AIEEE 2005

The relation between time t and distance x is t = ax2 + bx where a and b are constants.
The acceleration is

A parachutist after bailing out falls \(50\) \(m\) without friction. When parachute opens, it decelerates at \(2\,\,m/{s^2}.\) He reaches the ground with a speed of \(3\) \(m/s\). At what height, did he bail out?

A \(20\) \(cm\) long capillary tube is dipped in water. The water rises up to \(8\) \(cm.\) If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

If \(S\) is stress and \(Y\) is young's modulus of material of a wire, the energy stored in the wire per unit volume is

The moment of inertia of a uniform semicircular disc of mass \(M\) and radius \(r\) about a line perpendicular to the plane of the disc through the center is

An annular ring with inner and outer radii \({R_1}\) and \({R_2}\) is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $${{{F_...

If a simple harmonic motion is represented by \({{{d^2}x} \over {d{t^2}}} + \alpha x = 0.\) its time period is

Two simple harmonic motions are represented by the equations \({y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \right)\) and \({y_2} = 0.1\,\cos \,\pi t.\) The phase difference of the velocity of particle \(1\) with respect to the velo...

The function \({\sin ^2}\left( {\omega t} \right)\) represents

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

Out of the following pair, which one does NOT have identical dimensions is

Two point white dots are \(1\) \(mm\) apart on a black paper. They are viewed by eye of pupil diameter \(3\) \(mm.\) Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light $$=5...

If \({I_0}\) is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

When an unpolarized light of intensity \({{I_0}}\) is incident on a polarizing sheet, the intensity of the light which does not get transmitted is

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?

When two tuning forks (fork \(1\) and fork \(2\)) are sounded simultaneously, \(4\) beats per second are heated. Now, some tape is attached on the prong of the fork \(2.\) When the tuning forks are sounded again, \(6\) beats per second are ...

A bullet fired into a fixed target loses half of its velocity after penetrating \(3\) \(cm.\) How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A body of mass \(m\) is accelerated uniformly from rest to a speed \(v\) in a time \(T.\) The instantaneous power delivered to the body as a function of time is given by

A spherical ball of mass \(20\) \(kg\) is stationary at the top of a hill of height \(100\) \(m\). It rolls down a smooth surface to the ground, then climbs up another hill of height \(30\) \(m\) and finally rolls down to a horizontal base...

The upper half of an inclined plane with inclination \(\phi\) is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half i...