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Question 1 of 15
1. Question
1 pointsWith reference to the Delhi Sultanate’s administrative and economic reforms, consider the following statements:
- Alauddin Khalji was the first Sultan to insist that in the Doab, land revenue should be assessed on the basis of measuring the land.
- The ‘Ghari’ and ‘Chari’ taxes were introduced by Ghiyasuddin Tughlaq to offset the losses from the abolition of agrarian cesses.
- Muhammad bin Tughlaq established a separate department called ‘Diwan-i-Amir-Kohi’ to extend cultivation by providing crop loans (Sondhar).
Which of the statements given above are correct?
Correct
Answer: (c)
Explanation:
Statement I is correct. Alauddin Khalji introduced a system of land revenue assessment in the Doab based on measurement of land. This marked a shift towards a more rational and controlled revenue administration, enabling the state to directly assess and collect a substantial share of agricultural produce.
Statement II is incorrect. The taxes known as Ghari (house tax) and Chari (grazing tax) were imposed during the reign of Alauddin Khalji, not Ghiyasuddin Tughlaq. Moreover, these taxes were part of Alauddin’s broader fiscal measures to strengthen state revenue and not a compensatory mechanism linked to the abolition of agrarian cesses as stated.
Statement III is correct. Muhammad bin Tughlaq established the Diwan-i-Amir-Kohi as a separate department aimed at agricultural expansion. The state provided loans, known as Sondhar, to cultivators to bring uncultivated land under production, reflecting an interventionist approach towards agrarian development.
Incorrect
Answer: (c)
Explanation:
Statement I is correct. Alauddin Khalji introduced a system of land revenue assessment in the Doab based on measurement of land. This marked a shift towards a more rational and controlled revenue administration, enabling the state to directly assess and collect a substantial share of agricultural produce.
Statement II is incorrect. The taxes known as Ghari (house tax) and Chari (grazing tax) were imposed during the reign of Alauddin Khalji, not Ghiyasuddin Tughlaq. Moreover, these taxes were part of Alauddin’s broader fiscal measures to strengthen state revenue and not a compensatory mechanism linked to the abolition of agrarian cesses as stated.
Statement III is correct. Muhammad bin Tughlaq established the Diwan-i-Amir-Kohi as a separate department aimed at agricultural expansion. The state provided loans, known as Sondhar, to cultivators to bring uncultivated land under production, reflecting an interventionist approach towards agrarian development.
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Question 2 of 15
2. Question
1 pointsConsider the following statements regarding the architectural developments:
Statement I: The use of ‘Pietra Dura’ for decorative purposes reached its climax during the reign of Shah Jahan, as seen in the Taj Mahal.
Statement II: Mughal architecture evolved from the robust, structural styles of the Sultanate and early Mughals toward a focus on refined ornamentation and symmetry.
Statement III: The introduction of marble as a primary building material allowed for the extensive use of inlay techniques using semi-precious stones.
Which one of the following is correct in respect of the above statements?
Correct
Answer: (a)
Explanation:
Statement I is correct. The technique of Pietra Dura, involving the inlay of semi-precious stones into marble, reached its highest refinement under Shah Jahan, most notably in the Taj Mahal.
Statement II is correct and explains Statement I. Mughal architecture gradually evolved from the relatively massive and austere styles of the Delhi Sultanate and early Mughal period to a more refined aesthetic emphasizing symmetry, proportion, and intricate ornamentation. This stylistic evolution created the conditions for the flourishing of decorative techniques such as Pietra Dura.
Statement III is correct and also explains Statement I. The increased use of white marble as a primary building material, especially during Shah Jahan’s reign, provided an ideal surface for delicate inlay work. Marble’s smooth texture and visual appeal enabled the extensive use of Pietra Dura with semi-precious stones.
Incorrect
Answer: (a)
Explanation:
Statement I is correct. The technique of Pietra Dura, involving the inlay of semi-precious stones into marble, reached its highest refinement under Shah Jahan, most notably in the Taj Mahal.
Statement II is correct and explains Statement I. Mughal architecture gradually evolved from the relatively massive and austere styles of the Delhi Sultanate and early Mughal period to a more refined aesthetic emphasizing symmetry, proportion, and intricate ornamentation. This stylistic evolution created the conditions for the flourishing of decorative techniques such as Pietra Dura.
