loses its weight by 20% at a height of \( h = \frac{\sqrt{5}}{2} R \), where \( R \) is the radius of the Earth, then:
The equipotential surface is:
A man fires bullets at two hillocks, one shorter and the other taller. The taller one is behind the smaller one. If the first echo is heard after 6 s and the second echo after 12 s, then the distance between the hillocks is (velocity of sound in air = 330 m/s):
The shortest distance between the parallel straight lines \[ \overrightarrow{r_1} = \hat{k} + s(\hat{i} + \hat{j}), \quad t, s \in \mathbb{R} \quad {and} \quad \overrightarrow{r_2} = \hat{j} + t(\hat{i} + \hat{j}), \] is:
The value of \( \int_{-4}^{-2} \left[ (x+3)^3 + 2 + (x+3)\cos(x+3) \right] \, dx \) is equal to:
Variance of 6, 7, 8, 9 is
If a particle executing simple harmonic motion with period \( T \) and displacement \( x = A \cos(\omega t) \), then the acceleration and velocity of the particle at the time \( t = \frac{T}{2} \) are respectively:
Which of the following aqueous mixture is a buffer solution?
The analogy between linear motion and rotational motion are given. The FALSE one is:
The common point of the two straight lines \[ \overrightarrow{r_1} = (i - 2j + 3k) + s(2i + j + k) \quad {and} \quad \overrightarrow{r_2} = (-i + 2j + 7k) + t(i + j + k), \quad t, s \in \mathbb{R} \] is:
Simplify the following expression: \[ \cos 18^\circ \cos 42^\circ \cos 78^\circ. \] The simplified form is:
In an LCR resonance circuit at resonance frequency \( \omega_0 \), the quality factor \( Q \) is:
The symmetric form of the equation of the straight line \[ \overrightarrow{r} = \hat{i} + t \hat{j}, \quad t \in \mathbb{R}, \] is:
The work done by a source in taking unit charge from lower to higher potential energy is called the source's:
The ratio of the velocities of the electron in the second, third and fourth Bohr’s orbits of the hydrogen atom is:
Evaluate the sum \[ \sum_{n=1}^{24} \left( i^n + i^{n+1} \right) \] is:
Some enzyme catalysed reactions which occur at metal surfaces are:
The integral \( \int (x^4 - 8x^2 + 16x)(4x^3 - 16x + 16) \, dx \) is:
The length of the latus rectum of the parabola \( y^2 = x \) is:
For the flow of incompressible liquid through a pipe, the Venturi-meter is used to measure the: