List of practice Questions

Given below are two statements, one labeled as Assertion (A) and the other as Reason (R).
Assertion (A): In Young’s double slit experiment, the fringes produced by red light are closer compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light.
In the light of the above statements, choose the correct answer from the options given below:

Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5 A and 4 A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is $ 3 \times 10^{-5} $ T. The value of $ x $, which represents the distance of point P from wire X, is$ \_\_\_\_\_$ cm. (Take permeability of free space as $ \mu_0 = 4\pi \times 10^{-7} $ SI units.)

Consider an elementary reaction: \[ A(g) + B(g) \rightarrow C(g) + D(g) \] If the volume of the reaction mixture is suddenly reduced to $ \frac{1}{3} $ of its initial volume, the reaction rate will become $ x $ times of the original reaction rate. The value of $ x $ is:

The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :

Let A = (x, y) $\in$ {R $\times$ {R} : |x + y| $\geq$ 3} and} B = (x, y) $\in$ {R $\times$ {R} : |x| + |y| $\leq 3$}. If C = (x, y) $\in$ A $\cap$ B : x = 0 $\text{ or y = 0}$, then $\sum_{(x, y) \in C} |x| + |y|$ is:

Two capacitors $ C_1 $ and $ C_2 $ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $ U_1 $ and $ U_2 $, respectively. Which of the given statements is true?

Drug X becomes ineffective after 50% decomposition. The original concentration of drug in a bottle was 16 mg/mL which becomes 4 mg/mL in 12 months. The expiry time of the drug in months is ____ . Assume that the decomposition of the drug follows first order kinetics.

There are two vessels filled with an ideal gas where volume of one is double the volume of the other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).

A piston of mass M is hung from a massless spring whose restoring force law goes as F = -kx, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $ L_0 $ to $ L_1 $, the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 $ cm^3 $ and temperature 27°C. The change in temperature when the gas is adiabatically compressed to 200 $ cm^3 $ is: (Take $ \gamma $ = 1.5 : $ \gamma $ is the ratio of specific heats at constant pressure and at constant volume)

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is :

An ideal gas exists in a state with pressure $ P_0 $, volume $ V_0 $. It is isothermally expanded to 4 times of its initial volume $ (V_0) $, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is :

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is 30° in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is ____ $\mu$m.

For a given reaction $ R \rightarrow P $, $ t_{1/2} $ is related to $[A_0]$ as given in the table. Given: $ \log 2 = 0.30 $. Which of the following is true?

\[ \begin{array}{|c|c|} \hline \textbf{[A] (mol/L)} & \textbf{t$_{1/2}$ (min)} \\ \hline 0.100 & 200 \\ 0.025 & 100 \\ \hline \end{array} \]

As shown below, bob A of a pendulum having massless string of length $ R $ is released from $ 60^\circ $ to the vertical. It hits another bob B of half the mass that is at rest on a frictionless table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take $ g $ as acceleration due to gravity):

Two projectiles are fired with the same initial speed from the same point on the ground at angles of $ (45^\circ - \alpha) $ and $ (45^\circ + \alpha) $, respectively, with the horizontal direction. The ratio of their maximum heights attained is:

A particle of mass $ m $ and charge $ q $ is fastened to one end $ A $ of a massless string having equilibrium length $ l $, whose other end is fixed at point $ O $. The whole system is placed on a frictionless horizontal plane and is initially at rest. If a uniform electric field is switched on along the direction as shown in the figure, then the speed of the particle when it crosses the x-axis is:

The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet color in non-luminous flame under hot condition in borax bead test is:

For the reaction:

The correct order of set of reagents for the above conversion is :

Let $ A = [a_{ij}] $ be a matrix of order 3 $\times$ 3, with $a_{ij} = (\sqrt{2})^{i+j}$. If the sum of all the elements in the third row of $ A^2 $ is $ \alpha + \beta\sqrt{2} $, where $\alpha, \beta \in \mathbb{Z}$, then $\alpha + \beta$ is equal to:

A tube of length L is shown in the figure. The radius of cross section at point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be:

An ideal gas with an adiabatic exponent 1.5, initially at 27°C is compressed adiabatically from 800 cc to 200 cc. The final temperature of the gas is:

A convex lens $(f = 30 \, \text{cm})$ is in contact with a concave lens $(f = 20 \, \text{cm}).$ The object is placed on the left side at a distance of $20 \, \text{cm}.$ Find the image distance.

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 $ m^2 $. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 $ m/s^2 $)