The molar heats of fusion and vaporization of benzene are 10.9 and 31.0 kJ mol\(^{-1}\) respectively. The changes in entropy for the solid \(\rightarrow\) liquid and liquid \(\rightarrow\) vapor transitions for benzene are \(x\) and \(y\) J K\(^{-1}\) mol\(^{-1}\) respectively. The value of \(y(x)\) in J\(^2\) K\(^{-2}\) mol\(^{-2}\) is:
The volume of an ideal gas contracts from 10.0 L to 2.0 L under an applied pressure of 2.0 atm. During contraction, the system also evolved 90 J of heat. The change in internal energy (in J) involved in the system is (1 L·atm = 101.3 J):
Match the following elements with their correct classifications:
The graph shown below represents the variation of probability density, \( \Psi(r) \), with distance \( r \) of the electron from the nucleus. This represents:
If uncertainty in position and momentum of an electron are equal, then uncertainty in its velocity is:
The voltage gain and current gain of a transistor amplifier in common emitter configuration are respectively 150 and 50. If the resistance in the base circuit is 850 \(\Omega\), then the resistance in the collector circuit is:
One mole of radium has an activity of \( \frac{1}{6.3 \times 10^{37}} \) kilo curie. Its decay constant is:
The speed of the electron in a hydrogen atom in the \( n = 3 \) level is:
The ratio of the number of turns per unit length of two solenoids A and B is \(1:3\) and the lengths of A and B are in the ratio \(1:2\). If the two solenoids have the same cross-sectional area, the ratio of the self-inductances of the solenoids A and B is:
At a place where the magnitude of the earth's magnetic field is \(4 \times 10^{-5} \, T\), a short bar magnet is placed with its axis perpendicular to the earth's magnetic field direction. If the resultant magnetic field at a point at a distance of 40 cm from the center of the magnet on the normal bisector of the magnet is inclined at \(45^\circ\) with the earth's field, the magnetic moment of the magnet is:
Two long straight parallel conductors A and B carrying currents 4.5 A and 8 A respectively are separated by 25 cm in air. The resultant magnetic field at a point which is a distance of 15 cm from conductor A and 20 cm from conductor B is:
Three point charges \( +q, +2q, \) and \( +4q \) are placed along a straight line such that the charge \( +2q \) lies equidistant from the other two charges. The ratio of the net electrostatic force on charges \( +q \) and \( +4q \) is: