UPSC Insta–DART (Daily Aptitude and Reasoning Test) 26 Aug 2025

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. (a) 24 m (b) 32 m (c) 26 m (d) 28 m 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

#### 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.

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

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

• 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? a) ₹96 b) ₹102 c) ₹108 d) ₹120 Correct Answer : C Solution: Per-head ratio ⇒ group-weighted parts Teachers: 15×9=135 Staff: 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 Incorrect Answer : C Solution: Per-head ratio ⇒ group-weighted parts Teachers: 15×9=135 Staff: 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

#### 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?

Answer : C

Solution: Per-head ratio ⇒ group-weighted parts Teachers: 15×9=135

Staff: 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

Answer : C

Solution: Per-head ratio ⇒ group-weighted parts Teachers: 15×9=135

Staff: 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? a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone. b) The Question can be answered by using either Statement alone. c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. d) The Question can be answered even without using any of 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.

#### 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?

• a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.

• b) The Question can be answered by using either Statement alone.

• c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

• d) The Question can be answered even without using any of the Statements.

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.

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: (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 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.

#### 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:

• (a) 1 only

• (b) 2 only

• (c) Both 1 and 2

• (d) Neither 1 nor 2

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.

Solution: (a)

• Question 5 of 5 5. Question Which one of the following statements best reflects the central idea conveyed by the passage? (a) Rural-to-urban migration should be restricted to prevent overpopulation in cities. (b) Urban migration benefits everyone equally, as it expands economic opportunities. (c) Balanced urban development policies are essential to ensure that migration reduces, rather than deepens, inequalities. (d) Migrants should focus on improving their own living conditions rather than depending on public policy. 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.

#### 5. Question

Which one of the following statements best reflects the central idea conveyed by the passage?

• (a) Rural-to-urban migration should be restricted to prevent overpopulation in cities.

• (b) Urban migration benefits everyone equally, as it expands economic opportunities.

• (c) Balanced urban development policies are essential to ensure that migration reduces, rather than deepens, inequalities.

• (d) Migrants should focus on improving their own living conditions rather than depending on public policy.

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.

Solution: (c)

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