Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through diode \(D _1\) in the circuit is ___________mA . (Assume all diodes in the given circuit are identical)

A particle moves such that its position vector \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}\) where \(\omega\) is a constant and \(t\) is time. Then which of the following statements is true for the velocity \(\overrightarrow{\mathrm{v}}(\mathrm{t})\) and acceleration \(\overrightarrow{\mathrm{a}}(\mathrm{t})\) of the particle

A square aluminium (shear modulus is \(25 \times 10^{9}\,Nm ^{-2}\) ) slab of side \(60\,cm\) and thickness \(15\,cm\) is subjected to a shearing force (on its narrow face) of \(18.0 \times 10^{4}\,N\). The lower edge is riveted to the floor. The displacement of the upper edge is \(.......\mu\,m\).

Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from O . The net magnetic field at O is:

A damped harmonic oscillator has a frequency of \(5\) oscillations per second. The amplitude drops to half its value for every \(10\) oscillations. The time it will take to drop to \(\frac{1}{1000}\) of the original amplitude is close to .... \(s\)

\(N\,moles\) of a diatomic gas in a cylinder are at a temperature \(T\). Heat is supplied to the cylinder such that the temperature remains constant but \(n\,moles\) of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?

When a potential difference \(V\) is applied across a wire of resistance \(R\), it dissipates energy at a rate \(W\). If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the same supply, the energy dissipation rate will become what?

For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

Match List - I with List - II.

List - I	List - II
(A) Young’s Modulus	(I) \(M L^{-1} T^{-1}\)
(B) Torque	(II) \(M L^{-1} T^{-2}\)
(C) Coefficient of Viscosity	(III) \(M^{-1} L^3 T^{-2}\)
(D) Gravitational Constant	(IV) \(M L^2 T^{-2}\)

Choose the correct answer from the options given below :

Two long current carrying thin wires, both with current \(I\), are held by insulating threads oflength \(L\) and are in equilibrium as shown in the figure, with threads making an angle '\(\theta\)' with the vertical. If wires have mass \(\lambda\) per unit length then the value of \(l\) is 
(\(g =\) gravitational acceleration)

A point charge \(q_1=4 q_0\) is placed at origin. Another point charge \(q_2=-q_0\) is placed at \(x =12\,cm\). Charge of proton is \(q_0\). The proton is placed on \(x\)-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is \(..........cm\).

A block of mass 1 kg , moving along x with speed \(\mathrm{v}_{\mathrm{i}}=10 \mathrm{~m} / \mathrm{s}\) enters a rough region ranging from \(\mathrm{x}=0.1 \mathrm{~m}\) to \(\mathrm{x}=1.9 \mathrm{~m}\). The retarding force acting on the block in this range is \(\mathrm{F}_{\mathrm{r}}=-\mathrm{kx} \mathrm{N}\), with \(\mathrm{k}=10 \mathrm{~N} / \mathrm{m}\). Then the final speed of the block as it crosses rough region is