JEE Advanced 2015 Paper 2 Offline

For a radioactive material, its activity A and rate of change of its activity R are defined as \(A = - {{dN} \over {dt}}\) and \(R = - {{dA} \over {dt}}\), where N(t) is the number of nuclei at time t. Two radioactive source P(mean life $...

A fission reaction is given by \(_{92}^{236}U \to _{54}^{140}Xe + _{38}^{94}Sr + x + y\), where x and y are two particles. Considering \(_{92}^{236}U\) to be at rest, the kinetic energies of the products are denoted by $${K_{Xe}},{K_{Sr}},{...

A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities (\(\varepsilon\)1 = 2 and \(\varepsilon\)2 = 4) are introduced between the two...

In the following circuit, the current through the resistor R(=2\(\Omega\)) is I amperes. The value of I is :

An electron in an excited state of Li2+ ion has angular momentum \({{3h} \over {2\pi }}\). The de Broglie wavelength of the electron in this state is p\(\pi\)a0 (where a0 is the Bohr radius). The value of p is

In terms of potential difference V, electric current I, permittivity \({\varepsilon _0}\), permeability \({\mu _0}\) and speed of light c,
the dimensionally correct equation(s) is(are) :

Consider a uniform spherical charge distribution of radius \({R_1}\) centred at the origin \(O.\) In this distribution, a spherical cavity of radius \({R_2},\) centred at \(P\) with distance \(OP=a\) \(= {R_1} - {R_2}\) (see figure) is mad...

For two structures namely S1 with n1 = \({{\sqrt {45} } \over 4}\) and n2 = \({3 \over 2}\), and S2 with n1 = \({8 \over 5}\) and n2 = \({7 \over 5}\) and taking the refractive index of water to be \({4 \over 3}\) and that to air to be 1, t...

If two structures of same cross-sectional area, but different numeral apertures NA1 and NA2 (NA2 < NA1) are joined longitudinally, the numerical aperture of the combined structure is

A monochromatic beam of light is incident at 60\(^\circ\) on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle \(\theta\)(n) with the normal (see figure). For n = \(\sqrt 3\) the valu...

A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to mo...

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. The gas is then heate...

Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n1 and n2, respectively. Strip 1 is placed in magnetic field B1 and strip 2 is placed in magnetic field B2, both ...

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w1 and w2 and thickness are d1 and d2, respectively. Two points K and M are symmetrically located on the opposite faces parallel t...

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then, the correct statements is/are

Two spheres P and Q for equal radii have densities \(\rho\)1 and \(\rho\)2, respectively. The spheres are connected by a massless string and placed in liquids L1 and L2 of densities \(\sigma\)1 and \(\sigma\)2 and viscosities \({\eta _1}\) ...

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r (r < R), then the correct option(s) is(are)

The densities of two solid spheres A and B of the same radii R vary with radial distance r as \({\rho _A}(r) = k\left( {{r \over R}} \right)\) and \({\rho _B}(r) = k{\left( {{r \over R}} \right)^5}\), , respectively, where k is a constant. ...

The energy of a system as a function of time t is given as E(t) = \({A^2}\exp \left( { - \alpha t} \right)\), where \(\alpha = 0.2\,{s^{ - 1}}\). The
measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 ...

Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, \({\pi \over 3},{{2\pi } \over 3}\) and \(\pi\). When they are superposed, the intensity of the resulting wave is nI0. The value of n is