An object kept in a large room having an air temperature of \(25^\circ \text{C}\) takes \(12 ~\text{min}\) to cool from \(80^\circ \text{C}\) to \(70^\circ \text{C}.\) The time taken to cool for the same object from \(70^\circ \text{C}\) to \(60^\circ \text{C}\) would be nearly:
| 1. | \(10 ~\text{min}\) | 2. | \(12 ~\text{min}\) |
| 3. | \(20 ~\text{min}\) | 4. | \(15 ~\text{min}\) |
Two small spherical metal balls, having equal masses, are made from materials of densities \(\rho_1\) and \(\rho_2\) such that \(\rho_1=8\rho_2\)
| 1. | \(\dfrac{79}{72}\) | 2. | \(\dfrac{19}{36}\) |
| 3. | \(\dfrac{39}{72}\) | 4. | \(\dfrac{79}{36}\) |
| 1. | \( \dfrac{v_0}{n} ~\text{rad} / \text{s}^2\) | 2. | \( \dfrac{v_0^2}{2 \pi {nr}^2}~ \text{rad} / \text{s}^2 \) |
| 3. | \( \dfrac{v_0^2}{4 \pi {n}{r}^2}~ \text{rad} / \text{s}^2 \) | 4. | \( \dfrac{v_0^2}{4 \pi {nr}} ~\text{rad} / \text{s}^2 \) |
| 1. | \(t_1<t_2 \) or \(t_1>t_2 \) depending upon whether the lift is going up or down. |
| 2. | \(t_1<t_2 \) |
| 3. | \(t_1>t_2 \) |
| 4. | \(t_1=t_2 \) |
A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of \(a.\) In the frame of the truck, the pendulum will tilt:
| 1. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{sin}^{-1} \left( \dfrac{a}{g} \right )\) |
| 2. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{cos}^{-1} \left ( \dfrac{a}{g} \right )\) |
| 3. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \dfrac{a}{g} \right )\) |
| 4. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \dfrac{g}{a} \right )\) |
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. | \(1333~\text{kg/m}^{3}\) |
A deep rectangular pond of surface area \(A\), containing water (density = \(\rho,\) specific heat capacity = \(s\)), is located in a region where the outside air temperature is at a steady value of \(-26^{\circ}\text{C}\). The thickness of the ice layer in this pond at a certain instant is \(x\). Taking the thermal conductivity of ice as \(k\), and its specific latent heat of fusion as \(L\), the rate of increase of the thickness of the ice layer, at this instant, would be given by:
| 1. | \(\dfrac{26k}{x\rho L-4s}\) | 2. | \(\dfrac{26k}{x^2\rho L}\) |
| 3. | \(\dfrac{26k}{x\rho L}\) | 4. | \(\dfrac{26k}{x\rho L+4s}\) |
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. \(654\times 10^{-11}~\text{m}\)
The circuit diagram shown here corresponds to the logic gate:
1. \(\text{NOR}\)
2. \(\text{AND}\)
3. \(\text{OR}\)
4. \(\text{NAND}\)
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. | \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{7}{5}\) |
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