List of practice Questions

Find speed of 1 kg object when it reaches close to Earth's surface from a long distance after it is released from rest as shown in the diagram. [Given \( R_e = 6400 \, \text{km}, g_s = 9.8 \, \text{m/s}^2 \)]

Surface tension of soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is \( \alpha \pi \times 10^{-4} \) J. Find the value of \( \alpha \).

A paper is placed in front of lens at a distance 30 cm, such that paper gets burned in minimum time. Radius of curvature of bi-convex lens is 60 cm. If refractive index of lens is \( \mu = \frac{\alpha}{10} \), then value of \( \alpha \) is?

Force on a charge \( q = 10^{-9} \, \text{C} \) in uniform electric and magnetic fields is \( \vec{F} = (2 \times 10^{-10} \hat{i} + 3 \times 10^{-10} \hat{j}) \, \text{N} \).

Find the velocity (in m/s) of the charge if the electric field is \( 0.4 \hat{j} \, \text{V/m} \) and the magnetic field is \( 2 \times 10^{-3} \hat{k} \, \text{T} \).

There is a thin layer of refractive index \( \mu \) below the base of an equilateral prism. The path of a ray is shown in the figure. Find out \( \mu \).

If \( G \) is the Gravitational constant and \( h \) is Planck's constant, then the dimension of \( G \) is:

For given logic gate circuit, an equivalent gate will be

Find the ratio of electric flux passing through two spheres centered at the origin, having radii 4 m and 6 m respectively, with charges \( q_1 = 8 \, \mu C \) and \( q_2 = 2 \, \mu C \) respectively.

Side of square is \( L \) and \( R \ll L \).
Find mutual inductance of the system shown in the figure.

As shown in the figure in YDSE experiment, if intensity is \( \frac{3}{4} \) of maximum intensity at point P, and path difference at point 'P' is \( \Delta x = \frac{\lambda}{\alpha} \). Find the value of "α". (where \( \lambda \) is wavelength of light)

An ideal gas of 5 moles has \( C_p = 8 \, \text{cal/mol}^\circ \text{C} \). If its temperature changes from 10°C to 20°C, then calculate the change in its internal energy (in cal).

A small ball of mass 1 kg is released from a height of 20 m on the sand. It penetrates 10 cm in the sand and comes to rest. Find the average force exerted by the sand on the ball. (g = 10 m/s\(^2\))

For first order reaction:
2A(g) → 4B(g) + C(g)
Total pressure at \( t = 30 \, \text{sec} \) and \( t = \infty \) are 300 torr and 600 torr respectively. Calculate pressure of C(g) at 30 sec (in torr).

‘x’ be the osmotic pressure of a solution formed by dissolving 1g of a protein (M = 50,000 g/mol) in 0.5 litre and ‘y’ be the osmotic pressure of solution formed by dissolving 2g of the same protein in 1 litre at 300 K. If ‘z’ be the osmotic pressure of solution formed by mixing above two solutions. Then the value of ‘x’, ‘y’ and ‘z’ respectively are.
\text{Use: \( R = 0.083 \, \text{lit-bar/K-mol} \)}

A metal of work function 2.3 eV is irradiated with radiation of wavelength \( y \times 10^2 \) nm. The maximum kinetic energy of ejected electron is \( 2.8 \times 10^{-20} \) J. Then calculate \( y \) (in nearest integer).

A hydrocarbon has mass ratio of C and H in 12 : 1.
Each molecule of hydrocarbon has 2 carbon atoms.
Calculate mass of \( CO_2 \) (in gm) produced, when 3.38 gm hydrocarbon undergoes combustion.

A cell is formed using the below half-cell reactions, and the cell is working with 80% efficiency. Work obtained is utilized for isothermal expansion of gas against external pressure of 1 kPa. Find \( \Delta V \) (in \( \text{m}^3 \)). \[ \frac{1}{2} O_2 + 2H^+ + 2e^- \rightarrow H_2O; \, E^\circ = 1.23 \, \text{V} \] \[ 6H^+ + CO_2 + 6e^- \rightarrow CH_3OH + H_2O; \, E^\circ = 0.02 \, \text{V} \]

For process \( X \to Y \), work done by the gas is 10 J and heat absorbed in the process is 2 J. For the reverse process, heat evolved is 6 J. Find the work done for the reverse process.

For a reaction \( xA \rightarrow yB, \, k = 0.3 \, \text{M}^{-1} \text{sec}^{-1} \),
(i) If the concentration of A is made 4 times, then the rate of reaction becomes 16 times.
(ii) The decomposition of \( \text{N}_2\text{O}_5 \) is an example of this type of reaction.
(iii) The order of the reaction is 2.
(iv) A plot of \( \ln \left( \frac{[A]_0}{[A]_t} \right) \) vs. \( t \) is a straight line.
(v) The half-life of the reaction is independent of the concentration of the reactant.

Which of the following options has the correct set of statements:

0.1 mole of \( H_2S \) is added in 1 liter of 0.1 HCl solution. Calculate the concentration of \( HS^{-} \).
[Given \( K_{a1} = 8.3 \times 10^{-8} \) and \( K_{a2} = 10^{-13} \)]

20 ml of 0.2 M HA (\( K_a = 5 \times 10^{-4} \)) is titrated with 10 ml of 0.2 M NaOH solution. Calculate the initial and final value of pH of the solution. [Given \( \log 5 = 0.7 \)]

How many of the following are paramagnetic:
Lu\(^{3+}\), Yb\(^{2+}\), Gd\(^{2+}\), Ce\(^{4+}\), La\(^{3+}\), Zn\(^{2+}\), Cu\(^{2+}\), Mn\(^{2+}\), Sc\(^{3+}\), and Ti\(^{4+}\)

Which of the following are iso-structural with \( \text{SF}_4 \)?

The correct set that contains all kinds of oxides (Basic, acidic, amphoteric, and neutral) is: