A \(10 \Omega\) coil of 180 turns and diameter \(4 \mathrm{~cm}\) is placed in a uniform magnetic field so that the magnetic flux is maximum through the coil's cross-sectional area. When the field is suddenly removed a charge of \(360 \mu \mathrm{C}\) flows through a \(618 \Omega\) galvanometer connected to the coil, find the magnetic field.

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

Identify the correct statement among the following.

Two objects are located at height $10 \mathrm{m}$ above the ground. At some point of time, the objects are thrown with initial velocity $2\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $45°$ and $135°$ with the positive $X$-axis respectively. Assuming $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, the velocity vectors will be perpendicular to each other at time equal to

A conducting wire \(\mathrm{PQ}\) carries a current \(10 \mathrm{~A}\) as shown in the figure. It is placed in a uniform magnetic field 5 \(\mathrm{T}\) which is acting normally outside from the paper. Then the net force experienced by it is

A body of mass \(m_1=4 \mathrm{~kg}\) moves at \(5 \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\) and another body of mass \(m_2=2 \mathrm{~kg}\) moves at \(10 \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\). The kinetic energy of centre of mass is

The inductance L, Capacitance C and resistance R are the values of the components connected in series to an ac source of angular frequency \(\omega\). The inductive and capacitive reactances are \(X_L\) and \(X_C\) respectively. If the circuit is purely resistive, then

Which of the following statements is NOT true?

A printed page is kept pressed by a transparent cube of edge \(t\). The refractive index of the cube varies as \(\mu(z)=1+\frac{z}{t}\), where \(z\) is the vertical distance from bottom of the cube. If viewed from top, then the printed letters appear to be shifted by an amount

Water from a tap emerges vertically downwards with initial velocity \(4 \mathrm{~ms}^{-1}\). The cross-sectional area of the tap is \(A\). The flow is steady and pressure is constant throughout the stream of water. The distance \(h\) vertically below the tap, where the cross-sectional area of the stream becomes \(\left(\frac{2}{3}\right) A\), is \(\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)\)

If a disc of mass \(M\) and radius \(R\) rotates with an angular acceleration \(a_{\text {, }}\) of the torque acting on the disc is

A cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by $6\%$. The percentage increase in its length is

A message signal of frequency \(10 \mathrm{kHz}\) is used to modulate a carrier wave of frequency \(6 \mathrm{MHz}\), then the side band frequencies are