A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:
1.
a large aperture contributes to the quality and visibility of the images.
2.
a large area of the objective ensures better light-gathering power.
3.
a large aperture provides a better resolution.
4.
all of the above.
The electron concentration in an \(\mathrm{n\text-}\)type semiconductor is the same as the hole concentration in a \(\mathrm{p\text{-}}\)type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.
| 1. | current in \(\mathrm{n\text-}\)type \(>\) current in \(\mathrm{p\text{-}}\)type. |
| 2. | no current will flow in \(\mathrm{p\text{-}}\)type, current will only flow in \(\mathrm{n\text-}\)type. |
| 3. | current in \(\mathrm{n\text-}\)type \(=\) current in \(\mathrm{p\text{-}}\)type. |
| 4. | current in \(\mathrm{p\text{-}}\)type \(>\) current in \(\mathrm{n\text-}\)type. |
| 1. | \(3n\) | 2. | \(4n\) |
| 3. | \(n\) | 4. | \(2n\) |
A cup of coffee cools from \(90^{\circ}\text{C}\) \(80^{\circ}\text{C}\) in \(t\) minutes, when the room temperature is \(20^{\circ}\text{C}\). The time taken by a similar cup of coffee to cool from \(80^{\circ}\text{C}\) \(60^{\circ}\text{C}\) at room temperature same at \(20^{\circ}\text{C}\) is:
1. \(\dfrac{10}{13}t\)
2. \(\dfrac{5}{13}t\)
3. \(\dfrac{13}{10}t\)
4. \(\dfrac{13}{5}t\)
In a potentiometer circuit, a cell of emf \(1.5~\text{V}\) gives a balance point at 36 cm length of wire. If another cell of emf 2.5 V replaces the first cell, then at what length of the wire, the balance point occur?
1. 64 cm
2. 62 cm
3. 60 cm
4. 21.6 cm
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section, and same material is \(0.25~\Omega\). What will be the effective resistance if they are connected in series?
1. \(1~\Omega\)
2. \(4~\Omega\)
3. \(0.25~\Omega\)
4. \(0.5~\Omega\)
| 1. | \(\beta^{+}, ~\alpha, ~\beta^{-}\) | 2. | \(\beta^{-}, ~\alpha, ~\beta^{+}\) |
| 3. | \(\alpha, ~\beta^{-},~\beta^{+}\) | 4. | \(\alpha, ~\beta^{+},~\beta^{-}\) |
A dipole is placed in an electric field as shown. In which direction will it move?
| 1. | towards the left as its potential energy will decrease. |
| 2. | towards the right as its potential energy will increase. |
| 3. | towards the left as its potential energy will increase. |
| 4. | towards the right as its potential energy will decrease. |
An inductor of inductance \(L\), a capacitor of capacitance \(C\) and a resistor of resistance \(R\) are connected in series to an AC source of potential difference \(V\) volts as shown in Figure. The potential difference across \(L\), \(C\) and \(R\) is \(40~\text{V}\), \(10~\text{V}\) and \(40~\text{V}\), respectively. The amplitude of the current flowing through the \(LCR\) series circuit is \(10\sqrt{2}~\text{A}\). The impedance of the circuit will be:
| 1. | \(4~\Omega\) | 2. | \(5~\Omega\) |
| 3. | \(4\sqrt{2}~\Omega\) | 4. | \(\dfrac{5}{\sqrt{2}}~\Omega\) |
The equivalent capacitance of the combination shown in the figure is:
| 1. | \(\dfrac{C}{2}\) | 2. | \(\dfrac{3C}{2}\) |
| 3. | \(3C\) | 4. | \(2C\) |
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