JEE ADVANCED 2017 PAPER 2 OFFLINE

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is \(\delta T = 0.01\) seconds and he measures the depth of the well to be \(L=20\) meters. Take the acceleration due to gravity \(g = 10m{s^{ - 2}}\) and the velocity of sound is \(300\) \(m{s^{ - 1}}\). Then the fractional error in the measurement, \(\delta L/L,\) is closest to

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant \(K\) in terms of change in entropy is described by

Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let N_k be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N₁ + N₂ + N₃ + N₄ + N₅ =

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density \(\rho\) remains uniform throughout the volume. The rate of fractional change in density \(\left( {{1 \over \rho } {{d\rho } \over {dt}}} \right)\) is constant. The velocity \(v\) of any point on the surface of the expanding sphere is proportional to

The standard state Gibbs free energies of formation of \(C\)(graphite) and \(C\)(diamond) at \(T=298\) \(K\) are

\({\Delta _f}{G^0}\) [\(C\)(graphite)] \(= 0kJmo{l^{ - 1}}\)

\({\Delta _f}{G^0}\) [\(C\)(diamond)] \(= 2.9kJmo{l^{ - 1}}\)

The standard state means that the pressure should be \(1\) bar, and substance should be pure at a given temperature. The conversion of graphite [\(C\)(graphite)] to diamond [\(C\)(diamond)] reduces its volume by \(2 \times {10^{ - 6}}\,{m^3}\,mo{l^{ - 1}}\) If \(C\)(graphite) is converted to \(C\)(diamond) isothermally at \(T=298\) \(K,\) the pressure at which \(C\)(graphite) is in equilibrium with \(C\)(diamond), is

[Useful information : \(1\) \(J=1\) \(kg\,{m^2}{s^{ - 2}};1\,Pa = 1\,kg\,{m^{ - 1}}{s^{ - 2}};\) \(1\) bar \(= {10^5}\) \(Pa\)]

Let \(\alpha\) and \(\beta\) be non zero real numbers such that \(2(\cos \beta - \cos \alpha ) + \cos \alpha \cos \beta = 1\). Then which of the following is/are true?