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21. One block of 2·0 kg mass is placed on top of another block of 3·0 kg m

One block of 2·0 kg mass is placed on top of another block of 3·0 kg mass. The coefficient of static friction between the two blocks is 0·2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s², the maximum value of the frictional force is :

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50 N

30 N

4 N

10 N

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When the two blocks move together without slipping, the force responsible for the acceleration of the top block (mass 2.0 kg) is the static friction force exerted by the bottom block on the top block. The maximum value this static friction force can attain is given by the product of the coefficient of static friction and the normal force acting on the top block.

– The normal force on the top block is equal to its weight: N = m₁g.
– The maximum static friction force is given by $f_{s,max} = \mu_s N$.
– For the blocks to move together without slipping, the actual static friction force must be less than or equal to $f_{s,max}$. The question asks for the maximum value of the frictional force in this scenario, which is the maximum static friction force that can exist between the blocks.

Given: mass of top block m₁ = 2.0 kg, mass of bottom block m₂ = 3.0 kg, coefficient of static friction $\mu_s = 0.2$, acceleration due to gravity g = 10 m/s².
Normal force on the top block (due to the bottom block) N = m₁g = 2.0 kg × 10 m/s² = 20 N.
Maximum static friction force $f_{s,max} = \mu_s N = 0.2 \times 20 N = 4 N$.
For the blocks to move together, the actual friction force on the top block is $f = m_1 a$, where ‘a’ is the acceleration of the system. As the pulling force F on the bottom block increases, ‘a’ increases, and thus the required friction force ‘f’ increases. Slipping occurs when the required ‘f’ exceeds $f_{s,max}$. The maximum value the frictional force can reach while preventing slipping is $f_{s,max}$.

22. The power required to lift a mass of 8·0 kg up a vertical distance of

The power required to lift a mass of 8·0 kg up a vertical distance of 4 m in 2 s is (taking acceleration due to gravity as 10 m/s²):

80 W

160 W

320 W

640 W

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The power required to lift an object is equal to the work done in lifting the object divided by the time taken. Work done in lifting is equal to the force required to lift it multiplied by the vertical distance lifted. The minimum force required to lift a mass vertically at a constant speed or to overcome gravity is equal to its weight.

– Weight (Force) = mass × acceleration due to gravity (W = mg).
– Work done (W) = Force × distance (W = Fd).
– Power (P) = Work done / Time (P = W/t).

Given: mass m = 8.0 kg, distance d = 4 m, time t = 2 s, acceleration due to gravity g = 10 m/s².
Force required to lift the mass = W = mg = 8.0 kg × 10 m/s² = 80 N.
Work done = Fd = 80 N × 4 m = 320 Joules.
Power = Work done / Time = 320 J / 2 s = 160 Watts.

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23. Sand falls vertically on a conveyor belt at a rate of 0·1 kg/s. In ord

Sand falls vertically on a conveyor belt at a rate of 0·1 kg/s. In order to keep the belt moving at a uniform speed of 2 m/s, the force required to be applied on the belt is :

0 N

0·2 N

1·0 N

2·0 N

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To keep the conveyor belt moving at a uniform speed, a force must be applied to counteract the change in momentum of the sand as it lands on the belt and accelerates to the belt’s speed. Sand falls vertically with zero initial horizontal momentum. As it lands on the belt, it acquires the belt’s horizontal velocity of 2 m/s. The rate at which mass is added to the belt is dm/dt = 0.1 kg/s. The force required is equal to the rate of change of momentum in the horizontal direction. The momentum added per unit time is (dm/dt) * v, where v is the velocity of the belt. Force F = (dm/dt) * v = (0.1 kg/s) * (2 m/s) = 0.2 N. This force is needed to continuously accelerate the newly added sand horizontally from rest to the belt’s speed.

The force required to keep the belt moving at a uniform speed is equal to the rate of change of momentum of the sand added to the belt, which is the product of the rate of mass flow and the belt’s velocity.

This problem involves a variable mass system, specifically where mass is being added. The relevant physical principle is Newton’s second law in its momentum form: F_net = dP/dt. In this case, the external force applied to the belt is responsible for increasing the horizontal momentum of the sand falling onto it.

