A plane electromagnetic wave travels in free space along $z$- axis. At a particular point in space, the electric field along $x$-axis is $8.7 \mathrm{V} {\mathrm{m}}^{-1}$. The magnetic field along $\mathrm{y}$- axis is

A gas is expanded from an initial state to a final state along a path that consists of (a) an isothermal expansion doing \(40 \mathrm{~J}\) work, (b) an adiabatic expansion doing \(\mathrm{W}\) work, (c) an isothermal expansion doing \(30 \mathrm{~J}\) work. If the total change in the internal energy of the gas is \(-20 \mathrm{~J}\), the work done by the gas during the adiabatic expansion \(\mathrm{W}=\)

If the bonding energy of the electron in a hydrogen atom is 13.6 eV , then energy required to remove electron from first excited state of \(\mathrm{Li}^{2+}\) is

The energy released when one nucleus of \({ }_{92} \mathrm{U}^{235}\) undergoes fission is \(188 \mathrm{MeV}\). The energy released when \(100 \mathrm{~g}\) of \({ }_{92} \mathrm{U}^{235}\) undergoes fission is

A mercury drop of radius 1 cm is divided into \(10^6\) droplets of equal size. If surface tension of mercury is \(35 \times 10^{-3} \mathrm{Nm}^{-1}\), then the change in suface energy in the process is

A solid copper cube of \(7 \mathrm{~cm}\) edge is subjected to a hydraulic pressure of \(8000 \mathrm{kPa}\). The volume contraction of the copper cube is (Bulk modulus of copper \(=140 \mathrm{GPa}\) )

When an inductor of inductance \(\frac{6}{\pi} \mathrm{H}\), a capacitor of capacitance \(\frac{50}{\pi} \mu \mathrm{F}\) and resistor of resistance \(R\) are connected in series with an AC supply of rms voltage \(220 \mathrm{~V}\) and frequency \(50 \mathrm{~Hz}\), the rms current through the circuit is \(440 \mathrm{~mA}\). Match the inductive reactance, \(X_L\) the capacitive reactance, \(X_C\) the resistance \(R\) and the impedance \(Z\) of the circuit given in List-I with the corresponding values given in List-II.
\(\begin{array}{llll} \hline & \text { List- I } & & \text { List- II } \\ \hline \text {(A) } & X_L & \text { (i) } & 200 \Omega \\ \hline \text {(B) } & X_C & \text { (ii) } & 300 \Omega \\ \hline \text {(C) } & R & \text { (iii) } & 500 \Omega \\ \hline \text {(D) } & Z & \text { (iv) } & 600 \Omega \\ \hline \end{array}\)

Which of the following trigonometric values are negative?
\(\begin{aligned} & \text { I. } \sin \left(-292^{\circ}\right) \\ & \text { II. } \tan \left(-190^{\circ}\right) \\ & \text { III. } \cos \left(-207^{\circ}\right) \\ & \text { IV. } \cot \left(-222^{\circ}\right)\end{aligned}\)

In \(\triangle P Q R,(4 \hat{i}+3 \hat{j}+6 \hat{k}),(2 \hat{i}+2 \hat{j}+3 \hat{k})\) and \((3 \hat{i}+\hat{j}+3 \hat{k})\) are the position vectors of the vertices \(\mathrm{P}, \mathrm{Q}\) and R respectively. Then the position vector of the point of intersection of the angle bisector of P with QR is

Let \(2 \overline{\mathrm{i}}-\overline{\mathrm{j}}-\overline{\mathrm{k}}, 5 \overline{\mathrm{i}}+\overline{\mathrm{j}}-2 \overline{\mathrm{k}},-13 \overline{\mathrm{i}}-11 \overline{\mathrm{j}}+4 \overline{\mathrm{k}}\) be the position vectors of three points
A, \(\mathrm{B}, \mathrm{C}\) respectively. If \(\overline{\mathrm{AB}}=\lambda \overline{\mathrm{BC}}\) and \(\overline{\mathrm{AC}}=\mu \overline{\mathrm{CB}}\), then \(\lambda+\mu=\)

Two planets, A and B orbit around a star such that time period of \(A\) is 8 times the time period of \(B\). The ratio of orbital velocities of the planets A and B is

Identify the structure of the compound which is responsible for Bhopal disaster?

A part of a circuit is shown in the figure. The ratio of the potential differences between the points A and C, and the points D and E is