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

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

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

The mean free path of a molecule is inversely proportional to

The amount of heat to be withdrawn from 3 kg of water at \(0^{\circ}C\) to obtain 3 kg of ice at \(0^{\circ}C\) in an icemaker is (latent heat of fusion of ice is \(80 \text{ kcal/kg}\))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 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 heat supplied to an ideal gas is used up entirely to do work on the surrounding, then the process is called

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

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

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

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

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

The false statement is

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

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

The velocity of a swimmer in the direction of flow of river is \(10 \, \text{kmh}^{-1}\) and that against the flow of river is \(6 \, \text{kmh}^{-1}\). The velocity of the swimmer in still water in \(\text{kmh}^{-1}\) is