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24. Which one of the following astronomers proved that the Earth and other

Which one of the following astronomers proved that the Earth and other planets revolve around the Sun ?

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Copernicus

Kepler

Galileo

Newton

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While Nicolaus Copernicus first proposed the heliocentric model systematically in his work ‘De Revolutionibus Orbium Coelestium’ (published in 1543), providing the mathematical framework for planets revolving around the Sun, it was Galileo Galilei who provided the first strong observational evidence supporting this model. Using his telescope, Galileo observed phenomena like the phases of Venus (which are only possible if Venus orbits the Sun), the moons of Jupiter (showing that not everything orbits the Earth), and craters on the Moon. These observations directly challenged the long-accepted geocentric (Earth-centred) model and provided empirical proof favouring the heliocentric view proposed by Copernicus.

Galileo Galilei provided crucial observational evidence using his telescope that supported the heliocentric model, effectively proving that Earth and other planets revolve around the Sun against the prevailing geocentric view.

Johannes Kepler formulated the laws of planetary motion, describing *how* planets orbit the Sun (in elliptical paths). Isaac Newton provided the physical laws (gravity and motion) that explained *why* planets orbit the Sun. While Copernicus originated the modern heliocentric theory, Galileo’s empirical observations were key to its acceptance and ‘proof’ at the time.

25. Which one among the following rulers established Pataliputra as the ca

Which one among the following rulers established Pataliputra as the capital of the Magadhan Empire ?

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Bimbisara

Bindusara

Ajatashatru

Ashoka

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While the earliest capital of the Magadhan Empire was Rajagriha (Rajgir), Pataliputra became increasingly important due to its strategic location. Ajatashatru, the son of Bimbisara, is credited with fortifying the village of Pataligrama (which grew into Pataliputra) during his conflicts, particularly against the Vajjis. His son, Udayin (Udayibhadra), subsequently shifted the capital of the Magadhan Empire from Rajagriha to Pataliputra due to its central and strategic position. Among the given options, Ajatashatru initiated the process of establishing Pataliputra as a significant stronghold by building a fort, paving the way for it to become the capital under his successor.

Ajatashatru fortified Pataliputra, which was later established as the capital of the Magadhan Empire by his son Udayin. Among the given options, Ajatashatru is the ruler most directly associated with initiating Pataliputra’s rise.

Pataliputra (modern Patna) remained the capital of major empires, including the Nanda and Mauryan empires, for centuries due to its advantageous location at the confluence of several major rivers (Ganges, Gandak, Son, and Ghaghara), providing natural defence and facilitating trade.

26. Yashovarman was ruler of which one of the following kingdoms ?

Yashovarman was ruler of which one of the following kingdoms ?

Kannauj

Mewar

Marwar

Kalinga

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Yashovarman was a powerful king who ruled Kannauj (Kanyakubja) in the early 8th century CE. He is known for his military campaigns and patronage of arts and literature. The famous poet Bhavabhuti lived in his court. Yashovarman’s reign represents a period of prominence for Kannauj before the rise of the Pratiharas, Palas, and Rashtrakutas who contested control over the region.

Yashovarman was a ruler of the kingdom of Kannauj.

Kannauj was a strategically important city in North India and was the capital of the Harsha’s empire before becoming a major political centre contested by various dynasties after his death. Yashovarman’s achievements are mentioned in historical texts and inscriptions.

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27. Who among the following was the author of the famous Sanskrit work

Who among the following was the author of the famous Sanskrit work ‘Mrichchhakatika’?

Kalidasa

Bhasa

Valmiki

Shudraka

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‘Mrichchhakatika’ (The Little Clay Cart) is one of the most famous and celebrated plays of ancient Indian literature. It is a Prakrit/Sanskrit drama attributed to Shudraka. The play is a ten-act *Prakarana* (a type of drama) focusing on the love story between a Brahmin merchant named Charudatta and a courtesan named Vasantasena, intertwined with political intrigue.

