JEE Advanced 2013 Paper 1 Offline

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in t...

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance \(C.\) The switch \({S_1}\) is pressed first to fully charge the capacitor \({C_1}\) and then released. The switch \({S_2}\) is then pressed to ...

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is ___________.

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 \(\times\) 108 ms\(-\)1. The final momentum of the object is

Two non-conducting solid spheres of radii \(R\) and \(2R,\) having uniform volume charge densities \({\rho _1}\) and \({\rho _2}\) respectively, touch each other. The net electric field at a distance \(2\) \(R\) from the center of the small...

A ray of light travelling in the direction \({1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} \right)\) is incident on a plane mirror. After reflection, it travels along the direction $${1 \over 2}\left( {\widehat i - \sqrt 3 \widehat j}...

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
one-third the size of the object. The wavelength of light inside the lens is \({2 \over 3}\) times the wavelength in free space. The ...

Two rectangular blocks, having identical dimensions, can be arranged in either configuration-I or configuration-II as shown in the figure. One of the blocks has thermal conductivity \(\kappa\) and the other 2\(\kappa\). The temperature di...

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their
partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their
densities is

A particle of mass m is projected from the ground with an initial speed u0 at an angle \(\alpha\) with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which...

A particle of mass M and positive charge Q, moving with a constant velocity \({\overrightarrow u _1} = 4\widehat i\) ms\(-\)1 enters a region of uniform static magnetic field, normal to the xy plane. The region of the magnetic field extends...

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another
horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces
at two ends, the ratio of the elo...

A solid sphere of radius R and density \(\rho\) is attached to one end of a mass-less spring of force constant k.
The other end of the spring is connected to another solid sphere of radius R and density 3\(\rho\). The complete
arrangement...

A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s-1
about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m,
are gently placed symmetrica...

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero
of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions
equivalent to 2.45 cm...

In the Young's double-slit experiment using a monochromatic light of wavelength \(\lambda\), the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation
y(x, t) = (0.01 m) sin[(62.8 m\(-\)1)x] cos[(628 s\(-\)1)t]
Assuming \(\pi\) = 3.14, the correct statement(s) is(are)

A bob of mass m, suspended by a string of length l1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of leng...

The work done on a particle of mass m by a force
\($K\left[ {{x \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat i + {y \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat j} \right]\)$
(K being a constant of appropriate dime...

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to
the particle. If the initial speed (in m/s) of the particle is zero, the speed (in m/s) after 5 s is