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Question 1 of 15
1. Question
1 pointsWhich of the following rock-cut cave complexes is uniquely characterized as a “mixed” site, containing Buddhist, Hindu, and Jain religious architecture within a single complex?
Correct
Answer: (b)
Explanation
The Ellora Caves (locally known as Verul Leni) represent the pinnacle of Indian rock-cut architecture and are world-renowned for their religious harmony and technical brilliance.
- Unlike Ajanta (which is exclusively Buddhist), Ellora contains 34 monasteries and temples belonging to three different religions, all carved into the side of a single basaltic hill.
- Buddhist (Caves 1–12): These include large multi-storeyed monasteries and a famous Chaitya hall (Cave 10, Vishwakarma Cave).
- Hindu (Caves 13–29): This group contains the magnificent Kailasa Temple (Cave 16), the largest monolithic rock-cut structure in the world.
- Jain (Caves 30–34): These belong to the Digambara sect and are known for their intricate carvings and sense of asceticism (e.g., Indra Sabha).
- The complex was constructed between the 6th and 10th centuries CE, supported by various dynasties including the Rashtrakutas and Kalachuris.
Incorrect
Answer: (b)
Explanation
The Ellora Caves (locally known as Verul Leni) represent the pinnacle of Indian rock-cut architecture and are world-renowned for their religious harmony and technical brilliance.
- Unlike Ajanta (which is exclusively Buddhist), Ellora contains 34 monasteries and temples belonging to three different religions, all carved into the side of a single basaltic hill.
- Buddhist (Caves 1–12): These include large multi-storeyed monasteries and a famous Chaitya hall (Cave 10, Vishwakarma Cave).
- Hindu (Caves 13–29): This group contains the magnificent Kailasa Temple (Cave 16), the largest monolithic rock-cut structure in the world.
- Jain (Caves 30–34): These belong to the Digambara sect and are known for their intricate carvings and sense of asceticism (e.g., Indra Sabha).
- The complex was constructed between the 6th and 10th centuries CE, supported by various dynasties including the Rashtrakutas and Kalachuris.
-
Question 2 of 15
2. Question
1 pointsConsider the following architectural features:
- Vimana
- Mandapa
- Gopuram
- Garbhagriha
How many of the above are features associated with the Dravida style of temple architecture?
Correct
Answer: (d)
Explanation
The Dravida (South Indian) style of temple architecture, which flourished under the patronage of the Pallavas, Cholas, Pandyas, and Vijayanagara rulers, is defined by several distinct structural elements.
- Vimana: This is the high, pyramidal tower directly above the main sanctum. Unlike the curvilinear Shikhara of North Indian (Nagara) temples, the Vimana in the South is a stepped, tiered pyramid that rises geometrically.
- Mandapa: These are the pillared entrance halls or porches leading to the inner sanctum. They were used for various purposes, including religious gatherings, rituals, and classical dance performances.
- Gopuram: These are the monumental, often highly ornate, gateway towers located at the entrance of the temple complex. In later Dravidian styles (especially during the Pandya and Vijayanagara periods), the Gopurams often became taller and more prominent than the Vimana itself.
- Garbhagriha: Literally meaning “womb-house,” this is the innermost sanctum sanctorum where the main deity is housed. In Dravida temples, the Garbhagriha is usually a square chamber located directly beneath the Vimana.
Incorrect
Answer: (d)
Explanation
The Dravida (South Indian) style of temple architecture, which flourished under the patronage of the Pallavas, Cholas, Pandyas, and Vijayanagara rulers, is defined by several distinct structural elements.
- Vimana: This is the high, pyramidal tower directly above the main sanctum. Unlike the curvilinear Shikhara of North Indian (Nagara) temples, the Vimana in the South is a stepped, tiered pyramid that rises geometrically.
- Mandapa: These are the pillared entrance halls or porches leading to the inner sanctum. They were used for various purposes, including religious gatherings, rituals, and classical dance performances.
- Gopuram: These are the monumental, often highly ornate, gateway towers located at the entrance of the temple complex. In later Dravidian styles (especially during the Pandya and Vijayanagara periods), the Gopurams often became taller and more prominent than the Vimana itself.