‘Mrichchhakatika’, the famous Sanskrit play, was authored by Shudraka.

Unlike many other surviving Sanskrit dramas which are often mythological or epic in theme, ‘Mrichchhakatika’ stands out for its portrayal of everyday life, diverse characters (including courtesans, thieves, and gamblers), and social commentary. Kalidasa is famous for plays like ‘Abhijnanashakuntalam’, Bhasa for plays like ‘Swapnavasavadattam’, and Valmiki is the author of the epic ‘Ramayana’.

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28. Which one of the following statements about Rabatak inscription is no

Which one of the following statements about Rabatak inscription is not correct ?

It throws important light on Kushana genealogy.

It refers to Kanishka as 'a king of kings and a son of God'.

The 23-line inscription is written in Gandhari language.

It mentions names of States which were part of Kanishka's empire.

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The Rabatak inscription is a stone inscription discovered in 1993 at Rabatak, Afghanistan. It is written in the Bactrian language (a Middle Iranian language) using the Greek script. It is historically significant as it provides crucial information about the genealogy of the Kushana king Kanishka I, listing his ancestors. It also mentions Kanishka’s status, referring to him as “king of kings, great king, the son of God” (shaonano shao Bazodeo). Furthermore, it lists various cities and regions that were under Kanishka’s rule. The statement that the inscription is written in the Gandhari language is incorrect; Gandhari is a Prakrit language usually written in the Kharosthi script.

The Rabatak inscription is written in the Bactrian language using the Greek script, not the Gandhari language.

The inscription was commissioned by Kanishka I and provides details about his lineage (mentioning Kujula Kadphises, Vima Taktu, and Vima Kadphises), his religious patronage (listing various deities), and the extent of his empire. It is one of the most important epigraphic sources for understanding the Kushana period.

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29. Which one among the following districts of Eastern India held a refere

Which one among the following districts of Eastern India held a referendum in 1947 to decide whether or not to join Pakistan ?

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Sylhet

Goalpara

Cachar

Jalpaiguri

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During the Partition of India in 1947, the district of Sylhet, which was part of the Assam province of British India, held a referendum. The population was predominantly Muslim, and the referendum was held to decide whether the district would remain part of India (Assam) or join the newly created Pakistan (specifically East Bengal, which later became Bangladesh). The referendum resulted in a vote in favour of joining Pakistan.

The Sylhet Referendum in 1947 decided the fate of the district, leading to its accession to East Pakistan during the Partition of India.

Most of Assam remained part of India, but due to its Muslim majority population and geographical contiguity with East Bengal, Sylhet’s status was put to a vote. A boundary commission (the Radcliffe Line) demarcated the exact border, and most of Sylhet went to Pakistan, although a small area remained in India as part of the Karimganj district.

30. Airbags work on the principle of a chemical reaction triggered by the

Airbags work on the principle of a chemical reaction triggered by the impact producing a gaseous product that causes a sudden volume change. Which one among the following chemical conversions is responsible for this ?

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Sodium azide into nitrogen gas

Solid carbon dioxide into gaseous carbon dioxide

Carbon dioxide into carbon monoxide

Sudden conversion of gaseous carbon dioxide into carbon monoxide

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Modern automotive airbags typically rely on the rapid decomposition of sodium azide (NaN₃). Upon impact, a sensor triggers an electric current that ignites a small amount of a starter compound, which in turn initiates the decomposition of sodium azide. The chemical reaction is: 2 NaN₃(s) → 2 Na(s) + 3 N₂(g). The large volume of nitrogen gas (N₂) produced rapidly inflates the airbag. Potassium nitrate and silicon dioxide are often included to react with the highly reactive sodium metal produced.

The rapid inflation of an airbag is caused by the generation of a large volume of gas from a chemical reaction triggered by impact. Sodium azide decomposing to nitrogen gas is the basis of this process.

The complete reaction mixture in an airbag contains sodium azide, an oxidizer (like potassium nitrate) to react with the sodium produced, and a substance like silicon dioxide or aluminum oxide to react with the products to form harmless slag. This ensures that no harmful substances are released into the car cabin.