IIT-JEE 2012 Paper 1 Offline

For the resistance network shown in the figure, choose the correct option(s).

A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is ___...

A circular wire loop of radius R is placed in the xy plane centred at the origin O. A square loop of side a(a << R) having two turns is placed with its centre at z = \(\sqrt3\)R along the axis of the circular wire loop, as shown in the figu...

An infinitely long solid cylinder of radius R has a uniform volume charge density \(\rho\). It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at ...

A cubical region of side \(a\) has its center at the origin. It encloses three fixed point charges, \(-q\) at \(\left( {0, - a/4,0} \right), + 3q\) at \(\left( {0,0,0} \right)\) and \(-q\) at \(\left( {0, + a/4,0} \right).\) Choose the corr...

Consider a thin spherical shell of radius \(R\) with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field \(\left| {\overrightarrow E \left( r \right)} \right|\) and th...

Two large vertical and parallel metal plates having a separation of \(1\) \(cm\) are connected to a \(DC\) voltage source of potential difference \(X\). A proton is released at rest midway between the two plates. It is found to move at $${4...

A biconvex lens is formed with two planoconvex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both curved surface are of the same radius of curvature R = 14 cm. For this biconv...

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductively. The first and third plates are maintained at temperatures 2T and 3T, respec...

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $$\left( {{{{v_{rms}}\left( {helium} \right)} \over {{v_{rms}}\left( {\arg ...

A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle \(\theta\) with the horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure. The block remains stationary ...

Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields \(\overrightarrow E = {E_0}\widehat j\) and \(\overrightarrow B = {B_0}\widehat j\). At time t = 0, this charge has ve...

A cylinder cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field...

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the xy-plane with centre at O and constant angular speed \(\omega\). If the angular momentum of ...

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed \(\omega\), as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v, with respect to the rod towar...

A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is IO and IP respectively. Bo...

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and releas...

In the determination of Young's modulus \(\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)\)
by using Searle's method, a wire of length L = 2 m
and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length o...

Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe widths recorded are \(\beta\)G, \(\beta\)R and \(\beta\)B, respectively. Then,