IIT-JEE 2008 Paper 2 Offline

A radioactive sample S1 having activity of 5 \(\mu\)Ci has twice the number of nuclei as another sample S2 which has an activity of 10 \(\mu\)Ci. The half lives of S1 and S2 can be :

Consider a system of three charges \({q \over 3},{q \over 3}\) and \(- {{2q} \over 3}\) placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60\(^\circ\)

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is \(\frac{d}{3}\) initially. Suppose the liquid level decreases at a constant speed V, the tim...

STATEMENT 1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT 2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given ...

The electric field at r = R is :

For a = 0, the value of d (maximum value of \(\rho\) as shown in the figure) is

The electric field within the nucleus is generally observed to be linearly dependent on r. This implies

A light beam is travelling from Region I to Region IV
(Refer figure). The refractive index in Regions I, II, III and IV are \({n_0},{{{n_0}} \over 2},{{{n_0}} \over 6}\) and \({{{n_0}} \over 8}\), respectively. The angle of incidence $$\t...

An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images fro...

Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 ma...

STATEMENT 1 : It is easier to pull a heavy object than to push it on a level ground.
and
STATEMENT 2 : The magnitude of frictional force depends on the nature of the two surfaces in contact.

STATEMENT 1 : The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
and
STATEMENT 2 : Soft iron has a high magnetic permeability and cannot be easily magnetized or dema...

STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the
opposite direction to the train, while the distant objects appear to be stationary.
STATEMENT-2: If the observer an...

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as s...

The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is :

The centre of mass of the disk undergoes simple harmonic motion with angular frequency \(\omega\) equal to:

The maximum value of V\(_0\) for which the disk will roll without slipping is:

Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column I...

A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the waves is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The ...

A vibrating string of certain length 1 under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per seco...

A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have ne...

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle \(\theta\) at which the speed of the bob is half of that at A, satisfies,