List of practice Questions

Read the passage and answer the question:
1857: Shah Mal
Shah Mal lived in a large village in Uttar Pradesh. He belonged to a clan of Jat cultivators whose kinship ties extended over chaurasee des. The lands in the region were irrigated and fertile, with rich dark loam soil. Many of the villagers were prosperous and saw the British land revenue system as oppressive: the revenue demand was high and its collection inflexible. Consequently cultivators were losing land to outsiders, to traders and moneylenders who were coming into the area. Shah Mal mobilised the headmen and cultivators of chaurasee des, moving at night from village to village, urging people to rebel against the British. As in many other places, the revolt against the British turned into a general rebellion against all signs of oppression and injustice. Cultivators left their fields and plundered the houses of moneylenders and traders. Displaced proprietors took possession of the lands they had lost. Shah Mal's men attacked government buildings, destroyed the bridge over the river, and dug up metalled roads. They sent supplies to the sepoys who had mutinied in Delhi and stopped all official communication between British headquarters and Meerut. Locally acknowledged as the Raja, Shah Mal took over the bungalow of an English officer, turned it into a “hall of justice”, settling disputes and dispensing judgments. He also set up an amazingly effective network of intelligence. For a period the people of the area felt that firangi raj was over, and their raj had come. Shah Mal was killed in battle in July 1857.

Rail Transport
The Indian Railways network is one of the longest in the world. It facilitates the movement of both freight and passengers and contributes to the growth of the economy. Mahatma Gandhi said, the Indian railways "...brought people of diverse cultures together to contribute to India's freedom struggle". The Indian Railway was introduced in 1853, when a line was constructed from Bombay to Thane, covering a distance of 34 km. Indian Railways is the largest government undertaking in the country. The length of the Indian Railways network was 67,956 km (Railway yearbook 2019-20). Its very large size puts a lot of pressure on a centralised railway management system. Thus, in India, the railway system has been divided into 17 zones. Indian Railways has launched an extensive programme to convert the metre and narrow gauges to broad gauge. Moreover, steam engines have been replaced by diesel and electric engines. This step has increased the speed, as well as the haulage capacity. The replacement of steam engines run by coal has also improved the environment of the stations. Metro rail has revolutionised the urban transport system in India. Replacement of diesel buses by CNG-run vehicles along with the introduction of the metro is a welcome step towards controlling the air pollution in urban centres. Areas around towns, raw material producing areas and plantations and other commercial crops, hill stations and cantonment towns were well-connected by railways from the British colonial era. These were mostly developed for the exploitation of resources. After the Independence of the country, railway routes have been extended to other areas too. The most significant development has been the development of the Konkan Railway along the western coast, providing a direct link between Mumbai and Mangaluru. The railway continues to remain the main means of transport for the masses. The railway network is relatively less dense in the hill states, north eastern states, central parts of India and Rajasthan.

Concept of High Technology Industry
High technology, or simply high-tech, is the latest generation of manufacturing activities. It is best understood as the application of intensive research and development (R and D) efforts leading to the manufacture of products of an advanced scientific and engineering character. Professional (white collar) workers make up a large share of the total workforce. These highly skilled specialists greatly outnumber the actual production (blue collar) workers. Robotics on the assembly line, computer-aided design (CAD) and manufacturing, electronic controls of smelting and refining processes, and the constant development of new chemical and pharmaceutical products are notable examples of a high-tech industry. Neatly spaced, low, modern, dispersed, office-plant-lab buildings rather than massive assembly structures, factories and storage areas mark the high-tech industrial landscape. Planned business parks for high-tech start-ups have become part of regional and local development schemes. High-tech industries which are regionally concentrated, self-sustained and highly specialized are called technopolies. The Silicon Valley near San Francisco and Silicon Forest near Seattle are examples of technopolies.

Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance $U = \frac{1}{2}CV^2$, where symbols have their usual meanings.
Two capacitors, one of $3 \ \mu$F and the other of $6 \ \mu$F, are connected in series in the circuit as shown in the figure, for a long time. }

A charged particle $+q$ in an electric field $\vec{E}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\vec{B}$. But this magnetic force is perpendicular to both velocity $\vec{v}$ of the charged particle and the magnetic field $\vec{B}$, so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses $m$ and $\frac{m}{2}$ having charges $-q$ and $+2q$ respectively. They are accelerated from rest through the same potential difference $V$ and acquire kinetic energy $K_1$ and $K_2$. Then they enter in a region of uniform magnetic field $\vec{B}$ perpendicular to their velocities.

An astronomical telescope consists of two converging lenses. One of them of large aperture and large focal length is called objective lens and the other one, of smaller focal length and smaller aperture is called the eyepiece. It is used to see distant objects which are not seen clearly with naked eyes. The image formed by the objective lens acts as an object for the eyepiece and the final image produced by the eyepiece is magnified.

A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

Read the following paragraph and answer the questions that follow.
In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.

Read the following paragraph and answer the questions that follow.
A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. The motion of majority charge carriers causes diffusion current across the junction while the barrier electric field causes motion of minority carriers for drift current. In case of unbiased diode, the diffusion and drift currents are equal. This equilibrium is disturbed by the biasing batteries. Diodes, therefore, allow currents in one direction. This property of diode is used in making rectifiers.

Write two advantages of reflecting telescope over refracting telescope.

Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

Two air-filled capacitors of capacitances $C_1$ and $C_2$ are connected in parallel with a dc battery. After the capacitors are fully charged, a slab of dielectric constant K is inserted between the plates of each capacitor. How will the (i) charge on each capacitor and (ii) energy stored in the capacitor affected after the slab is introduced.

An electric field $\vec{E}$ is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this ‘average velocity’ of electrons.

This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

Deduce an expression for the induced emf in the coil of the generator.

If T is the time period of the rotation of the coil, at what values of t in a cycle, the emf generator is maximum ?

What are coherent sources ? Why they are necessary for observing stable interference pattern ? Draw a graph showing the variation of intensity of light with the position on the screen in Young’s double-slit experiment.

Find the intensity of light at a point on the screen when two interfering waves of the same intensity ($I_0$) have a path difference of (i) $\frac{\lambda}{4}$ and (ii) $\frac{\lambda}{3}$.

Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power.

In a telescope the objective has much larger aperture than the eye piece. Why ?

A series combination of L, C and R is connected to an a.c. source. Using a phasor diagram, derive an expression for the impedance of the circuit and phase difference between V and I.

Under what conditions the (i) impedance of the circuit is minimum ? (ii) Wattless current flows in the circuit ?

Use Kirchhoff’s rules to find the current through $3 \Omega$ resistor in the circuit shown in the figure :