Statement III is correct and also explains Statement I. The increased use of white marble as a primary building material, especially during Shah Jahan’s reign, provided an ideal surface for delicate inlay work. Marble’s smooth texture and visual appeal enabled the extensive use of Pietra Dura with semi-precious stones.
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Question 3 of 15
3. Question
1 pointsConsider the following pairs regarding Medieval Southern Kingdoms:
Kingdom Capital I. Hoysalas Dwarasamudra II. Yadavas Devagiri III. Kakatiyas Warangal IV. Pandyas Madurai How many of the above pairs are correctly matched?
Correct
Answer: (d)
Explanation
All four pairs are correctly matched.
- The Hoysalas had their capital at Dwarasamudra, identified with present-day Halebidu in Karnataka. It emerged as an important political and cultural centre under Hoysala rule and is especially noted for its temple architecture.
- The Yadavas, also known as the Seuna Yadavas, ruled from Devagiri, located in present-day Maharashtra. Devagiri later became well known in medieval Indian history because of its strategic location and its later association with the name Daulatabad.
- The Kakatiyas had their capital at Warangal in present-day Telangana. Warangal was the principal seat of their power and became prominent for its fortifications, irrigation works, and temple patronage.
- The Pandyas ruled from Madurai, one of the most important historic urban centres in South India. Madurai was not only their political capital but also a major centre of trade, religion, and Tamil culture.
Incorrect
Answer: (d)
Explanation
All four pairs are correctly matched.
- The Hoysalas had their capital at Dwarasamudra, identified with present-day Halebidu in Karnataka. It emerged as an important political and cultural centre under Hoysala rule and is especially noted for its temple architecture.
- The Yadavas, also known as the Seuna Yadavas, ruled from Devagiri, located in present-day Maharashtra. Devagiri later became well known in medieval Indian history because of its strategic location and its later association with the name Daulatabad.
- The Kakatiyas had their capital at Warangal in present-day Telangana. Warangal was the principal seat of their power and became prominent for its fortifications, irrigation works, and temple patronage.
- The Pandyas ruled from Madurai, one of the most important historic urban centres in South India. Madurai was not only their political capital but also a major centre of trade, religion, and Tamil culture.
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Question 4 of 15
4. Question
1 pointsWith reference to the Vijayanagar Empire, consider the following statements:
- The ‘Amara-nayaka’ system was a major political innovation derived from the Iqta system of the Delhi Sultanate.
- Under the ‘Ayagar’ system, every village was a separate unit and its affairs were managed by 12 functionaries who were salaried officials paid in cash by the central administration.
- Abdur Razzaq, an ambassador of Shah Rukh of Persia, visited Vijayanagar during the reign of Deva Raya II and praised its fortification.
Which of the statements given above is/are correct?
Correct
Answer: (c)
Explanation:
Statement I is correct. The Amara-nayaka system of the Vijayanagar Empire involved the assignment of revenue-yielding territories to military chiefs (Nayakas) in return for maintaining troops and rendering military service to the state. This arrangement bore functional resemblance to the Iqta system of the Delhi Sultanate, where revenue assignments were granted in lieu of service, particularly military obligations. Although adapted to local conditions, the underlying principle of delegated revenue rights linked to service obligations indicates a degree of institutional borrowing or parallel development.
Statement II is incorrect. Under the Ayagar system, villages were administered by a group of functionaries, often described as twelve officials responsible for various administrative, fiscal, and social functions. However, these officials were not salaried in cash by the central administration. Instead, they were typically compensated through grants of land, shares in agricultural produce, or other customary rights. Therefore, the assertion regarding cash payment by the central authority is not accurate.
Statement III is correct. Abdur Razzaq, the ambassador of Shah Rukh of Persia, visited the Vijayanagar Empire during the reign of Deva Raya II in the 15th century. His accounts provide valuable descriptions of the empire’s prosperity, urban planning, and especially its impressive fortifications, which he praised for their scale and strength.
Incorrect
Answer: (c)
Explanation:
Statement I is correct. The Amara-nayaka system of the Vijayanagar Empire involved the assignment of revenue-yielding territories to military chiefs (Nayakas) in return for maintaining troops and rendering military service to the state. This arrangement bore functional resemblance to the Iqta system of the Delhi Sultanate, where revenue assignments were granted in lieu of service, particularly military obligations. Although adapted to local conditions, the underlying principle of delegated revenue rights linked to service obligations indicates a degree of institutional borrowing or parallel development.