- Garbhagriha: Literally meaning “womb-house,” this is the innermost sanctum sanctorum where the main deity is housed. In Dravida temples, the Garbhagriha is usually a square chamber located directly beneath the Vimana.
-
Question 3 of 15
3. Question
1 pointsConsider the following statements regarding Vijayanagara architecture:
- It is characterized by the presence of Kalyana Mandapas and highly carved pillars featuring the Yali motif.
- Temples of this tradition often show a marked development in pillared halls and ornate sculptural decoration.
Which of the statements given above is/are correct?
Correct
Answer: (c)
Explanation
The Vijayanagara Empire (14th–17th Century) produced a distinctive style of architecture that was a synthesis of earlier Dravida styles (Chola, Hoysala, and Pandya), but with a much higher degree of ornamentation and structural scale.
- Statement 1 is correct: One of the most unique contributions of the Vijayanagara style is the Kalyana Mandapa (marriage hall). These were elaborate, open-pillared halls used for the symbolic wedding ceremonies of the deity. Furthermore, the pillars are iconic; they are often monolithic and feature the Yali motif—a mythical creature with the body of a lion and the head of an elephant, often depicted in a rearing position.
- Statement 2 is correct: There was a marked development in the complexity and number of pillared halls (Mandapas). The Thousand Pillar Mandapa at the Vitthala Temple in Hampi is a prime example. The decoration became incredibly intricate, with pillars often featuring small relief carvings of gods, dancers, and scenes from the epics, or even “musical pillars” that produce different notes when struck.
The Vijayanagara style wasn’t limited to temples. The ruins of Hampi showcase sophisticated secular structures like the Lotus Mahal and the Elephant Stables, which display an Indo-Islamic influence through the use of arches and domes.
The era is also known for massive monolithic statues, such as the Ugra Narasimha and the Sasivekalu Ganesha at Hampi.
Incorrect
Answer: (c)
Explanation
The Vijayanagara Empire (14th–17th Century) produced a distinctive style of architecture that was a synthesis of earlier Dravida styles (Chola, Hoysala, and Pandya), but with a much higher degree of ornamentation and structural scale.
- Statement 1 is correct: One of the most unique contributions of the Vijayanagara style is the Kalyana Mandapa (marriage hall). These were elaborate, open-pillared halls used for the symbolic wedding ceremonies of the deity. Furthermore, the pillars are iconic; they are often monolithic and feature the Yali motif—a mythical creature with the body of a lion and the head of an elephant, often depicted in a rearing position.
- Statement 2 is correct: There was a marked development in the complexity and number of pillared halls (Mandapas). The Thousand Pillar Mandapa at the Vitthala Temple in Hampi is a prime example. The decoration became incredibly intricate, with pillars often featuring small relief carvings of gods, dancers, and scenes from the epics, or even “musical pillars” that produce different notes when struck.
The Vijayanagara style wasn’t limited to temples. The ruins of Hampi showcase sophisticated secular structures like the Lotus Mahal and the Elephant Stables, which display an Indo-Islamic influence through the use of arches and domes.
The era is also known for massive monolithic statues, such as the Ugra Narasimha and the Sasivekalu Ganesha at Hampi.
-
Question 4 of 15
4. Question
1 pointsConsider the following categories of puppetry, their forms, and the regions to which they belong:
Category of puppetry Form Region 1. String Kathputli Rajasthan 2. Shadow Tholu Bommalata Andhra Pradesh 3. Rod Yampuri Bihar How many of the above entries are correctly matched?
Correct
Answer: (c)
Explanation
Puppetry is one of the oldest forms of entertainment and storytelling in India, deeply rooted in local folklore and religious myths. The various forms are classified based on the mechanism used to manipulate the puppets.
- Entry 1 is correctly matched: Kathputli is the most popular form of string puppetry in India, originating from Rajasthan. The puppets are carved from wood (hence the name Kath meaning wood and Putli meaning doll) and are controlled by strings attached to the fingers of the puppeteer. A unique feature is the lack of legs, with long trailing skirts used instead.
