A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:
| 1. | decreases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 2. | increases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 3. | is zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
| 4. | is zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
Pick the wrong statement in the context with a rainbow.
| 1. | Rainbow is a combined effect of dispersion, refraction, and reflection of sunlight. |
| 2. | When the light rays undergo two internal reflections in a water drop, a secondary rainbow is formed. |
| 3. | The order of colors is reversed in the secondary rainbow. |
| 4. | An observer can see a rainbow when his front is towards the sun. |
| 1. | \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\) | 2. | \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\) |
| 3. | \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\) | 4. | \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\) |
Which of the following acts as a circuit protection device?
| 1. | Fuse | 2. | Conductor |
| 3. | Inductor | 4. | Switch |
| 1. | \(\frac{4F}{3}\) | 2. | \(F\) |
| 3. | \(\frac{9F}{16}\) | 4. | \(\frac{16F}{9}\) |
The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.
The \(y\)-projection of the radius vector of rotating particle \(P\) will be:
| 1. | \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m |
| 2. | \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m |
| 3. | \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m |
| 4. | \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m |
| 1. | \(2\) protons only. |
| 2. | \(2\) protons and \(2\) neutrons only. |
| 3. | \(2\) electrons, \(2\) protons, and \(2\) neutrons. |
| 4. | \(2\) electrons and \(4\) protons only. |
A solid cylinder of mass \(2~\text{kg}\) and radius \(4~\text{cm}\) is rotating about its axis at the rate of \(3~\text{rpm}.\) The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6~\text{N-m}\)
2. \(2\times 10^{-6}~\text{N-m}\)
3. \(2\times 10^{-3}~\text{N-m}\)
4. \(12\times 10^{-4}~\text{N-m}\)
In a double-slit experiment, when the light of wavelength \(400~\text{nm}\) was used, the angular width of the first minima formed on a screen placed \(1~\text{m}\) away, was found to be \(0.2^{\circ}.\) What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? \(\left(\mu_{\text{water}} = \dfrac{4}{3}\right)\)
1. \(0.1^{\circ}\)
2. \(0.266^{\circ}\)
3. \(0.15^{\circ}\)
4. \(0.05^{\circ}\)
© 2026 GoodEd Technologies Pvt. Ltd.