Statement II is incorrect. Under the Ayagar system, villages were administered by a group of functionaries, often described as twelve officials responsible for various administrative, fiscal, and social functions. However, these officials were not salaried in cash by the central administration. Instead, they were typically compensated through grants of land, shares in agricultural produce, or other customary rights. Therefore, the assertion regarding cash payment by the central authority is not accurate.
Statement III is correct. Abdur Razzaq, the ambassador of Shah Rukh of Persia, visited the Vijayanagar Empire during the reign of Deva Raya II in the 15th century. His accounts provide valuable descriptions of the empire’s prosperity, urban planning, and especially its impressive fortifications, which he praised for their scale and strength.
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Question 5 of 15
5. Question
1 pointsConsider the following elements with regard to the Deccan Sultanates:
- Introduction of the ‘Dakhni’ language as a medium of courtly expression.
- Construction of the ‘Gol Gumbaz’ by the Qutb Shahi dynasty of Golconda.
- The ‘Charminar’ was built to commemorate the victory over the Vijayanagar Empire at the Battle of Talikota.
- The founding of the city of Hyderabad by Muhammad Quli Qutb Shah.
How many of the above statements are correct?
Correct
Answer: (b)
Explanation:
Statement I is correct. The Dakhni language, an early form of Urdu influenced by Persian, Arabic, and local Deccan languages, emerged as an important medium of literary and courtly expression in the Deccan Sultanates. Both the Qutb Shahi rulers of Golconda and the Adil Shahi rulers of Bijapur actively patronised Dakhni literature, contributing to its growth as a distinct cultural and linguistic tradition.
Statement II is incorrect. The Gol Gumbaz, one of the most remarkable architectural achievements of medieval India, was constructed under the Adil Shahi dynasty at Bijapur during the reign of Muhammad Adil Shah. It is noted for its massive dome and the famous whispering gallery. It was not built by the Qutb Shahi dynasty of Golconda, making the statement factually incorrect.
Statement III is incorrect. The Charminar, located in Hyderabad, was constructed by Muhammad Quli Qutb Shah in 1591. It is widely believed to have been built to commemorate the end of a devastating plague and to mark the founding of the new capital. It was not associated with the victory over the Vijayanagar Empire at the Battle of Talikota (1565), which predates its construction and involved a coalition of Deccan Sultanates.
Statement IV is correct. Muhammad Quli Qutb Shah, the fifth ruler of the Qutb Shahi dynasty, founded the city of Hyderabad as a planned urban centre, shifting the focus from the older capital of Golconda. The establishment of Hyderabad marked an important phase in the political and cultural consolidation of the Qutb Shahi state.
Incorrect
Answer: (b)
Explanation:
Statement I is correct. The Dakhni language, an early form of Urdu influenced by Persian, Arabic, and local Deccan languages, emerged as an important medium of literary and courtly expression in the Deccan Sultanates. Both the Qutb Shahi rulers of Golconda and the Adil Shahi rulers of Bijapur actively patronised Dakhni literature, contributing to its growth as a distinct cultural and linguistic tradition.
Statement II is incorrect. The Gol Gumbaz, one of the most remarkable architectural achievements of medieval India, was constructed under the Adil Shahi dynasty at Bijapur during the reign of Muhammad Adil Shah. It is noted for its massive dome and the famous whispering gallery. It was not built by the Qutb Shahi dynasty of Golconda, making the statement factually incorrect.
Statement III is incorrect. The Charminar, located in Hyderabad, was constructed by Muhammad Quli Qutb Shah in 1591. It is widely believed to have been built to commemorate the end of a devastating plague and to mark the founding of the new capital. It was not associated with the victory over the Vijayanagar Empire at the Battle of Talikota (1565), which predates its construction and involved a coalition of Deccan Sultanates.
Statement IV is correct. Muhammad Quli Qutb Shah, the fifth ruler of the Qutb Shahi dynasty, founded the city of Hyderabad as a planned urban centre, shifting the focus from the older capital of Golconda. The establishment of Hyderabad marked an important phase in the political and cultural consolidation of the Qutb Shahi state.
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Question 6 of 15
6. Question
1 pointsConsider the following statements:
Statement I: The Sufi Silsilas (orders) were generally divided into ‘Ba-shara’ (those who followed Islamic Law) and ‘Be-shara’ (those who did not follow Islamic Law).
