A gas mixture consists of \(8\) moles of argon and \(6\) moles of oxygen at temperature \(T\). Neglecting all vibrational modes, the total internal energy of the system is _______.

An ideal gas occupies a volume of \(2\, m^3\) at a pressure of \(3\times10^6\, Pa\). The energy of  the gas is

A cricket ball of mass \(0.15\, kg\) is thrown vertically up by a bowling machine so that it rises to a maximum height of \(20 \;m\) after leaving the machine. If the part pushing the ball applies a constant force \(F\) on the ball and moves horizontally a distance of \(0.2\, m\) while launching the ball, the value of \(F(\) in \(N)\) is  \(\left(g=10\, m s^{-2}\right)\)

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of \(0.8 \mathrm{~cm}^3\). If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was _______ litre. \(\left(\right.\) Take \(\left.1 \mathrm{~atm}=10^5 \mathrm{~Pa}\right)\)

The rms speed of oxygen molecule in a vessel at particular temperature is \(\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v\), where \(v\) is the average speed of the molecule. The value of \(x\) will be:(Take \(\pi=\frac{22}{7}\) )

An electric bulb is rated as \(200 \,W\). What will be the peak magnetic field (\(\times 10^{-8}\, T\)) at \(4\, m\) distance produced by the radiations coming from this bulb\(?\) Consider this bulb as a point source with \(3.5 \%\) efficiency.

An \(emf\) of \(0.08\,V\) is induced in a metal rod of length \(10\,cm\) held normal to a uniform magnetic field of \(0.4\,T\), when moves with a velocity of ...........\(ms^{-1}\)

One plano-convex and one plano-concave lens of same radius of curvature \(‘R’\) but of different materials are joined side by side as shown in the figure. If the refractive index of the material of \(1\) is \(\mu_1\) and that of \(2\) is \(\mu _2\), then the focal length of the combination is

A particle of mass \(M\) is moving in a circle of fixed radius \(R\) in such a way that its centripetal acceleration at time \(t\) is given by \(n^2Rt^2\) where \(n\) is a constant. The Power delivered to the particle by the force acting on it, is

The maximum and minimum distances of a comet from the Sun are \(1.6 \times 10^{12}\, m\) and \(8.0 \times 10^{10}\, m\) respectively. If the speed of the comet at the nearest point is \(6 \times 10^{4}\, ms ^{-1},\) the speed at the farthest point is ......... \(\times 10^{3}\, m / s\)

In the figure shown below, a resistance of \(150.4 \Omega\) is connected in series to an ammeter A of resistance \(240 \Omega\). A shunt resistance of \(10 \Omega\) is connected in parallel with the ammeter. The reading of the ammeter is _____ mA.

A bowl filled with very hot soup cools from \(98^{\circ}\,C\) to \(86^{\circ}\,C\) in \(2\) minutes when the room temperature is \(22^{\circ}\,C\). \(..........\,minutes\) long it will take to cool from \(75^{\circ}\,C\) to \(69^{\circ}\,C\) ?