Two similar coils of radius \(R\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\) and \(2I,\) respectively. What will be the resultant magnetic field induction at the centre?
| 1. | \(\sqrt{5} \mu_0I \over 2R\) | 2. | \({3} \mu_0I \over 2R\) |
| 3. | \( \mu_0I \over 2R\) | 4. | \( \mu_0I \over R\) |
| 1. | \(\dfrac{B}{A}\) | 2. | \(\dfrac{B}{2A}\) |
| 3. | \(\dfrac{2A}{B}\) | 4. | \(\dfrac{A}{B}\) |
When a biconvex lens of glass having a refractive index of \(1.47\) is dipped in a liquid, it acts as a plane sheet of glass. The liquid must have a refractive index:
| 1. | equal to that of glass. |
| 2. | less than one. |
| 3. | greater than that of glass. |
| 4. | less than that of glass. |
| 1. | \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\) | 2. | \(\theta = \tan^{-1}(4)\) |
| 3. | \(\theta = \tan^{-1}(2)\) | 4. | \(\theta = 45^{\circ}\) |
In an electrical circuit \(R,\) \(L,\) \(C\) and an AC voltage source are all connected in series. When \(L\) is removed from the circuit, the phase difference between the voltage and the current in the circuit is \(\tan^{-1}\sqrt{3}\). If instead, \(C\) is removed from the circuit, the phase difference is again \(\tan^{-1}\sqrt{3}\). The power factor of the circuit is:
| 1. | \(\dfrac{1}{2} \) | 2. | \(\dfrac{1}{\sqrt{2}}\) |
| 3. | \(1 \) | 4. | \(\dfrac{\sqrt{3}}{2}\) |
| 1. | \(\dfrac{Q}{4\pi R^2\sigma}\) | 2. | \(\left(\dfrac{Q}{4\pi R^2\sigma}\right )^{\dfrac{-1}{2}}\) |
| 3. | \(\left(\dfrac{4\pi R^2 Q}{\sigma}\right )^{\dfrac{1}{4}}\) | 4. | \(\left(\dfrac{Q}{4\pi R^2 \sigma}\right)^{\dfrac{1}{4}}\) |
The current \((I)\) in the inductance is varying with time \((t)\) according to the plot shown in the figure.
Which one of the following is the correct variation of voltage with time in the coil?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A millivoltmeter of \(25~\text{mV}\) range is to be converted into an ammeter of \(25~\text{A}\) range. The value (in ohm) of the necessary shunt will be:
1. \(0.001\)
2. \(0.01\)
3. \(1\)
4. \(0.05\)
Two persons of masses \(55~\text{kg}\) and \(65~\text{kg}\) respectively, are at the opposite ends of a boat. The length of the boat is \(3.0~\text{m}\) and weighs \(100~\text{kg}.\) The \(55~\text{kg}\) man walks up to the \(65~\text{kg}\) man and sits with him. If the boat is in still water, the centre of mass of the system shifts by:
1. \(3.0~\text{m}\)
2. \(2.3~\text{m}\)
3. zero
4. \(0.75~\text{m}\)
A mixture consists of two radioactive materials A1 and A2 with half-lives of 20 s and 10 s respectively. Initially, the mixture has 40 g of A1 and 160 g of A2. The amount of the two in the mixture will become equal after:
1. 60 s
2. 80 s
3. 20 s
4. 40 s
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