An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ \(\times 10^{-1} \mathrm{~J}\).
(Take \(\pi=3.14\))

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in\(P-V\) diagram. The relation between the ratio \(\frac{V_a}{V_d}\) and the ratio \(\frac{V_b}{V_c}\) is _______.

A pendulum bob has a speed of \(3\, {m} / {s}\) at its lowest position. The pendulum is \(50 \,{cm}\) long. The speed of bob, when the length makes an angle of \(60^{\circ}\) to the vertical will be \( .......\,{m} / {s}\) \(\left(g=10 \,{m} / {s}^{2}\right)\)

Three identical resistors with resistance \(R=12 \Omega\) and two identical inductors with sell inductance \(L=5 mH\) are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _________ A.

A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is

An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

A \(750\, Hz,\) \(20\) \(V\) (rms ) source is connected to a resistance of \(100\, \Omega\) an inductance of \(0.1803\, H\) and a capacitance of \(10\mu ,\) \(F\) all in series. The time in which the resistance (heat capacity \(2 J /{ }^{\circ} C\) ) will get heated by \(10^{\circ} C\). (assume no \(105 s\) of heat to the surroundings) is close to\(.....s\)

The force of interaction between two atoms is given by \(F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);\) where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha \) and \(\beta \) are two constants. The dimension of \(\beta \) is

The work functions of Aluminium and Gold are \(4.1\,eV\) and \(5.1\,eV\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is \(.......\)

Given below are two statements: Statement \(I :\) \(PN\) junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement \(II :\) In the study of transistor, the amplification factor \(\beta\) indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer from the options given below :

In the given figure \(R_1=10 \Omega, R_2=8 \Omega, R_3=4 \Omega\) and \(R_4=8 \Omega\). Battery is ideal with emf \(12 \mathrm{~V}\). Equivalent resistant of the circuit and current supplied by battery are _______ respectively.