A heat source at \(T = 10^3\, K\) is connected to another heat reservoir at \(T = 10^2\, K\) by a copper slab which is \(1\, m\) thick. Given that the thermal conductivity of copper is \(0.1\, WK^{-1}\, m^{-1}\), the energy flux through it in the steady state is ........... \(Wm^{-2}\)

A sample of an ideal gas is taken through the cyclic process \(ABCA\) as shown in figure. It absorbs, \(40\,J\) of heat during the part \(A B\), no heat during \(BC\) and rejects \(60\,J\) of heat during \(CA\). \(A\) work \(50\,J\) is done on the gas during the part \(BC\). The internal energy of the gas at \(A\) is \(1560\,J\). The work done by the gas during the part \(CA\) is.............\(J\)

The Boolean expression \(\mathrm{Y}=\mathrm{A} \overline{\mathrm{B}} \mathrm{C}+\overline{\mathrm{A}} \overline{\mathrm{C}}\) can be realised with which of the following gate configurations.
A. One 3-input AND gate, 3 NOT gates and one 2input OR gate, One 2-input AND gate,
B. One 3-input AND gate, 1 NOT gate, One 2input NOR gate and one 2-input OR gate
C. 3-input OR gate, 3 NOT gates and one 2-input AND gate
Choose the correct answer from the options given below.

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification \( m_{1} \), when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to \( m_{2} \).
The value of \(\left|\frac{m_1}{m_2}\right|\) is __________ .

Two blocks of masses \(10 \; kg\) and \(30 \; kg\) are placed on the same straight line with coordinates \((0,0) \; cm\) and \(( x , 0) \; cm\) respectively. The block of \(10 \; kg\) is moved on the same line through a distance of \(6 \; cm\) towards the other block. The distance through which the block of \(30 \; kg\) must be moved to keep the position of centre of mass of the system unchanged is

A disc of radius \(R\) and mass \(M\) is rolling horizontally without slipping with speed \(v\). It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is _______.

A total of \(48 \mathrm{~J}\) heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by \(2^{\circ} \mathrm{C}\). The work done by the gas is _______. (Given, \(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\).)

A uniform disc of radius \(R\) and mass \(M\) is free to oscillate about the axis \(A\) as shown in the figure. For small oscillations the time period is ______.
(\(g\) is acceleration due to gravity)

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of \(100\, V\). What should nearly be the ratio of their wavelengths ? \(\left( m _{ P }=1.00727\, u , m _{ e }=0.00055 \,u \right)\)

A boy of mass \(20\, kg\) is standing on a \(80\, kg\) free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing \(25\, m\) from a wall. If he walks \(10\, m\) on the cart towards the wall, then the final distance of the boy from the wall will be ........ \(m\)

1. A wire of resistance \( R \) and length \( L \) is cut into 5 equal parts. If these parts are joined in parallel, then the resultant resistance will be:

A stationary particle breaks into two parts of masses \(m_A\) and \(m_B\) which move with velocities \(v_A\) and \(V_B\) respectively. The ratio of their kinetic energies \(\left(\mathrm{K}_B: \mathrm{K}_{\mathrm{A}}\right)\) is _______.