When an inductor \(L\) and a resistor \(R\) in series are connected across a \(12 \mathrm{~V}, 50 \mathrm{~Hz}\) supply, a current of 0.5 A flows in the circuit. The current differs in the phase from applied voltage by \(\frac{\pi}{3}\) radian. Then the value of \(R\) is

A wooden plank of mass 90 kg and length 3.3 m is floating on still water. A girl of mass 20 Kg walks from one end to the other end of the plank. The distance through which the plank moves is

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.
\(\begin{array}{llll} \hline & \text { List- I } & & \text { List- II } \\ \hline \text {(A) } & X_L & \text { (i) } & 200 \Omega \\ \hline \text {(B) } & X_C & \text { (ii) } & 300 \Omega \\ \hline \text {(C) } & R & \text { (iii) } & 500 \Omega \\ \hline \text {(D) } & Z & \text { (iv) } & 600 \Omega \\ \hline \end{array}\)

A \(0.5 \mathrm{~kg}\) block of brass (density \(=8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}\) ) is suspended from a string. What is the tension in the string if the block is completely immersed in water? \(\left(g=10 \mathrm{~ms}^{-2}\right)\)

The correct order of electromagnetic waves with increasing frequency is

When a wave enters into a rarer medium from a denser medium, the property of the wave which remains constant is

Electrostatic force between two identical charges placed in vacuum at distance of $r$ is $F$. A slab of width $\frac{\mathrm{r}}{5}$ and dielectric constant $9$ is inserted between these two charges, then the force between the charges is

Let \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be non-zero vectors such that \((\mathbf{a} \times \mathbf{b}) \times \mathbf{c}=\frac{1}{3}|\mathbf{b} \| \mathbf{c}| \mathbf{a}\). If \(\theta\) is the acute angle between the vectors \(\mathbf{b}\) and \(\mathbf{c}\), then \(\sin \theta\) is equal to

The magnetic susceptibility of a paramagnetic substance at $-173 °\mathrm{C}$ is $1.5\times {10}^{-2}$. To have the susceptibility $0.5\times {10}^{-2}$, the change in temperature in $°\mathrm{C}$ is

For television broadcasting the frequency employed is normally in range,

Which of the following is true about sodium chloride?

Frequencies in the UHF range normally propagate by means of

Two long parallel straight metal wires A and B carrying currents \(12 \mathrm{~A}\) and \(36 \mathrm{~A}\) respectively, in the same direction are separated by \(50 \mathrm{~cm}\). The point relative to \(A\), where the resultant magnetic induction between the two wires due to the currents is zero, will be