A stone is thrown vertically downwards with an initial velocity of \(40\) m/s from the top of a building. If it reaches the ground with a velocity of \(60\) m/s, then the height of the building is: (Take \(g=10\) m/s2)
1. \(120\) m
2. \(140\) m
3. \(80\) m
4. \(100\) m
1. \(120\) m
2. \(140\) m
3. \(80\) m
4. \(100\) m
Rain is falling vertically downward with a speed of \(35~\text{m/s}\). Wind starts blowing after some time with a speed of \(12~\text{m/s}\) in East to West direction. The direction in which a boy standing at the place should hold his umbrella is:
| 1. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to rain |
| 2. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to wind |
| 3. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to rain |
| 4. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to wind |
An electromagnetic wave is moving along negative \(\text{z (-z)}\) direction and at any instant of time, at a point, its electric field vector is \(3\hat j~\text{V/m}\). The corresponding magnetic field at that point and instant will be: (Take \(c=3\times10^{8}~\text{ms}^{-1}\) )
| 1. | \(10\hat i~\text{nT}\) | 2. | \(-10\hat i~\text{nT}\) |
| 3. | \(\hat i~\text{nT}\) | 4. | \(-\hat i~\text{nT}\) |
In a photoelectric experiment, blue light is capable of ejecting a photoelectron from a specific metal while green light is not able to eject a photoelectron. Ejection of photoelectrons is also possible using light of the colour:
1. yellow
2. red
3. violet
4. orange
Three capacitors, each of capacitance \(0.3~\mu \text{F}\) are connected in parallel. This combination is connected with another capacitor of capacitance \(0.1~\mu \text{F}\) in series. Then the equivalent capacitance of the combination is:
| 1. | \(0.9~\mu\text{F}\) | 2. | \(0.09~\mu\text{F}\) |
| 3. | \(0.1~\mu\text{F}\) | 4. | \(0.01~\mu\text{F}\) |
A string of length \(l\) is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is \(2\) mm. The amplitude of a particle at a distance \(l/8\) from the fixed end is:
1. \(2\sqrt2~\text{mm}\)
2. \(4~\text{mm}\)
3. \(\sqrt2~\text{mm}\)
4. \(2\sqrt3~\text{mm}\)
The circuit represents a full wave bridge rectifier when switch \(S\) is open. The output voltage \((\text V_0)\) pattern across \(R_L\) when \(S\) is closed:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
| Assertion (A): | Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. |
| Reason (R): | The magnetic monopoles do not exist. North and South poles occur in pairs, allowing vanishing net magnetic flux through the surface. |
| 1. | (A) is true but (R) is false. |
| 2. | (A) is false but (R) is true. |
| 3. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
An AC source given by \(V=V_m\sin\omega t\) is connected to a pure inductor \(L\) in a circuit and \(I_m\) is the peak value of the AC current. The instantaneous power supplied to the inductor is:
1. \(\frac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
2. \(-\frac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
3. \({V_mI_m}\mathrm{sin}^{2}(\omega t)\)
4. \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\)
The fraction of the original number of radioactive atoms that disintegrates (decays) during the average lifetime of a radioactive substance will be:
1. \(\frac{1}{e}\)
2. \(\frac{1}{1+e}\)
3. \(\frac{e-1}{e+1}\)
4. \(\frac{e-1}{e}\)
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