A concave lens with a focal length of \(-25~\text{cm}\) is sandwiched between two convex lenses, each with a focal length of \(40~\text{cm}.\) The power (in diopters) of the combined lens system would be:
| 1. | \(55\) | 2. | \(9\) |
| 3. | \(1\) | 4. | \(0.01\) |
A beam of light is incident vertically on a glass slab of thickness \(1~\text{cm},\) and refractive index \(1.5.\) A fraction \(A\) is reflected from the front surface while another fraction \(B\) enters the slab and emerges after reflection from the back surface. The time delay between them is:
1. \(10^{-10}~\text{s}\)
2. \(5\times 10^{-10}~\text{s}\)
3. \(10^{-11}~\text{s}\)
4. \(5\times 10^{-11}~\text{s}\)
At some instant, the number of radioactive atoms in a sample is \(N_0\) and after time \(t\), the number decreases to \(N\). It is found that the graphical representation \(\mathrm{ln} N\) versus \(t\) along the \(y\) and \(x\) axis respectively is a straight line. Then the slope of this line is:
1. \(\lambda\)
2. \(-\lambda\)
3. \(\lambda^{-1}\)
4. \(-\lambda^{-1}\)
When the circular scale of a screw gauge completes \(2\) rotations, it covers \(1\) mm over the pitch scale. The total number of circular scale divisions is \(50.\) The least count of the screw gauge in metres is:
1. \(10^{-4}\)
2. \(10^{-5}\)
3. \(10^{-2}\)
4. \(10^{-3}\)
A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
| 1. | \(u\sqrt{\dfrac{m}{k}} \) | 2. | \(4u\sqrt{\dfrac{m}{k}}\) |
| 3. | \(2u\sqrt{\dfrac{m}{k}}\) | 4. | \(\dfrac12u\sqrt{\dfrac{k}{m}}\) |
| 1. | \(\lambda_\gamma<\lambda_X<\lambda_I<\lambda_M\) |
| 2. | \(\lambda_M<\lambda_I<\lambda_X<\lambda_\gamma\) |
| 3. | \(\lambda_X<\lambda_\gamma<\lambda_M<\lambda_I\) |
| 4. | \(\lambda_X<\lambda_I<\lambda_\gamma<\lambda_M\) |
Twelve point charges each of charge \(q~\text C\) are placed at the circumference of a circle of radius \(r~\text{m}\) with equal angular spacing. If one of the charges is removed, the net electric field (in \(\text{N/C}\)) at the centre of the circle is:
(\(\varepsilon_0\text- \)permittivity of free space)
| 1. | \(\dfrac{13q}{4\pi \varepsilon_0r^2}\) | 2. | zero |
| 3. | \(\dfrac{q}{4\pi \varepsilon_0r^2}\) | 4. | \(\dfrac{12q}{4\pi \varepsilon_0r^2}\) |
| 1. | \(1:2\) | 2. | \(2:1\) |
| 3. | \(3:2\) | 4. | \(2:3\) |
The output of the logic circuit shown is equivalent to a/an:
1. \(\text{OR}\) gate
2. \(\text{NOR}\) gate
3. \(\text{AND}\) gate
4. \(\text{NAND}\) gate
| 1. | a parabolic path |
| 2. | the original path |
| 3. | a helical path |
| 4. | a circular path |
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