IIT-JEE 2011 Paper 1 Offline

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 \(\mathop A\limits^o\). The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

A \(2\) \(\mu F\) capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch \(S\) is turned to position \(2\) is

A meter bridge is set up as shown, to determine an unknown resistance X using a standard 10 \(\Omega\) resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm, respectively, for t...

The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10\(-\)25 kg. The mass (in mg) of the radioactive sample is _________.

Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side a. The surface tension of the soap film is \(\gamma\). The system of charges and planar film are in equilibrium, and $$a = k{\left[ {...

Consider an electric field \(\overrightarrow E = {E_0}\widehat x\) where \({E_0}\) is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A spherical metal shell A of radius \({R_A}\) and a solid metal sphere \(B\) of radius \({R_B}\left( { < {R_A}} \right)\) are kept far apart and each is given charge \(' + Q'.\) Now they are connected by a thin metal wire. Then

5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be
T1, the work done in the process is

Steel wire of lenght ‘L’ at 40oC is suspended from the ceiling and then a mass ‘m’ is hung from its free
end. The wire is cooled down from 40oC to 30oC to regain its original length ‘L’. The coefficient of linear
thermal expansion of the st...

A block is moving on an inclined plane making an angle \(45^\circ\) with the horizontal and the coefficient of friction is \(\mu\). The force required to just push it up the inclined plane is 3 times the force required to just
prevent it ...

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The
maximum possible value o...

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 \(\Omega\) and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of t...

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing
fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of
free e...

A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat Q flows only from lef...

A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R ( < L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached : (case A). The disc is not free to rotate abou...

A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.2 m/s2. The coefficient of friction between the ...

Four solid spheres each of diameter \(\sqrt 5\) cm and mass 0.5 kg are placed with their centers at the corners of
a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N \(\times\) 10−4
kg-m2, t...

The phase space diagram for a ball thrown vertically up from ground is

The phase space diagram for simple harmonic motion is a circle centred at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respect...

Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing
fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of
free e...

A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall
building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren
heard by the car driver is