The rate of radioactive disintegration at an instant for a radioactive sample of half-life 2.2 . The number of radioactive atoms in that sample at that instant is:
1. 3.7
2. 3.17
3. 3.17
4. 3.17
A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination . The centre of mass of the cylinder has a speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be
| 1. | 2.2 m | 2. | 1.6 m |
| 3. | 1.2 m | 4. | 2.4 m |
In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are \(15~\text{cm}\) and \(20~\text{cm}\) respectively. The density of the oil is:
\(\left[\text{take}~\rho_{\text{water}}= 1000~\text{kg/m}^{3}\right]\)
| 1. | \(1200~\text{kg/m}^{3}\) | 2. | \(750~\text{kg/m}^{3}\) |
| 3. | \(1000~\text{kg/m}^{3}\) | 4. | \(1333~\text{kg/m}^{3}\) |
An LED is constructed from a \(\mathrm{p\text{-}n}\) junction diode using \(\mathrm{GaAsP}.\) The energy gap is \(1.9~\text{eV}.\) The wavelength of the light emitted will be equal to:
1. \(10.4 \times 10^{-26}~ \text{m}\)
2. \(654~ \text{nm}\)
3. \(654~ \text{m}\)
4. \(654\times 10^{-11}~\text{m}\)
A biconvex lens has power \(P.\) It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be:
| 1. | \(0\) | 2. | \(\dfrac{P}{2}\) |
| 3. | \(\dfrac{P}{4}\) | 4. | \(P\) |
A particle of mass \(5m\) at rest suddenly breaks on its own into three fragments. Two fragments of mass \(m\) each move along mutually perpendicular directions with speed \(v\) each. The energy released during the process is:
| 1. | \(\dfrac{3}{5}mv^2\) | 2. | \(\dfrac{5}{3}mv^2\) |
| 3. | \(\dfrac{3}{2}mv^2\) | 4. | \(\dfrac{4}{3}mv^2\) |
The radius of the first permitted Bohr orbit for the electron in a hydrogen atom is 0.5 Å, and its ground state energy is \(-13.6~\text{eV}.\) If the electron in the hydrogen atom is replaced by a muon \((\mu^{-}),\) which has the same charge as the electron but is \(207\) times more massive, what will be the new values for the first Bohr radius and ground state energy?
| 1. | \(0.53\times10^{-13}~\text{m}, ~-3.6~\text{eV}\) |
| 2. | \(25.6\times10^{-13}~\text{m}, ~-2.8~\text{eV}\) |
| 3. | \(2.56\times10^{-13}~\text{m}, ~-2.8~\text{keV}\) |
| 4. | \(2.56\times10^{-13}~\text{m}, ~-13.6~\text{eV}\) |
| 1. | \(2.5\times 10^{8}~\text{m/s}\) | 2. | \(3\times 10^{8}~\text{m/s}\) |
| 3. | \(2.08\times 10^{8}~\text{m/s}\) | 4. | \(4.32\times 10^{8}~\text{m/s}\) |
The value \(\gamma = \frac{C_P}{C_V}\) for hydrogen, helium, and another ideal diatomic gas \(X\) (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:
| 1. | \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{9}{7}\) | 2. | \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{9}{7}\) |
| 3. | \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{7}{5}\) | 4. | \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{7}{5}\) |
A double convex lens has a focal length of \(25\) cm. The radius of curvature of one of the surfaces is double of the other. What would be the radii if the refractive index of the material of the lens is \(1.5?\)
1. \(100\) cm, \(50\) cm
2. \(25\) cm, \(50\) cm
3. \(18.75\) cm, \(37.5\) cm
4. \(50\) cm, \(100\) cm
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