Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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Question 1 of 5
1. Question
A container is formed by surmounting a hemisphere on a right circular cylinder of the same radius as that of the hemisphere. If the volume of the container is 1863π m3 and the radius of the cylinder is 9 m, then find the height of the container.
Correct
Answer: c
Volume of the container = Volume of the cylinder + Volume of the hemisphere Volume of the container = π 92h + (2/3) π 93 = 1863π
= 81π (h + 6) = 1863π
Solving we get h = 17
So the height of the container = 17 + 9 = 26 m
Incorrect
Answer: c
Volume of the container = Volume of the cylinder + Volume of the hemisphere Volume of the container = π 92h + (2/3) π 93 = 1863π
= 81π (h + 6) = 1863π
Solving we get h = 17
So the height of the container = 17 + 9 = 26 m
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Question 2 of 5
2. Question
A fund of ₹27,900 is to be shared among 15 teachers, 25 staff, and 90 students in the per-head ratio 9 : 6 : 2. Before distributing, 10% of the total is kept aside for a welfare fund and then deducted proportionately from each group’s allocation. What is the final per-student share?
Correct
Answer : C
Solution:
Per-head ratio ⇒ group-weighted parts
Teachers: 15×9=135Staff: 25×6=150
Students: 90×2=180
Total parts =135+150+180=465.Each part (before the 10% deduction):
27,900/465=60
So initial allocations:
- Teachers = 135×60=₹8,100
- Staff = 150×60=₹9,000
- Students = 180×60=₹10,800
Per student (initial) =10,800/90=₹120
Now 10% is set aside proportionately, i.e., everyone loses 10% of their initial allocation.
Thus, final per-student = 120×0.9=₹108Incorrect
Answer : C
Solution:
Per-head ratio ⇒ group-weighted parts
Teachers: 15×9=135Staff: 25×6=150
Students: 90×2=180
Total parts =135+150+180=465.Each part (before the 10% deduction):
27,900/465=60
So initial allocations:
- Teachers = 135×60=₹8,100
- Staff = 150×60=₹9,000
- Students = 180×60=₹10,800
Per student (initial) =10,800/90=₹120
Now 10% is set aside proportionately, i.e., everyone loses 10% of their initial allocation.
Thus, final per-student = 120×0.9=₹108 -
Question 3 of 5
3. Question
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Is (p + q)² – 4pq, where p, q are natural numbers, positive?
Statement I: p < q.
Statement II: p > q.
Which one of the following is correct in respect of the above Question and the Statements?
Correct
Answer: B
Solution
(p + q)2 – 4pq, where p and q are natural numbers.
= p2 + q2 + 2pq – 4pq
= p2 + q2 – 2pq
= (p – q)2
The expression (p – q)2 will be positive if p > q or q > p.
However, if p = q, then (p – q)2 = 0, which is not a positive number.
Thus, the question can be answered if we know that p ≠ q, i.e. if either statement I or II is correct.
Hence, option (b) is correct.
Incorrect
Answer: B
Solution
(p + q)2 – 4pq, where p and q are natural numbers.
= p2 + q2 + 2pq – 4pq
= p2 + q2 – 2pq
= (p – q)2
The expression (p – q)2 will be positive if p > q or q > p.
However, if p = q, then (p – q)2 = 0, which is not a positive number.
Thus, the question can be answered if we know that p ≠ q, i.e. if either statement I or II is correct.
Hence, option (b) is correct.
-
Question 4 of 5
4. Question
The rapid pace of urban migration in India is reshaping the social and economic landscape of cities. While migration often offers better employment prospects and access to services, it has also intensified housing shortages, traffic congestion, and pressure on public infrastructure. Migrants from rural areas frequently end up in informal settlements, lacking adequate sanitation, healthcare, and security. At the same time, middle- and upper-income residents benefit disproportionately from city growth through better services and employment networks. Experts argue that unless urban planning integrates affordable housing, public transport expansion, and equitable access to amenities, migration will continue to deepen urban inequalities rather than reduce them.
Q24. Based on the above passage, the following assumptions have been made:
- Without inclusive urban planning, migration may increase inequality in cities.
- Improving infrastructure alone will automatically lead to equitable outcomes for all urban residents.
Select the correct answer using the code given below:
Correct
Solution: (a)
Explanation:
• Statement 1 is valid: The passage clearly warns that without measures like affordable housing and equitable access to services, migration will worsen inequality.
• Statement 2 is invalid: The passage stresses integrated planning, not just infrastructure upgrades, as key to reducing disparities.Incorrect
Solution: (a)
Explanation:
• Statement 1 is valid: The passage clearly warns that without measures like affordable housing and equitable access to services, migration will worsen inequality.
• Statement 2 is invalid: The passage stresses integrated planning, not just infrastructure upgrades, as key to reducing disparities. -
Question 5 of 5
5. Question
Which one of the following statements best reflects the central idea conveyed by the passage?
Correct
Solution: (c)
Explanation:
• The passage emphasizes that migration’s benefits depend on inclusive and balanced planning to avoid worsening inequality.
• Options (a) and (d) are restrictive or dismissive, not supported by the passage.
• Option (b) is inaccurate — the passage states benefits are unevenly distributed.Incorrect
Solution: (c)
Explanation:
• The passage emphasizes that migration’s benefits depend on inclusive and balanced planning to avoid worsening inequality.
• Options (a) and (d) are restrictive or dismissive, not supported by the passage.
• Option (b) is inaccurate — the passage states benefits are unevenly distributed.