Statement II: The Chishti Silsila, founded in India by Moinuddin Chishti, adopted many local Indian practices like yogic breathing exercises and musical gatherings (Sama).
Which one of the following is correct in respect of the above statements?
Correct
Answer: (b)
Explanation:
Statement I is correct. Within the broader tradition of Sufism, the Sufi orders (Silsilas) were often classified into two broad categories—Ba-shara and Be-shara. The Ba-shara Sufis adhered strictly to the prescriptions of Islamic law (Sharia) and integrated mystical practices within the framework of orthodox religious norms. In contrast, the Be-shara Sufis were more heterodox in orientation and did not strictly conform to the legalistic aspects of Islam, often emphasizing personal spiritual experience over formal religious observance. This classification reflects doctrinal and behavioural differences within Sufi traditions.
Statement II is also correct. The Chishti Silsila, founded in India by Moinuddin Chishti, became one of the most influential Sufi orders in the subcontinent due to its inclusive and accommodative approach. The Chishtis consciously adopted several local Indian practices to connect with the broader population. These included the use of Sama (musical assemblies) as a medium of spiritual expression, as well as the incorporation of certain yogic breathing techniques for meditative purposes. Such adaptations facilitated cultural synthesis and enhanced the appeal of the order among diverse social groups.
However, Statement II does not explain Statement I. The classification into Ba-shara and Be-shara is based on the degree of adherence to Islamic law and represents an internal doctrinal categorisation within Sufism. On the other hand, the practices mentioned in Statement II relate to the Chishti order’s method of engaging with local traditions and expanding its social base.
Incorrect
Answer: (b)
Explanation:
Statement I is correct. Within the broader tradition of Sufism, the Sufi orders (Silsilas) were often classified into two broad categories—Ba-shara and Be-shara. The Ba-shara Sufis adhered strictly to the prescriptions of Islamic law (Sharia) and integrated mystical practices within the framework of orthodox religious norms. In contrast, the Be-shara Sufis were more heterodox in orientation and did not strictly conform to the legalistic aspects of Islam, often emphasizing personal spiritual experience over formal religious observance. This classification reflects doctrinal and behavioural differences within Sufi traditions.
Statement II is also correct. The Chishti Silsila, founded in India by Moinuddin Chishti, became one of the most influential Sufi orders in the subcontinent due to its inclusive and accommodative approach. The Chishtis consciously adopted several local Indian practices to connect with the broader population. These included the use of Sama (musical assemblies) as a medium of spiritual expression, as well as the incorporation of certain yogic breathing techniques for meditative purposes. Such adaptations facilitated cultural synthesis and enhanced the appeal of the order among diverse social groups.
However, Statement II does not explain Statement I. The classification into Ba-shara and Be-shara is based on the degree of adherence to Islamic law and represents an internal doctrinal categorisation within Sufism. On the other hand, the practices mentioned in Statement II relate to the Chishti order’s method of engaging with local traditions and expanding its social base.
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Question 7 of 15
7. Question
1 pointsWhat is the common characteristic of the medieval terms ‘Kuta-khada’, ‘Kudivaram’ and ‘Melvaram’ often mentioned in the context of Southern Kingdoms?
Correct
Answer: (b)
Explanation:
The terms Kudivaram and Melvaram are central to understanding agrarian relations in medieval South India, particularly under the Chola administration. Kudivaram referred to the rights of the cultivator or peasant over the land, including occupancy and cultivation rights. Melvaram, on the other hand, denoted the share of produce or revenue that was due to the state or superior landlord.
The term Kuta-khada is also associated with agrarian and revenue arrangements in South India and is used in the context of landholding and assessment practices. Collectively, these terms reflect a structured system of land rights and the division of agricultural produce between different stakeholders, especially the state and the cultivator.
Incorrect
Answer: (b)
Explanation:
The terms Kudivaram and Melvaram are central to understanding agrarian relations in medieval South India, particularly under the Chola administration. Kudivaram referred to the rights of the cultivator or peasant over the land, including occupancy and cultivation rights. Melvaram, on the other hand, denoted the share of produce or revenue that was due to the state or superior landlord.
The term Kuta-khada is also associated with agrarian and revenue arrangements in South India and is used in the context of landholding and assessment practices. Collectively, these terms reflect a structured system of land rights and the division of agricultural produce between different stakeholders, especially the state and the cultivator.