- Entry 2 is correctly matched: Tholu Bommalata is a traditional shadow puppetry form from Andhra Pradesh. The puppets are large, made of translucent leather, and are intricately painted. They are manipulated behind a white screen with a light source behind them, creating colorful shadows for the audience.
- Entry 3 is correctly matched: Yampuri is a traditional rod puppetry form from Bihar. Unlike the jointed rod puppets of West Bengal (Putul Nautch), Yampuri puppets are usually made of wood and are manipulated by rods from below. The plays typically revolve around the court of Yama (the God of Death) and carry moral lessons.
All three entries are correctly matched.
Incorrect
Answer: (c)
Explanation
Puppetry is one of the oldest forms of entertainment and storytelling in India, deeply rooted in local folklore and religious myths. The various forms are classified based on the mechanism used to manipulate the puppets.
- Entry 1 is correctly matched: Kathputli is the most popular form of string puppetry in India, originating from Rajasthan. The puppets are carved from wood (hence the name Kath meaning wood and Putli meaning doll) and are controlled by strings attached to the fingers of the puppeteer. A unique feature is the lack of legs, with long trailing skirts used instead.
- Entry 2 is correctly matched: Tholu Bommalata is a traditional shadow puppetry form from Andhra Pradesh. The puppets are large, made of translucent leather, and are intricately painted. They are manipulated behind a white screen with a light source behind them, creating colorful shadows for the audience.
- Entry 3 is correctly matched: Yampuri is a traditional rod puppetry form from Bihar. Unlike the jointed rod puppets of West Bengal (Putul Nautch), Yampuri puppets are usually made of wood and are manipulated by rods from below. The plays typically revolve around the court of Yama (the God of Death) and carry moral lessons.
All three entries are correctly matched.
-
Question 5 of 15
5. Question
1 pointsConsider the following statements regarding Odissi:
- The Tribhanga posture, marked by three bends in the body, is a foundational element of its aesthetic expression.
- It has traditionally been associated with Mahari and Gotipua performance traditions.
Which of the statements given above is/are correct?
Correct
Answer: (c)
Explanation
Odissi is the traditional classical dance form of Odisha, known for its fluid movements, lyrical quality, and deep connection to temple sculpture.
Statement 1 is correct: The Tribhanga (three-bend) posture is the hallmark of Odissi. It involves a three-fold deflection of the body—at the neck, the torso, and the knees. This creates a soft ‘S’ curve that mimics the graceful silhouettes of the “Alasa Kanyas” found in the carvings of the Sun Temple at Konark and other Odishan temples.
Statement 2 is correct: Odissi has two primary historical lineages:
- Maharis: These were female temple dancers (similar to Devadasis) who performed in the service of Lord Jagannath at the Puri temple. They were the original repositories of the dance.
- Gotipuas: These were young boys who dressed as girls to perform the dance outside the temple precincts. They introduced more acrobatic elements and helped sustain the tradition during periods when the Mahari system faced decline.
The dance is accompanied by Odissi music, which has its own unique system of Ragas and Talas, distinct from both Carnatic and Hindustani traditions.
Hence, both statements 1 and 2 are correct.
Incorrect
Answer: (c)
Explanation
Odissi is the traditional classical dance form of Odisha, known for its fluid movements, lyrical quality, and deep connection to temple sculpture.
Statement 1 is correct: The Tribhanga (three-bend) posture is the hallmark of Odissi. It involves a three-fold deflection of the body—at the neck, the torso, and the knees. This creates a soft ‘S’ curve that mimics the graceful silhouettes of the “Alasa Kanyas” found in the carvings of the Sun Temple at Konark and other Odishan temples.
Statement 2 is correct: Odissi has two primary historical lineages:
- Maharis: These were female temple dancers (similar to Devadasis) who performed in the service of Lord Jagannath at the Puri temple. They were the original repositories of the dance.
- Gotipuas: These were young boys who dressed as girls to perform the dance outside the temple precincts. They introduced more acrobatic elements and helped sustain the tradition during periods when the Mahari system faced decline.
The dance is accompanied by Odissi music, which has its own unique system of Ragas and Talas, distinct from both Carnatic and Hindustani traditions.
Hence, both statements 1 and 2 are correct.
