A monoatomic gas at pressure \(P\) and volume \(V\) is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be \(.....P\)

Two long parallel conductors \(S_{1}\) and \(S_{2}\) are separated by a distance \(10 \,cm\) and carrying currents of \(4\, A\) and \(2 \,A\) respectively. The conductors are placed along \(x\)-axis in \(X - Y\) plane. There is a point \(P\) located between the conductors (as shown in figure). A charge particle of \(3 \pi\) coulomb is passing through the point \(P\) with velocity \(\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s\); where \(\hat{i}\) and \(\hat{j} \quad\) represents unit vector along \(x\) and \(y\) axis respectively. The force acting on the charge particle is \(4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N\). The value of \(x\) is

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\)

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \(P, V, T\). Heating is started from left side until pressure changes to \(\dfrac{27P}{8}\). If initial volume of each compartment was \(9\) litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas \(C_P/C_V = 1.5\))

A magnetic compass needle oscillates \(30\) times per minute at a place where the dip is \(45^o\), and \(40\) times per minute where the dip is \(30^o\). If \(B_1\) and \(B_2\) are respectively the total magnetic field due to the earth at the two places, then the ratio \(B_1/B_2\) is best given by 

On celcius scale the temperature of body increases by \(40^{\circ} \mathrm{C}\). The increase in temperature on Fahrenheit scale is _______.

Acceleration due to gravity on the surface of earth is ' \(g\) '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \(\ldots\ldots\) g.

Two liquids of densities \(\rho_{1}\) and \(\rho_{2}\left(\rho_{2}=2 \rho_{1}\right)\) are filled up behind a square wall of side \(10\; \mathrm{m}\) as shown in figure. Each liquid has a height of \(5 \;\mathrm{m} .\) The ratio of the forces due to these liquids exerted on upper part \(MN\) to that at the lower pait \(NO\) is (Assume that the liquids are not mixing)

In an ac generator, a rectangular coil of \(100\) turns each having area \(14 \times 10^{-2}\,m ^2\) is rotated at \(360\,rev / min\) about an axis perpendicular to a uniform magnetic field of magnitude \(3.0 T\). The maximum value of the emf produced will be \(............V\). \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\)

A capacitor of capacitance \(C\) is charged to a potential \(V\). The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is \(......\)

A coil of cross-sectional area  \(A\) having \(n\)  turns is placed in a uniform magnetic field \(B.\)  When it is rotated with an angular velocity \(\omega ,\)  the maximum \(e.m.f.\)  induced in the coil will be

A vector in \(x-y\) plane makes an angle of \(30^{\circ}\) with \(y\)-axis The magnitude of \(y\)-component of vector is \(2 \sqrt{3}\). The magnitude of \(x\)-component of the vector will be

A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\)