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Question 8 of 15
8. Question
1 pointsWith reference to the administrative and revenue systems of the Mughal Empire, consider the following statements:
- The ‘Sawar’ rank indicated the personal status and salary of the Mansabdar, while the ‘Zat’ rank indicated the number of cavalrymen he was required to maintain.
- The ‘Dahsala’ system was a method of land revenue assessment where the state demand was fixed based on the average produce and prices of the last ten years.
- Under the ‘Jagirdari’ system, the Mansabdars were granted hereditary ownership rights over the land assigned to them in lieu of their service to the state.
Which of the statements given above are INCORRECT?
Correct
Answer: (c)
Explanation:
Statement I is incorrect. In the Mansabdari system, the Zat rank indicated the personal status, rank, and salary of the Mansabdar, whereas the Sawar rank denoted the number of cavalrymen he was required to maintain. The statement reverses these roles, making it incorrect.
Statement II is correct. The Dahsala system, introduced during Akbar’s reign, fixed state demand based on the average produce and prevailing prices over the preceding ten years. It aimed at stabilizing revenue assessment and reducing fluctuations.
Statement III is incorrect. Under the Jagirdari system, Mansabdars were not granted hereditary ownership of land. They were only assigned the right to collect revenue from a jagir in lieu of salary, while ultimate ownership of land remained with the state.
Incorrect
Answer: (c)
Explanation:
Statement I is incorrect. In the Mansabdari system, the Zat rank indicated the personal status, rank, and salary of the Mansabdar, whereas the Sawar rank denoted the number of cavalrymen he was required to maintain. The statement reverses these roles, making it incorrect.
Statement II is correct. The Dahsala system, introduced during Akbar’s reign, fixed state demand based on the average produce and prevailing prices over the preceding ten years. It aimed at stabilizing revenue assessment and reducing fluctuations.
Statement III is incorrect. Under the Jagirdari system, Mansabdars were not granted hereditary ownership of land. They were only assigned the right to collect revenue from a jagir in lieu of salary, while ultimate ownership of land remained with the state.
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Question 9 of 15
9. Question
1 pointsConsider the following statements regarding the Vijayanagar temple architecture:
- The introduction of ‘Kalyana Mandapa’ (divine marriage halls) and ‘Amman Shrines’ were distinct features.
- The ‘Rayagopurams’ or monumental entrance gateways were often taller than the central shrines.
- Monolithic carvings such as the ‘Ugra Narasimha’ and the ‘Stone Chariot’ at Hampi represent the pinnacle of their sculpture.
- Most of the temples were built using soft soapstone, allowing for intricate carvings similar to the Hoysala style.
Which of the statements given above is/are correct?
Correct
Answer: (a)
Explanation:
Statement I is correct. Vijayanagar temple architecture introduced distinctive features such as Kalyana Mandapas, used for divine marriage rituals, and Amman shrines, dedicated to the consort of the main deity, reflecting ritual expansion and temple-centered socio-religious life.
Statement II is correct. The Rayagopurams, or monumental entrance gateways, became a hallmark of Vijayanagar architecture. These towering structures often dominated the temple complex and were frequently taller than the central shrine, marking a shift in architectural emphasis.
Statement III is correct. The monolithic sculptures at Hampi, such as the Ugra Narasimha and the Stone Chariot in the Vittala temple complex, exemplify the high level of craftsmanship and represent some of the finest achievements in Vijayanagar sculptural art.
Statement IV is incorrect. Vijayanagar temples were primarily constructed using hard granite, not soft soapstone. Soapstone was characteristic of Hoysala architecture, which allowed for highly intricate and detailed carvings, unlike the comparatively robust and less intricate carvings of Vijayanagar structures.
Incorrect
Answer: (a)
Explanation:
Statement I is correct. Vijayanagar temple architecture introduced distinctive features such as Kalyana Mandapas, used for divine marriage rituals, and Amman shrines, dedicated to the consort of the main deity, reflecting ritual expansion and temple-centered socio-religious life.
Statement II is correct. The Rayagopurams, or monumental entrance gateways, became a hallmark of Vijayanagar architecture. These towering structures often dominated the temple complex and were frequently taller than the central shrine, marking a shift in architectural emphasis.
Statement III is correct. The monolithic sculptures at Hampi, such as the Ugra Narasimha and the Stone Chariot in the Vittala temple complex, exemplify the high level of craftsmanship and represent some of the finest achievements in Vijayanagar sculptural art.
