The kinetic energy of translation of the molecules in 50 g of \(\mathrm{CO}_2\) gas at \(17^{\circ} \mathrm{C}\) is

\(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\).

A capacitor C is first charged fully with potential difference of \( V_{0} \) and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In time t, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is

A source of sound \(A\) emitting waves of frequency \(1800\,Hz\) is falling towards ground with a terminal speed \(v.\) The observer \(B\) on the ground directly beneath the source receives waves of frequency \(2150\,Hz.\) The source \(A\) receives waves, reflected from ground of frequency nearly ..... \(Hz\) (Speed of sound \(= 343\,m/s\) )

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of \(\left[M^a L^b T^c\right]\). If \(b=-3\), the value of \(c\) is ________

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where \(\lambda\) is the decay constant)

A ray of light is incident from air on a glass plate having thickness \(\sqrt{3} \,cm\) and refractive index \(\sqrt{2}\). The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is \(.......\times 10^{-2}\) (given \(\sin 15^{\circ}=0.26\) )

A ray of light passing through a prism \((\mu=\sqrt{3})\) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ..... . (in degrees)

Two parallel long current carrying wire separated by a distance \(2 \mathrm{r}\) are shown in the figure. The ratio of magnetic field at \(\mathrm{A}\) to the magnetic field produced at \(C\) is \(\frac{x}{7}\). The value of \(x\) is _______.

Given below are two statements :
Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.
Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.

Two forces \(\vec{F}_1\) and \(\vec{F}_2\) are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between \(\vec{F}_1\) and \(\overrightarrow{\mathrm{F}}_2\) is \(\cos ^{-1}\left(\frac{1}{\mathrm{n}}\right)\). The value of \(|\mathrm{n}|\) is __________.