A cup of coffee cools from \(90^{\circ}\mathrm{C}\) \(80~^{\circ}\mathrm{C}\) in t minutes, when the room temperature is \(20^{\circ}\mathrm{C}\). The time taken by a similar cup of coffee to cool from \(80^{\circ}\mathrm{C}\) \(60^{\circ}\mathrm{C}\) at room temperature same at \(20^{\circ}\mathrm{C}\) is:
1. \(\frac{10}{13}t\)
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)
1. \(\frac{10}{13}t\)
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)
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. \(0.5~\Omega\)
A radioactive nucleus \(_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}\) undergoes spontaneous decay in the sequence \(_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}\rightarrow \mathrm{B}_{\mathrm{Z-1}}\rightarrow \mathrm{C}_{\mathrm{Z-3}}\rightarrow \mathrm{D}_{\mathrm{Z-2}}\) where \(\mathrm{Z}\) is the atomic number of element \(\mathrm{X}\). The possible decay particles in the sequence are:
| 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. \(\frac{5}{\sqrt{2}}~\Omega\)
The equivalent capacitance of the combination shown in the figure is:
| 1. | \(\frac{C}{2}\) | 2. | \(\frac{3C}{2}\) |
| 3. | \(3C\) | 4. | \(2C\) |
Consider the following Statements (A) and (B) and identify the correct answer.
| (A) | A Zener diode is connected in reverse bias when used as a voltage regulator. |
| (B) | The potential barrier of p-n junction lies between \(0.2\) V to \(0.3\) V. |
| 1. | (A) is correct and (B) is incorrect. |
| 2. | (A) is incorrect and (B) is correct. |
| 3. | (A) and (B) both are correct. |
| 4. | (A) and (B) both are incorrect. |
1. \(\hat{j}+\hat{k},~-\hat{j}-\hat{k}\)
2. \(-\hat{j}+\hat{k},~-\hat{j}+\hat{k}\)
3. \(\hat{j}+\hat{k},~\hat{j}+\hat{k}\)
4. \(-\hat{j}+\hat{k},~-\hat{j}-\hat{k}\)
The number of photons per second on an average emitted by a source of monochromatic light of wavelength \(600~\text{nm}\), when it delivers the power of \(3.3\times 10^{-3}\) watt will be: \((h = 6.6\times10^{-34}~\text{J-s})\)
1. \(10^{16}\)
2. \(10^{15}\)
3. \(10^{18}\)
4. \(10^{17}\)
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