Statement IV is incorrect. Vijayanagar temples were primarily constructed using hard granite, not soft soapstone. Soapstone was characteristic of Hoysala architecture, which allowed for highly intricate and detailed carvings, unlike the comparatively robust and less intricate carvings of Vijayanagar structures.
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Question 10 of 15
10. Question
1 pointsConsider the following statements about the Vaishnavaite movement in Medieval India:
- Chaitanya Mahaprabhu popularized the ‘Sankirtana’ (congregational chanting) in Bengal as a form of devotion.
- Sankaradeva of Assam preached ‘Ekasarana Dharma’ and introduced the use of ‘Sattras’ (monasteries).
Which of the statements given above is/are correct?
Correct
Answer: (c)
Explanation:
Statement I is correct. Chaitanya Mahaprabhu was a prominent leader of the Vaishnavite Bhakti movement in eastern India. He popularized Sankirtana, or congregational chanting of the names of Krishna, as a central mode of devotional expression, especially in Bengal.
Statement II is correct. Sankaradeva propagated Ekasarana Dharma, a monotheistic form of Vaishnavism centered on devotion to Vishnu/Krishna. He also established Sattras (monastic and cultural institutions), which became important centers for religious, cultural, and social activities in Assam.
Incorrect
Answer: (c)
Explanation:
Statement I is correct. Chaitanya Mahaprabhu was a prominent leader of the Vaishnavite Bhakti movement in eastern India. He popularized Sankirtana, or congregational chanting of the names of Krishna, as a central mode of devotional expression, especially in Bengal.
Statement II is correct. Sankaradeva propagated Ekasarana Dharma, a monotheistic form of Vaishnavism centered on devotion to Vishnu/Krishna. He also established Sattras (monastic and cultural institutions), which became important centers for religious, cultural, and social activities in Assam.
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Question 11 of 15
11. Question
1 pointsA committee of 4 members is to be formed from a group of 5 men and 4 women. In how many ways can the committee be formed such that it contains at least one woman, but the number of women does not exceed the number of men?
Correct
Answer: (c)
Solution:
Total members = 4
Conditions:- At least one woman (W ≥ 1)
- Women ≤ Men (W ≤ M)
Possible valid cases:
- 1 Woman, 3 Men
- 2 Women, 2 Men
Case 1:
Ways = 4C1 × 5C3 = 4 × 10 = 40Case 2:
Ways = 4C2 × 5C2 = 6 × 10 = 60Total ways = 40 + 60 = 100
Incorrect
Answer: (c)
Solution:
Total members = 4
Conditions:- At least one woman (W ≥ 1)
- Women ≤ Men (W ≤ M)
Possible valid cases:
- 1 Woman, 3 Men
- 2 Women, 2 Men
Case 1:
Ways = 4C1 × 5C3 = 4 × 10 = 40Case 2:
Ways = 4C2 × 5C2 = 6 × 10 = 60Total ways = 40 + 60 = 100
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Question 12 of 15
12. Question
1 pointsHow many numbers between 100 and 1000 can be formed using the digits {1, 2, 3, 4, 5, 6, 7} such that the digits are in strictly increasing order?
Correct
Answer: (b)
Solution:
Strictly increasing order ⇒ arrangement is fixed once digits are chosenExample: choosing {2,5,7} → number formed = 257
So, we only need to select 3 distinct digits from 7
Number of ways = 7C3 = (7 × 6 × 5)/(3 × 2 × 1) = 35
Incorrect
Answer: (b)
Solution:
Strictly increasing order ⇒ arrangement is fixed once digits are chosenExample: choosing {2,5,7} → number formed = 257
So, we only need to select 3 distinct digits from 7
Number of ways = 7C3 = (7 × 6 × 5)/(3 × 2 × 1) = 35
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Question 13 of 15
13. Question
1 pointsThree unbiased dice are thrown together. What is the probability that the sum of the numbers appearing on the dice is a perfect square?