-
Question 6 of 15
6. Question
1 pointsConsider the following statements about the murals of the Lepakshi Temple:
- They portray episodes from the Ramayana and the Mahabharata.
- They are marked by a complete absence of primary colours, particularly blue.
- The Lepakshi Temple is situated in present-day Tamil Nadu.
Which of the statements given above are incorrect?
Correct
Answer: (b)
Explanation
The murals of the Veerabhadra Temple at Lepakshi represent some of the finest examples of the Vijayanagara style of painting, showcasing the artistic transition from the medieval to the early modern period in South India.
- Statement 1 is correct: The ceilings of the temple are covered with extensive murals depicting various scenes from the Ramayana, the Mahabharata, and the Puranas. One of the most famous panels depicts the Kirataruniya (Arjuna’s penance) and the incarnations of Vishnu.
- Statement 2 is incorrect: While the Lepakshi paintings are known for their distinct earthy palette (using ochre, black, and green), they do not feature a “complete absence” of primary colours. However, it is a notable stylistic feature that blue is very rarely used in these murals. This distinguishes them from the earlier Chola paintings or later Tanjore styles where blue became more prominent.
- Statement 3 is incorrect: The Lepakshi Temple is situated in the Anantapur district of Andhra Pradesh, not Tamil Nadu. It was built during the 16th century by the brothers Virupanna and Viranna, who were governors under the Vijayanagara King Achyuta Deva Raya.
Hence, statements 2 and 3 are incorrect.
Incorrect
Answer: (b)
Explanation
The murals of the Veerabhadra Temple at Lepakshi represent some of the finest examples of the Vijayanagara style of painting, showcasing the artistic transition from the medieval to the early modern period in South India.
- Statement 1 is correct: The ceilings of the temple are covered with extensive murals depicting various scenes from the Ramayana, the Mahabharata, and the Puranas. One of the most famous panels depicts the Kirataruniya (Arjuna’s penance) and the incarnations of Vishnu.
- Statement 2 is incorrect: While the Lepakshi paintings are known for their distinct earthy palette (using ochre, black, and green), they do not feature a “complete absence” of primary colours. However, it is a notable stylistic feature that blue is very rarely used in these murals. This distinguishes them from the earlier Chola paintings or later Tanjore styles where blue became more prominent.
- Statement 3 is incorrect: The Lepakshi Temple is situated in the Anantapur district of Andhra Pradesh, not Tamil Nadu. It was built during the 16th century by the brothers Virupanna and Viranna, who were governors under the Vijayanagara King Achyuta Deva Raya.
Hence, statements 2 and 3 are incorrect.
-
Question 7 of 15
7. Question
1 pointsConsider the following UNESCO-inscribed elements of India’s intangible cultural heritage:
- Ramlila
- Kutiyattam
- Tradition of Vedic chanting
- Durga Puja in Kolkata
How many of the above are inscribed on the UNESCO Representative List of the Intangible Cultural Heritage of Humanity?
Correct
Answer: (d)
Explanation
The UNESCO Representative List of the Intangible Cultural Heritage of Humanity was established to ensure better protection of important intangible cultural heritages worldwide and create awareness of their significance.
- Ramlila: Inscribed in 2008. It is the traditional performance of the Ramayana and is performed across northern India during the festival of Dussehra.
- Kutiyattam: Inscribed in 2008. It is a Sanskrit theatrical tradition from Kerala and is one of India’s oldest living theatrical forms. It was recognized by UNESCO as a Masterpiece of the Oral and Intangible Heritage of Humanity even before the formal list was created.
- Tradition of Vedic chanting: Inscribed in 2008. This recognizes the traditional way of chanting the Vedas, which has been preserved through an oral tradition for thousands of years, characterized by specific nuances of pronunciation and intonation.
- Durga Puja in Kolkata: Inscribed in 2021. This recognized the festival not just as a religious event, but as a public performance of art and community, involving complex installations (pandals), traditional drumming (dhak), and craftsmanship.
Hence, all four elements are inscribed on the list.
Incorrect
Answer: (d)
Explanation
The UNESCO Representative List of the Intangible Cultural Heritage of Humanity was established to ensure better protection of important intangible cultural heritages worldwide and create awareness of their significance.
