Truth table for the given circuit will be

A vessel contains \(14\,g\) of nitrogen gas at a temperature of \(27^{\circ}\,C\). The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be \(......J\) \(\left(\right.\) Take \(R =8.32\,J\,mol ^{-1} k ^{-1}\) )

Two short magnetic dipoles \({m}_{1}\) and \({m}_{2}\) each having magnetic moment of \(1\, {Am}^{2}\) are placed at point \({O}\) and \(P\) respectively. The distance between \(OP\) is \(1\, meter.\) The torque experienced by the magnetic dipole \({m}_{2}\) due to the presence of \({m}_{1}\) is ...... \(\times 10^{-7}\, {Nm}\)

The recoil speed of a hydrogen atom after it emits a photon in going from \(n =5\) state to \(n =1\) state will be ..... \(m/s\)

The electric field in an electromagnetic wave is given by \(E =56.5 \sin \omega( t - x / c ) \;NC ^{-1}\). Find the intensity of the wave if it is propagating along \(x-\)axis in the free space. (Given \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \;C ^{2} N ^{-1} m ^{-2}\right)\)

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is \(20 cm / s\). The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _________ \(cm / s\).

Speed of an electron in Bohr's \(7^{\text {th }}\) orbit for Hydrogen atom is \(3.6 \times 10^6\,m / s\). The corresponding speed of the electron in \(3^{\text {rd }}\) orbit, in \(m / s\) is \(........\times 10^6\)

The dimension of \(\frac{\mathrm{B}^{2}}{2 \mu_{0}}\), where \(\mathrm{B}\) is magnetic field and \(\mu_{0}\) is the magnetic permeability of vacuum, is

Consider a frame that is made up of two thin massless rods \(AB\) and \(AC\) as shown in the figure. \(A\) vertical force \(\overrightarrow{ P }\) of magnitude \(100 \;N\) is applied at point \(A\) of the frame. Suppose the force is \(\overrightarrow{ P }\) resolved parallel to the arms \(AB\) and \(AC\) of the frame. The magnitude of the resolved component along the arm \(AC\) is \(xN\). The value of \(x\), to the nearest integer, is ............ [Given : \(\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819\) \(\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]\)  

India's Mangalyan was sent to the Mars by launching it into a transfer orbit \(EOM\) around the sun . It leaves the earth at \(E\) and meets Mars at \(M\) . If the semi-major axis of Earth's orbit is \(a_e = 1.5 \times 10^{11}\, m\), that of Mars orbit \(a_m= 2.28 \times 10^{11}\, m\), taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to ........ \(days\).