IIT-JEE 2010 Paper 2 Offline

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column...

To determine the half-life of a radioactive element, a student plots a graph of \(\ln \left| {{{dN(t)} \over {dt}}} \right|\) versus t. Here, \({{dN(t)} \over {dt}}\) is the rate of radioactive decay at time t. If the number of radioactive ...

A diatomic molecule has moment of inertia I. By Bohr's quantization condition, its rotational energy in the nth level (n = 0 is not allowed) is

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to \({4 \over \pi } \times {10^{11}}\) Hz. Then, the moment of inertia of CO molecule about its centre of mass is clos...

In a CO molecule, the distance between C (mass = 12 amu) and O (mass = 16 amu), where 1 amu \(= {5 \over 3} \times {10^{ - 27}}\) kg, is close to :

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)

A uniformly charged thin spherical shell of radius \(R\) carries uniform surface charge density of \(\sigma\) per unit area. It is made of two hemispherical shells, held together by pressing them with force \(F\) (see figure). \(F\) is pro...

A tiny spherical oil drop carrying a net charge \(q\) is balanced in still air with a vertical uniform electric field of strength \({{81\pi } \over 7} \times {10^5}\,\,V{m^{ - 1}}.\) When the field is switched off, the drop is observed to f...

A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

A large glass slab (\(\mu\) = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from \({{25} \over 3}\) m to \({{50} \over 7}\) m in 30 s. What is the speed of the object in km per hour?

Two transparent media of refractive indices $\mu_1$ and $\mu_3$ have a solid lens shaped transparent material of refractive index $\mu_2$ between them as shown in figures in Column II. A ray traversing these media is also shown in the figur...

A diatomic ideal gas is compressed adiabatically \({1 \over {32}}\) of its initial volume. If the initial temperature of the gas is Ti (in Kelvin) and the final temperature is a Ti, the value of \(a\) is

When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop...

When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop...

When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop...

A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating
in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the
wire is 50 N and the spee...

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the b...