\(\left(P+\frac{a}{V^2}\right)(V-b)=R T\) represents the equation of state of some gases. Where \(P\) is the pressure, \(V\) is the volume, \(T\) is the temperature and \(a, b, R\) are the constants. The physical quantity, which has dimensional formula as that of \(\frac{b^2}{a}\), will be

In a series \(L R\) circuit with \(X_L=R\). power factor is \(P_1\). If a capacitor of capacitance \(C\) with \(X _{ C }= X _{ L }\) is added to the circuit the power factor becomes \(P _2\). The ratio of \(P_1\) to \(P_2\) will be :

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from \(300\, nm\) to \(400\, nm\). The decrease in the stopping potential is close to ................ \(V\) \(\left( {\frac {{hc}}{e} = 1240\,nm - V} \right)\)

The density and breaking stress of a wire are \(6 \times\) \(10^4 \mathrm{~kg} / \mathrm{m}^3\) and \(1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2\) respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is \(\frac{1^{\text {rd }}}{3}\) of the value on the surface of earth. The maximum length of the wire with breaking is _______ \(\mathrm{m}\) (take, \(\mathrm{g}=\) \(\left.10 \mathrm{~m} / \mathrm{s}^2\right)\)

From a solid sphere of mass \(M\) and radius \(R\) a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is _______.

To raise the temperature of a certain mass of gas by \(50^{\circ} C\) at a constant pressure, \(160\) calories of heat is required. When the same mass of gas is cooled by \(100^{\circ} C\) at constant volume, \(240\) calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal) \(?\)

In the following circuit, the reading of the ammeter will be : (Take Zener breakdown voltage \(=4 \mathrm{~V})\)

Given below are two statements: one is labelled as Assertion\((A)\) and the other is labelled as Reason \((R).\) \(Assertion\) \((A)\) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. \(Reason\) \((R)\) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

In a double -slit experiment, green light \(\left( {5303\,\mathop A\limits^o } \right)\) falls on a double slit having a separation of \(19.44\,\mu m\) and a width of \(4.05\,\mu m\). The number of bright fringes between the first and the second diffraction minima is

To measure the temperature coefficient of resistivity \(\alpha\) of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at \(25^{\circ} \mathrm{C}\) and resistance of the semiconductor arm is \(3 \mathrm{~m} \Omega\). Arm BC is cooled at a constant rate of \(2^{\circ} \mathrm{C} / \mathrm{s}\). If the galvanometer \(\mathrm{G}\) shows no deflection after \(10 \mathrm{~s}\), then \(\alpha\) is _______.

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross sectional areas at \(A\) is \(1.5\,cm ^2\), and \(B\) is \(25\,mm ^2\), if the speed of liquid at \(B\) is \(60\,cm / s\) then \(\left( P _{ A }- P _{ B }\right)\) is :(Given \(P _{ A }\) and \(P _{ B }\) are liquid pressures at \(A\) and \(B\) points.Density \(\rho=1000\,kg\,m ^{-3}\) \(A\) and \(B\) are on the axis of tube \(............\,Pa\)