A plane-convex lens of unknown material and unknown focal length is given. With the help of a spherometer, we can measure the
| 1. | focal length of the lens. |
| 2. | radius of curvature of the curved surface. |
| 3. | aperture of the lens. |
| 4. | refractive index of the material. |
The angular speed of the wheel of a vehicle is increased from \(360~\text{rpm}\) to \(1200~\text{rpm}\) in \(14\) seconds. Its angular acceleration will be:
1. \(2\pi ~\text{rad/s}^2\)
2. \(28\pi ~\text{rad/s}^2\)
3. \(120\pi ~\text{rad/s}^2\)
4. \(1 ~\text{rad/s}^2\)
Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is \(0.05.\)
( \(g=10~\text{m/s}^2,\) the mass of the string is negligible and no other friction exists)
| 1. | \( 1.25~\text{m/s}^2\) | 2. | \( 1.50~\text{m/s}^2\) |
| 3. | \(1.66~\text{m/s}^2\) | 4. | \( 1.00~\text{m/s}^2\) |
The total energy of an electron in the \(n^{th}\) stationary orbit of the hydrogen atom can be obtained by:
1. \(E_n = \frac{13.6}{n^2}~\text{eV}\)
2. \(E_n = -\frac{13.6}{n^2}~\text{eV}\)
3. \(E_n = \frac{1.36}{n^2}~\text{eV}\)
4. \(E_n = -{13.6}\times{n^2}~\text{eV}\)
A wheel with \(20\) metallic spokes, each \(1\) m long, is rotated with a speed of \(120\) rpm in a plane perpendicular to a magnetic field of \(0.4~\text{G}\). The induced emf between the axle and rim of the wheel will be:
\((1~\text{G}=10^{-4}~\text{T})\)
1. \(2.51 \times10^{-4}\) V
2. \(2.51 \times10^{-5}\) V
3. \(4.0 \times10^{-5}\) V
4. \(2.51\) V
Which of the following gate is called the universal gate?
1. \(\mathrm{OR}\) gate
2. \(\mathrm{AND}\) gate
3. \(\mathrm{NAND}\) gate
4. \(\mathrm{NOT}\) gate
(\(r\gg\) separation of two charges forming the dipole, \(\varepsilon_{0} =\) permittivity of free space)
| 1. | \(\overrightarrow{E}=\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\) | 2. | \(\overrightarrow{E}=\dfrac{2\overrightarrow{P}}{\pi \varepsilon _{0}r^{3}}\) |
| 3. | \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{2}}\) | 4. | \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\) |
The equivalent resistance between \(A\) and \(B\) for the mesh shown in the figure is:
| 1. | \(7.2~\Omega\) | 2. | \(16~\Omega\) |
| 3. | \(30~\Omega\) | 4. | \(4.8~\Omega\) |
A liquid does not wet the solid surface if the angle of contact is:
1. equal to \(45^{\circ}\)
2. equal to \(60^{\circ}\)
3. greater then \(90^{\circ}\)
4. zero
What happens to the mass number and the atomic number of an element when it emits \(\gamma\text{-}\)radiation?
| 1. | mass number decreases by four and atomic number decreases by two. |
| 2. | mass number and atomic number remain unchanged. |
| 3. | mass number remains unchanged while the atomic number decreases by one. |
| 4. | mass number increases by four and the atomic number increases by two. |
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