- Ramlila: Inscribed in 2008. It is the traditional performance of the Ramayana and is performed across northern India during the festival of Dussehra.
- Kutiyattam: Inscribed in 2008. It is a Sanskrit theatrical tradition from Kerala and is one of India’s oldest living theatrical forms. It was recognized by UNESCO as a Masterpiece of the Oral and Intangible Heritage of Humanity even before the formal list was created.
- Tradition of Vedic chanting: Inscribed in 2008. This recognizes the traditional way of chanting the Vedas, which has been preserved through an oral tradition for thousands of years, characterized by specific nuances of pronunciation and intonation.
- Durga Puja in Kolkata: Inscribed in 2021. This recognized the festival not just as a religious event, but as a public performance of art and community, involving complex installations (pandals), traditional drumming (dhak), and craftsmanship.
Hence, all four elements are inscribed on the list.
-
Question 8 of 15
8. Question
1 pointsThe Bidriware craft, noted for its distinctive silver inlay on a blackened surface, is traditionally made on which of the following base metals?
Correct
Answer: (b)
Explanation
Bidriware is a renowned metal handicraft that originated in Bidar, Karnataka, during the 14th century under the patronage of the Bahmani Sultans. Its striking appearance comes from the contrast between the shiny silver inlay and the deep black matte background.
- The Base Metal: The craft is unique because the base is not pure iron or steel, but an alloy of zinc and copper (usually in a ratio of 16:1). Zinc is the primary component because it reacts specifically with the soil used in the blackening process.
- The Inlay: Pure silver wire or sheets are inlaid into grooves carved into this zinc-based alloy.
The base metal used is a zinc-based alloy.
Incorrect
Answer: (b)
Explanation
Bidriware is a renowned metal handicraft that originated in Bidar, Karnataka, during the 14th century under the patronage of the Bahmani Sultans. Its striking appearance comes from the contrast between the shiny silver inlay and the deep black matte background.
- The Base Metal: The craft is unique because the base is not pure iron or steel, but an alloy of zinc and copper (usually in a ratio of 16:1). Zinc is the primary component because it reacts specifically with the soil used in the blackening process.
- The Inlay: Pure silver wire or sheets are inlaid into grooves carved into this zinc-based alloy.
The base metal used is a zinc-based alloy.
-
Question 9 of 15
9. Question
1 pointsWith reference to UNESCO’s Creative Cities Network (UCCN), consider the following statements about Lucknow:
- It has been designated as a Creative City of Gastronomy by UNESCO.
- It is the first Indian city to receive recognition in the field of Gastronomy under UCCN.
Which of the statements given above is/are correct?
Correct
Answer: (a)
Explanation
The UNESCO Creative Cities Network (UCCN) was created in 2004 to promote cooperation among cities that have identified creativity as a strategic factor for sustainable urban development.
- Statement 1 is correct: Lucknow was officially designated as a UNESCO Creative City of Gastronomy in late 2025. The city is world-renowned for its “Awadhi Cuisine,” characterized by the Dum Pukht (slow cooking) style, refined use of spices, and its iconic kebabs and biryanis. This recognition acknowledges Lucknow’s culinary heritage as a vital part of its cultural and economic identity.
- Statement 2 is incorrect: Lucknow is not the first Indian city to receive this recognition. Hyderabad was the first Indian city to be designated as a Creative City of Gastronomy in 2019.
- Criteria for Gastronomy: To be recognized, a city must have a well-developed gastronomy that is characteristic of the city/region, a vibrant gastronomy community, and traditional restaurants/chefs that preserve local cooking methods.
- Cities in the network commit to sharing best practices and developing partnerships that involve the public and private sectors, as well as civil society, to strengthen the creation, production, and distribution of cultural activities.
Only statement 1 is correct.
Incorrect
Answer: (a)
Explanation
The UNESCO Creative Cities Network (UCCN) was created in 2004 to promote cooperation among cities that have identified creativity as a strategic factor for sustainable urban development.
