Two identical long parallel wires carry currents ' \(\mathrm{I}_1\) ' and ' \(\mathrm{I}_2\) ' such that \(\mathrm{I}_1>\mathrm{I}_2\). When the currents are in the same direction, the magnetic field at a point midway between the wires is \(8 \times 10^{-6} \mathrm{~T}\). If the direction of \(\mathrm{I}_2\) is reversed, the field becomes \(3.2 \times 10^{-5} \mathrm{~T}\). The ratio of \(\mathrm{I}_2\) to \(\mathrm{I}_1\) is

The stopping potential as a function of frequency of incident radiation is plotted for two different photoelectric surfaces A and B. The graph shows that the work function of A is

In a CE transistor, a change of \(8.0 \mathrm{~mA}\) in the emitter current produces a change of \(7.8 \mathrm{~mA}\) in the collector current. What change in the base current is necessary to produce the same change in the collector current?

An electron of mass ' \(m\) ' and a photon have same energy ' \(E\) '. The ratio of de-Broglie wavelength of electron to the wavelength of photon is \((\mathrm{c}=\) velocity of light \()\)

If the length of the oscillating simple pendulum is made \(\frac{1}{3}\) times the original keeping amplitude same then increase in its total energy at a place will be

Two concentric circular coils having radii \(r_{1}\) and \(r_{2},\left(r_{2}< < r_{1}\right)\) are placed co-
axially with centres coinciding. The mutual induction of the arrangement is
(Both coils have single turn) \(\left(\mu_{0}=\right.\) permeability of free space)

A thin uniform rod \(A B\) of mass ' \(\mathrm{m}\) ' and length ' \(l\) ' is hinged at one end A to the ground level. Initially the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its end B strikes the ground is ( \(g\) = acceleration due to gravity)

The derivative of \(\sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)\) w.r.t. \(\cos ^{-1} x\) is

If \(y=2 \sin x+3 \cos x\) and \(y+A \frac{d^2 y}{d x^2}=B\), then the values of \(A\), \(\mathrm{B}\) are respectively

If \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}\) are three non coplanar vectors and \(\overrightarrow{\mathbf{p}}, \overrightarrow{\mathbf{q}}, \overrightarrow{\mathbf{r}}\) are defined by the relations
\(\overrightarrow{\mathbf{p}}=\frac{\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}, \quad \overrightarrow{\mathbf{q}}=\frac{\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}\) and \(\overrightarrow{\mathbf{r}}=\frac{\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}\)
then \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{p}}+\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{q}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{r}}\) is equal to

If \(A=\left[\begin{array}{ll}2 & -3 \\ 5 & -7\end{array}\right]\), then \(2 A-3 A^{-1}=\)

As shown in the figure, \(S_1\) and \(S_2\) are identical springs with spring constant \(K\) each. The oscillation frequency of the mass ' \(m\) ' is ' \(f\) '. If the spring \(S_2\) is removed, the oscillation frequency will become

What will be the self inductance of a coil of 100 turns if a current of 5 A produces a magnetic flux \(5 \times 10^{-5} \mathrm{~Wb}\) ?