In a carnot engine, the temperature of reservoir is \(527^{\circ} C\) and that of \(\operatorname{sink}\) is \(200 \; K\). If the workdone by the engine when it transfers heat from reservoir to sink is \(12000 \; kJ\), the quantity of heat absorbed by the engine from reservoir is \(\times 10^{6} \; J\)

Taking the wavelength of first Balmer line in hydrogen spectrum (\( n = 3\) to \(n = 2\) ) as \(660\,nm ,\) the wavelength of the \(2^{nd}\) Balmer line ( \(n =4\) to \(n = 2\) ) will be....\(nm\)

A copper rod of mass \(m\) slides under gravity on two smooth parallel rails, with separation \(l\) and set at an angle of \(\theta\) with the horizontal. At the bottom, rails are joined by a resistance \(R\). There is a uniform magnetic field \(B\) normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is

Two small spheres each of mass \(10 \,mg\) are suspended from a point by threads \(0.5 \,m\) long. They are equally charged and repel each other to a distance of \(0.20 \,m\). The charge on each of the sphere is \(\frac{ a }{21} \times 10^{-8} \, C\). The value of \(a\) will be ...... . \(\left[\right.\) Given \(\left.g=10 \,ms ^{-2}\right]\)

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from \(27^{\circ} C\) to \(87^{\circ} C\).
The rate of consumption of the gas is ___________ \(g / s\).
(Take heat of combustion of gas \(=5.0 \times 10^4 J / g\) ) specific heat capacity of water \(=4200 J / kg.~{ }^{\circ} C\)

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 _______.

A gas is compressed adiabatically, which one of the following statement is NOT true.

Two projectiles are thrown with same initial velocity making an angle of \(45^{\circ}\) and \(30^{\circ}\) with the horizontal respectively. The ratio of their respective ranges will be.

The equation of state for a gas is given by \(PV = nRT + \alpha V\), where \(n\) is the number of moles and \(\alpha \) is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are \(T_o\) and \(P_o\) respectively. The work done by the gas when its temperature doubles isobarically will be

A conductor lies along the \(z-\)axis \(a\) \(-1.5\)\( \le Z < 1.5\,m\) carries a fixed current of \(10.0\ A\) in \( - {\hat a_z}\) direction (see figure). For a field \(\vec B\) \(=\) \(3.0 \times  10^{-4}\)  \(e^{-0.2x}\) \({\hat a_y}\,T\) find the power required to move the conductor at constant speed to \(x = 2.0\ m, y = 0\ m\) in \(5 \times 10^{-3}\ s\). Assume parallel motion along the \(x-\)axis........\( W\)

A photo-emissive substance is illuminated with a radiation of wavelength \(\lambda_i\) so that it releases electrons with de-Broglie wavelength \(\lambda_e\). The longest wavelength of radiation that can emit photoelectron is \(\lambda_0\). Expression for de-Broglie wavelength is given by :
( \(\mathrm{m}:\) mass of the electron, \(\mathrm{h}:\) Planck's constant and \(c\) : speed of light)

A deviation of \(2^{\circ}\) is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are \(0.02\) and \(0.03\) respectively and refractive index for yellow light for these glasses are \(1.5\) and \(1.6\) respectively. The refracting angles for crown glass prism will be \(........\,^{\circ}\) (in degree) (Round off to the Nearest Integer)