- Statement 1 is correct: Lucknow was officially designated as a UNESCO Creative City of Gastronomy in late 2025. The city is world-renowned for its “Awadhi Cuisine,” characterized by the Dum Pukht (slow cooking) style, refined use of spices, and its iconic kebabs and biryanis. This recognition acknowledges Lucknow’s culinary heritage as a vital part of its cultural and economic identity.
- Statement 2 is incorrect: Lucknow is not the first Indian city to receive this recognition. Hyderabad was the first Indian city to be designated as a Creative City of Gastronomy in 2019.
- Criteria for Gastronomy: To be recognized, a city must have a well-developed gastronomy that is characteristic of the city/region, a vibrant gastronomy community, and traditional restaurants/chefs that preserve local cooking methods.
- Cities in the network commit to sharing best practices and developing partnerships that involve the public and private sectors, as well as civil society, to strengthen the creation, production, and distribution of cultural activities.
Only statement 1 is correct.
-
Question 10 of 15
10. Question
1 pointsWhich of the following architectural features was a significant innovation introduced during the Delhi Sultanate, enabling the construction of large domes and spacious interiors free of pillars?
Correct
Answer: (a)
Explanation:
The arcuate system was a significant architectural innovation introduced during the Delhi Sultanate period. This system involved the use of true arches constructed with voussoirs (interlocking wedge-shaped stones) and keystones, allowing for the weight of the superstructure to be evenly distributed. This technique enabled architects to span large spaces and build domes resting on pendentives and squinches, creating interiors free of pillars and supports.
- Trabeate system with corbelled arches: Involves stacking stones or bricks so that each layer slightly overhangs the one below, commonly used in pre-Islamic Indian architecture.
- Use of trusses and beams: Pertains to wooden constructions, not significant in monumental Indo-Islamic architecture.
- Post and lintel system with bracket supports: Traditional Indian architectural method using vertical posts and horizontal lintels, limiting in creating large interior spaces.
Incorrect
Answer: (a)
Explanation:
The arcuate system was a significant architectural innovation introduced during the Delhi Sultanate period. This system involved the use of true arches constructed with voussoirs (interlocking wedge-shaped stones) and keystones, allowing for the weight of the superstructure to be evenly distributed. This technique enabled architects to span large spaces and build domes resting on pendentives and squinches, creating interiors free of pillars and supports.
- Trabeate system with corbelled arches: Involves stacking stones or bricks so that each layer slightly overhangs the one below, commonly used in pre-Islamic Indian architecture.
- Use of trusses and beams: Pertains to wooden constructions, not significant in monumental Indo-Islamic architecture.
- Post and lintel system with bracket supports: Traditional Indian architectural method using vertical posts and horizontal lintels, limiting in creating large interior spaces.
-
Question 11 of 15
11. Question
1 pointsA committee of 6 members is to be formed from a group of 5 men and 4 women such that at least 2 women and at most 3 men are included. How many such committees can be formed?
Correct
Answer: C
Solution:
Total members required = 6
Men available = 5, Women available = 4Conditions:
- Women ≥ 2
- Men ≤ 3
Possible valid cases:
Case 1: 3 women and 3 men
Ways = selecting 3 women from 4 × selecting 3 men from 5
= 4C3 × 5C3
= 4 × 10 = 40Case 2: 4 women and 2 men
= 4C4 × 5C2
= 1 × 10 = 10Case 3: 2 women and 4 men → not allowed (men exceed limit)
Total ways = 40 + 10 = 50
Incorrect
Answer: C
Solution:
Total members required = 6
Men available = 5, Women available = 4Conditions:
- Women ≥ 2
- Men ≤ 3
Possible valid cases:
Case 1: 3 women and 3 men
Ways = selecting 3 women from 4 × selecting 3 men from 5
= 4C3 × 5C3
= 4 × 10 = 40Case 2: 4 women and 2 men
= 4C4 × 5C2
= 1 × 10 = 10Case 3: 2 women and 4 men → not allowed (men exceed limit)
Total ways = 40 + 10 = 50
-
Question 12 of 15
12. Question
1 pointsEight persons are seated around a circular table. Two particular persons do not wish to sit together. In how many ways can the seating arrangement be made?
