List of practice Questions

The figure represents the variation of the electric potential \(V\) at a point in a region of space as a function of its position along the \(x\)-axis. A charged particle will experience the maximum force at:

Four long straight thin wires are held vertically at the corners \(A\), \(B\), \(C\) and \(D\) of a square of side \(a\), kept on a table and carry equal current \(I\). The wire at \(A\) carries current in upward direction whereas the current in the remaining wires flows in downward direction. The net magnetic field at the centre of the square will have the magnitude:

A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when :
(I) an iron bar is inserted inside the coil, and
(II) the frequency of the source is decreased ?
Justify your answers. Assume that in each above case other factors remain unchanged.

An ac voltage \(V = 280 \sin (100\pi t)\) volt is connected across a series LCR circuit in which \(R = 400 \, \Omega\), \(L = \frac{5}{\pi} \, \text{H}\) and \(C = \frac{50}{\pi} \, \mu\text{F}\). Taking \(\sqrt{2} = 1.4\), calculate :
(I) impedance of the circuit.
(II) rms value of current that flows in the circuit.
(III) power factor of the circuit.

State Lenz’s law and explain that it follows the law of conservation of energy.

Write the dimensional formula for self-inductance.
The current in a coil changes from 8·0 A to 2·0 A in 0·6 s. If an average emf induced in the coil is 50 V, calculate the self-inductance of the coil.

A point object is kept in front of a convex spherical surface of radius of curvature $R$. Draw the ray diagram to show the formation of image and derive the relation between the object and image distance ($u$ and $v$) in terms of refractive index $n$ of the medium and $R$.

A convex lens of focal length of $20\text{ cm}$ is used to form the image of an object placed $30\text{ cm}$ away from the lens. Find the position and nature of the image formed.

In the figure, OA and OB show the variation of electric potential \(V\) at a point due to two point charges \(Q_1\) and \(Q_2\) with \(\frac{1}{r}\) respectively. Here \(r\) represents the distance of the point from the two point charges.

(I) Identify the nature of the two charges \(Q_1\) and \(Q_2\).
(II) What is the value of \(\left(\frac{Q_1}{Q_2}\right)\)? Justify your answer.

Two point charges \(-2\,\mu\text{C}\) and \(5\,\mu\text{C}\) are placed at \((-30\,\text{cm}, 0)\) and \((30\,\text{cm}, 0)\) respectively in an external electric field \(\vec{E} = \frac{A}{x^2} \hat{i}\), where \(A = 9 \times 10^5\,\text{N}\cdot\text{m}^2\cdot\text{C}^{-1}\). Find the electrostatic potential energy of this configuration.

Two infinitely long straight wires having linear charge densities \(-\lambda\) and \(3\lambda\) are held vertically parallel to each other, distance \(r\) apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other.

A small hollow conducting sphere of radius \(r_1\) is given a charge \(Q\). It is surrounded by a concentric conducting spherical shell of inner radius \(r_2\) and outer radius \(r_3\), having charge \(-3q\). If a point charge \(2q\) were kept at the centre, find:
(I) the electric flux through a concentric spherical Gaussian surface of radius \(x\) for (1) \(x < r_1\), and (2) \(r_1 < x < r_2\).
(II) electric field at a point distant \(x\) from the centre for (1) \(x > r_3\), and (2) \(r_1 < x < r_2\).
(III) surface charge density on the inner surface of (1) sphere, and (2) shell.

A ray of light is travelling through a rectangular glass slab (refractive index \(\frac{3}{2}\)) and is incident on the horizontal glass-air surface at the critical angle for the two media. The slab is then brought in contact with water (refractive index \(\frac{4}{3}\)) such that a thin horizontal layer of water is formed on the surface of the slab. Find the angle at which the ray will emerge into air from the water-air surface.

Differentiate between nuclear fission and nuclear fusion. Give one example for each with nuclear reaction.

With the help of circuit diagrams, briefly explain the forward biasing and the reverse biasing of a p-n junction diode.

The Strait of Hormuz is located between which countries?

The half-life periods of decomposition of $\mathrm{NH_3}$ for different initial pressures are given below :

The order of the reaction is :

Filarial disease (filariasis) is transmitted by which of the following mosquitoes?

A circular coil of 100 turns and radius \( \left(\frac{10}{\sqrt{\pi}}\right) \, \text{cm}\) carrying current of \( 5.0 \, \text{A} \) is suspended vertically in a uniform horizontal magnetic field of \( 2.0 \, \text{T} \). The field makes an angle \( 30^\circ \) with the normal to the coil. Calculate:
the magnetic dipole moment of the coil, and
the magnitude of the counter torque that must be applied to prevent the coil from turning.

Explain the three domains of AI: Data Science, Computer Vision (CV), and Natural Language Processing (NLP).

Study the given data and answer the question that follows:
Comparative Data of few States \[ \begin{array}{|c|c|c|c|} \hline \textbf{States} & \textbf{Infant Mortality Rate (2020)} & \textbf{Literacy Rate (2017--18)} & \textbf{Net Attendance Rate (Class 1 to 5)} \\ \hline \text{State A} & 28 & 82 & 73 \\ \text{State B} & 6 & 94 & 94 \\ \text{State C} & 27 & 62 & 69 \\ \hline \end{array} \]
By how many of the following points does State B’s literacy rate exceed from State A in 2017--18?

Which of following is correct?

How many times does oxidation occur in the Krebs cycle?

Mention the source and the functions of the above mentioned hormones.