List of top Questions asked in KEAM

Let $A(-1,\,2)$, $B(1,\,-2)$ and $C(-2,\,-2)$ be vertices of the triangle $ABC$. The equation of the line passing through $C$ and parallel to $AB$ is

\(x = \frac{1 + \cos 2\theta}{\tan \theta - \sec \theta}\) and \(y = \frac{\tan \theta + \sec \theta}{\sec^2 \theta}\), then \(\frac{y}{x} =\)

If \(\cos^{-1} x - \sin^{-1} x = \frac{\pi}{6}\), then \(x\) is equal to

\(\sin 60^{\circ} - \sin 80^{\circ} + \sin 100^{\circ} - \sin 120^{\circ} =\)

If the ratio of the Young's moduli and densities of two rods of different materials are respectively, \(3:2\) and \(3:1\), then the ratio of the velocities of sound in the rods is

If the heat supplied to an ideal gas is used up entirely to do work on the surrounding, then the process is called

Two particles A and B move in concentric circles with radii in the ratio \(2:1\). If for every completion of one circle of A, B completes 5 circles, then the ratio of their respective orbital velocities is

The amount of heat to be withdrawn from 3 kg of water at \(0^{\circ}C\) to obtain 3 kg of ice at \(0^{\circ}C\) in an icemaker is (latent heat of fusion of ice is \(80 \text{ kcal/kg}\))

The mean free path of a molecule is inversely proportional to

The product of the pressure P and volume V of an ideal gas in a container is related to the translational part of the internal energy, E as

If the period of a simple pendulum of length \(l\) is 5 seconds, then the period of the pendulum of length \(\frac{l}{4}\) is

Heat is conducted through a uniform rod ABC of length 1 m keeping the end A at \(100^{\circ}C\). If the temperature at the point B at a distance 0.4 m from the end A is \(80^{\circ}C\) and that at the other end C is \(40^{\circ}C\), then the ratio of heat conducted through AB to that through BC is

If a satellite of mass M is spinning about its own axis and revolves around the earth in a circular orbit, then it does not have

If the moment of inertia of a solid sphere of mass M and radius R about its diameter is I, then that of another sphere of mass 2M and radius 2R about its diameter is

If a black body at a temperature T radiates the maximum energy at a wavelength \(\lambda_{m}\), then to radiate the maximum energy at the wavelength \(\frac{\lambda_{m}}{3}\), its temperature should be

If the ultimate strength and fracture points are far apart in a stress - strain curve of a material, then the material is said to be

Four identical point masses are placed at the corners of a square ABCD and the centre of mass lies at the centre O of the square. If the mass at B is removed, then the centre of mass lies at the point

The ratio between the gravitational potential energies of 1 kg of mass on the surface of two planets having masses and radii in the ratio \(1 : 2\) and \(1 : 3\) respectively, is

If a ball of mass 0.02 kg bowled by a bowler straight to a batsman is hit back with the same speed with an impulse of 2 Ns, then the speed of the ball bowled is

If the kinetic energy of a moving body reduces to \(49\%\), then its velocity is reduced to

If \(f_{s}\) and \(f_{k}\) represent the coefficients of static friction and kinetic friction of the relative motion between two surfaces in contact with area A, then

The false statement is

With usual notations for a rigid body in rotational motion about a fixed axis, its

If a freely falling body from the top of a tower takes 3 s and 5 s to cross the \(28^{th}\) floor and \(4^{th}\) floor respectively, then the height difference between these floors is \((g = 10 \, \text{ms}^{-2})\)