In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to .................

In an \(n-p-n\) common emitter (\(CE\)) transistor the collector current changes from \(5\,mA\) to \(16\,mA\) for the change in base current from \(100\,\mu A\) and \(200\,\mu A\), respectively. The current gain of transistor is

A piston of mass \(M\) is hung from a massless spring whose restoring force law goes as \(\mathrm{F}=-\mathrm{kx}^3\), where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' \(n\) ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height \(\mathrm{L}_0\) to \(\mathrm{L}_1\), the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

A planet having mass \(9\,Me\) and radius \(4 R _e\), where Me and \(\operatorname{Re}\) are mass and radius of earth respectively, has escape velocity in \(km / s\) given by:(Given escape velocity on earth \(\left.V_e=11.2 \times 10^3\,m / s \right)\)

A parallel plate capacitor has \(1\,\mu F\) capacitance. One of its two plates is given \(+2\,\mu C\) charge and the other plate, \(+4\,\mu C\) charge. The potential difference developed across the capacitor is......\(V\)

\(300 \,cal\). 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____\({ }^{\circ} C\).

Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum)

The area bounded by the curve \(y=\left|x^{2}-9\right|\) and the line \(y=3\) is

\(n-\) \(moles\) of an ideal gas with constant volume heat capacity \(C_v\) undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

In an experiment on photoelectric effect, a student plots stopping potential \(V_0\) against reciprocal of the wavelength \(\lambda \) of the incident light for two different metals \(A\) and \(B\). These are shown in the figure Looking at the graphs, you can most appropriately say that

Let \(r_{1}\) and \(r_{2}\) be the radii of the largest and smallest circles, respectively, which pass through the point \((-4,1)\) and having their centres on the circumference of the circle \(x^{2}+y^{2}+2 x+4 y-4= 0.\) If \(\frac{r_{1}}{r_{2}}=a+b \sqrt{2}\), then \(a+b\) is equal to:

The mean and standard deviation of the marks of \(10\) students were found to be \(50\) and \(12\) respectively. Later, it was observed that two marks \(20\) and \(25\) were wrongly read as \(45\) and \(50\) respectively. Then the correct variance is \(............\).

\(10\) divisions on the main scale of a Vernier calliper coincide with \(11\) divisions on the Vernier scale. If each division on the main scale is of \(5\) units, the least count of the instrument is _______.