A uniform magnetic field \(B\) exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of \(4\, mm\) and a total length of \(30\, cm\) The magnetic field changes with time at a steady rate \(dB / dt =0.032\, Ts ^{-1} .\) The induced current in the \(100 p\) is close to \(....A\) (Resistivity of the metal wire is \(\left.1.23 \times 10^{-8}\, \Omega m \right)\)

A liquid drop of diameter \(2\) mm breaks into \(512\) droplets. The change in surface energy is \(\alpha \times 10^{-6}\) J. The value of \(\alpha\) is _______. (Take surface tension of liquid \(= 0.08\) N/m)

Following statements are given : \((1)\) The average kinetic energy of a gas molecule decreases when the temperature is reduced. \((2)\) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. \((3)\) The average kinetic energy of a gas molecule decreases with increases in volume. \((4)\) Pressure of a gas increases with increase in temperature at constant pressure. \((5)\) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below:

7.9 MeV \( \alpha \)-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) __________m.
\(\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 Nm ^2 / C ^2\right.\) and electron charge \(\left.=1.6 \times 10^{-19} C \right]\)

Temperature difference of \(120\,^oC\) is maintained between two ends of a uniform rod \(AB\) of length \(2L\). Another bent rod \(PQ\), of same cross-section as \(AB\) and length \(\frac{{3L}}{2}\),  is connected across \(AB\) (See figure). In steady state, temperature difference between \(P\) and \(Q\) will be close to .......... \(^oC\)

An experiment is performed to obtain the value of acceleration due to gravity \(g\) by using a simple pendulum of length \(L\). In this experiment time for \(100\, oscillations\) is measured by using a watch of \(1\, second\) least count and the value is \(90.0\, seconds\). The length \(L\) is measured by using a meter scale of least count \(1\, mm\) and the value is \(20.0\, cm\). The  error in the determination of \(g\) would be  ........... \(\%\)

Two wires A and B are made of same material having ratio of lengths \(\frac{L_A}{L_B}=\frac{1}{3}\) and their diameters ratio \(\frac{d_A}{d_B}=2\). If both the wires are stretched using same force, what would be the ratio of their respective elongations?

A source and a detector move away from each other in absence of wind with a speed of \(20\, {m} / {s}\) with respect to the ground. If the detector detects a frequency of \(1800\, {Hz}\) of the sound coming from the source, then the original frequency of source considering speed of sound in air \(340\, {m} / {s}\) will be \({Hz}\)

A prism of refractive index \(n_{1}\) and another prism of refractive index \(n_{2}\) are stuck together (as shown in the figure). \(n_{1}\) and \(n_{2}\) depend on \(\lambda\), the wavelength of light, according to the relation \({n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text { and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}\) The wavelength for which rays incident at any angle on the interface \(B C\) pass through without bending at that interface will be \(....\,nm.\)

The velocity-time graphs of a car and a scooter are shown in the figure. \((i)\) the difference between the distance travelled by the car and the scooter in \(15\, s\) and \((ii)\) the time at which the car will catch up with the scooter are, respectively

A balloon is moving up in air vertically above a point \(A\) on the ground. When it is at a height \(h _{1},\) a girl standing at a distance \(d\) (point \(B\) ) from \(A\) (see figure) sees it at an angle \(45^{\circ}\) with respect to the vertical. When the balloon climbs up a further height \(h _{2},\) it is seen at an angle \(60^{\circ}\) with respect to the vertical if the girl moves further by a distance \(2.464\, d\) (point \(C\) ). Then the height \(h _{2}\) is (given tan \(\left.30^{\circ}=0.5774\right)\)\(.......\)

A rectangular loop of length \(2.5 \mathrm{~m}\) and width \(2 \mathrm{~m}\) is placed at \(60^{\circ}\) to a magnetic field of \(4 \mathrm{~T}\). The loop is removed from the field in \(10 \ \mathrm{sec}\). The average emf induced in the loop during this time is