Correct
Answer: B
Solution:
Total circular arrangements of 8 persons = (8 − 1)! = 7! = 5040
Now calculate arrangements where the two particular persons sit together:
Treat them as one unit → total units = 7
Circular arrangements = (7 − 1)! = 6! = 720Internal arrangement of the pair = 2
Total cases where they sit together = 720 × 2 = 1440
Required arrangements = 5040 − 1440 = 3600
Incorrect
Answer: B
Solution:
Total circular arrangements of 8 persons = (8 − 1)! = 7! = 5040
Now calculate arrangements where the two particular persons sit together:
Treat them as one unit → total units = 7
Circular arrangements = (7 − 1)! = 6! = 720Internal arrangement of the pair = 2
Total cases where they sit together = 720 × 2 = 1440
Required arrangements = 5040 − 1440 = 3600
-
Question 13 of 15
13. Question
1 pointsIn how many ways can 5 identical balls be distributed among 3 distinct boxes such that no box remains empty?
Correct
Answer: D
Solution:
Let the number of balls in the three boxes be x1, x2, x3
x1 + x2 + x3 = 5, with each xi ≥ 1
Put yi = xi − 1
Then y1 + y2 + y3 = 2
Number of non-negative integer solutions = (2 + 3 − 1)C(3 − 1)
= 4C2 = 6Incorrect
Answer: D
Solution:
Let the number of balls in the three boxes be x1, x2, x3
x1 + x2 + x3 = 5, with each xi ≥ 1
Put yi = xi − 1
Then y1 + y2 + y3 = 2
Number of non-negative integer solutions = (2 + 3 − 1)C(3 − 1)
= 4C2 = 6 -
Question 14 of 15
14. Question
1 pointsA box contains 4 red, 3 blue and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of different colours?
Correct
Answer: B
Solution:
Total balls = 10
Total ways of selecting 2 balls = 10C2 = 45
Now find probability of same colour:
Red-red = 4C2 = 6
Blue-blue = 3C2 = 3
Green-green = 3C2 = 3Total same colour = 12
Different colour cases = 45 − 12 = 33
Probability = 33/45 = 11/15
Incorrect
Answer: B
Solution:
Total balls = 10
Total ways of selecting 2 balls = 10C2 = 45
Now find probability of same colour:
Red-red = 4C2 = 6
Blue-blue = 3C2 = 3
Green-green = 3C2 = 3Total same colour = 12
Different colour cases = 45 − 12 = 33
Probability = 33/45 = 11/15
-
Question 15 of 15
15. Question
1 pointsRead the following passage and answer the question:
In recent years, the increasing reliance on artificial intelligence in governance has sparked a debate about accountability. While AI systems promise efficiency and data-driven decisions, they often operate as “black boxes,” making it difficult to trace how a particular decision was reached. This opacity raises concerns about fairness, especially when such systems are used in sensitive domains like criminal justice or welfare distribution. Critics argue that delegating authority to machines without adequate transparency may erode democratic principles, whereas proponents maintain that with proper regulation, AI can enhance objectivity and reduce human bias.
What is the central argument of the passage?
Correct
Answer: C
Solution:
The central argument of the passage is (c).
Reasoning: The passage presents a balanced view of the issue. It highlights the primary concern (the “black box” nature and lack of transparency) while also acknowledging the potential benefits mentioned by proponents (efficiency, objectivity, and reduction of human bias).
- (a) is too extreme; the passage mentions concerns but doesn’t conclude it is inherently harmful.
- (b) is incorrect because the passage says AI can reduce bias if regulated.
- (d) is not stated; the passage actually suggests AI can be more objective than humans.
Incorrect
Answer: C
Solution:
The central argument of the passage is (c).
Reasoning: The passage presents a balanced view of the issue. It highlights the primary concern (the “black box” nature and lack of transparency) while also acknowledging the potential benefits mentioned by proponents (efficiency, objectivity, and reduction of human bias).
- (a) is too extreme; the passage mentions concerns but doesn’t conclude it is inherently harmful.
- (b) is incorrect because the passage says AI can reduce bias if regulated.
- (d) is not stated; the passage actually suggests AI can be more objective than humans.
Click Here to Download the Insta Test PDF – Question Paper Click Here to Download the Insta Test PDF – Synopsis
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