Correct
Answer: (a)
Solution:
Total outcomes = 6³ = 216Possible sums range from 3 to 18
Perfect squares in this range: 4, 9, 16Sum = 4:
(1,1,2) and permutations → 3 waysSum = 9:
(1,2,6) → 6 ways
(1,3,5) → 6 ways
(1,4,4) → 3 ways
(2,2,5) → 3 ways
(2,3,4) → 6 ways
(3,3,3) → 1 way
Total = 25Sum = 16:
(6,6,4) → 3 ways
(6,5,5) → 3 ways
Total = 6Total favourable = 3 + 25 + 6 = 34
Probability = 34/216 = 17/108
Incorrect
Answer: (a)
Solution:
Total outcomes = 6³ = 216Possible sums range from 3 to 18
Perfect squares in this range: 4, 9, 16Sum = 4:
(1,1,2) and permutations → 3 waysSum = 9:
(1,2,6) → 6 ways
(1,3,5) → 6 ways
(1,4,4) → 3 ways
(2,2,5) → 3 ways
(2,3,4) → 6 ways
(3,3,3) → 1 way
Total = 25Sum = 16:
(6,6,4) → 3 ways
(6,5,5) → 3 ways
Total = 6Total favourable = 3 + 25 + 6 = 34
Probability = 34/216 = 17/108
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Question 14 of 15
14. Question
1 pointsA bag contains 4 white and 2 black balls. Another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, what is the probability that one is white and the other is black?
Correct
Answer: (c)
Solution:
Bag 1:
P(W₁) = 4/6, P(B₁) = 2/6Bag 2:
P(W₂) = 3/8, P(B₂) = 5/8Case 1: White from Bag 1 and Black from Bag 2
= (4/6) × (5/8) = 20/48Case 2: Black from Bag 1 and White from Bag 2
= (2/6) × (3/8) = 6/48Total probability = 20/48 + 6/48 = 26/48 = 13/24
Incorrect
Answer: (c)
Solution:
Bag 1:
P(W₁) = 4/6, P(B₁) = 2/6Bag 2:
P(W₂) = 3/8, P(B₂) = 5/8Case 1: White from Bag 1 and Black from Bag 2
= (4/6) × (5/8) = 20/48Case 2: Black from Bag 1 and White from Bag 2
= (2/6) × (3/8) = 6/48Total probability = 20/48 + 6/48 = 26/48 = 13/24
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Question 15 of 15
15. Question
1 pointsReading Comprehension
Passage:
The concept of ‘Universal Basic Income’ (UBI) is often critiqued as a fiscal burden that incentivizes sloth. However, this perspective ignores the changing nature of the labor market where automation threatens even high-skill cognitive roles. In a future where ‘decoupling’ of labor from income becomes a systemic necessity rather than a radical choice, UBI could serve as the foundational floor for human dignity. The challenge lies not in the morality of the grant, but in the structural redesign of the social contract to ensure that leisure leads to creative contribution rather than social stagnation.Question:
Which of the following is the most logical and critical inference that can be drawn from the passage?Correct
Answer: (b)
Solution:
Why (b) is correct: The passage explicitly mentions the “changing nature of the labor market” and a future where “‘decoupling’ of labor from income becomes a systemic necessity.” This indicates that the historical/traditional relationship where income is strictly a result of human labor is being disrupted by technological shifts like automation.Why (a) is incorrect: The author describes UBI as a potential “foundational floor,” but the word “only” is too restrictive and extreme. The passage doesn’t rule out other complementary solutions.
Why (c) is incorrect: The author states that ensuring leisure leads to creative contribution is a “challenge” that requires a “structural redesign of the social contract.” This means it is not an automatic outcome of providing UBI.
Why (d) is incorrect: While the author defends UBI against the “fiscal burden” critique by focusing on human dignity, the passage never claims the costs are “negligible.” It simply shifts the focus from the cost to the necessity of the grant.
Incorrect
Answer: (b)
Solution:
Why (b) is correct: The passage explicitly mentions the “changing nature of the labor market” and a future where “‘decoupling’ of labor from income becomes a systemic necessity.” This indicates that the historical/traditional relationship where income is strictly a result of human labor is being disrupted by technological shifts like automation.Why (a) is incorrect: The author describes UBI as a potential “foundational floor,” but the word “only” is too restrictive and extreme. The passage doesn’t rule out other complementary solutions.
Why (c) is incorrect: The author states that ensuring leisure leads to creative contribution is a “challenge” that requires a “structural redesign of the social contract.” This means it is not an automatic outcome of providing UBI.
Why (d) is incorrect: While the author defends UBI against the “fiscal burden” critique by focusing on human dignity, the passage never claims the costs are “negligible.” It simply shifts the focus from the cost to the necessity of the grant.
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