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 thief runs at 9 m/s. A policeman starts chasing him from the same point but 2 minutes later, running at 12 m/s. How long will it take the policeman to catch the thief after starting the chase?
Correct
Answer: (a)
Solution:
In 2 minutes, thief’s head start = 9 × 120 = 1080 m
Relative speed = 12 − 9 = 3 m/s
Time to catch = 1080 ÷ 3 = 360 s = 6 minutes
So, option (a) is correct.Incorrect
Answer: (a)
Solution:
In 2 minutes, thief’s head start = 9 × 120 = 1080 m
Relative speed = 12 − 9 = 3 m/s
Time to catch = 1080 ÷ 3 = 360 s = 6 minutes
So, option (a) is correct. -
Question 2 of 5
2. Question
X, Y and Z can complete a work alone in 5, 10 and 20 hours respectively. Only one person works per hour, and no one works two consecutive hours. All are engaged to finish the work. What is the minimum time required?
Correct
Answer: (a)
Solution:
Total work = LCM(5, 10, 20) = 20 units
Efficiency: X = 4 units/hr, Y = 2 units/hr, Z = 1 unit/hrStrategy: alternate X and Y.
Hour 1: X → 4
Hour 2: Y → 2, total 6
Hour 3: X → 4, total 10
Hour 4: Y → 2, total 12
Hour 5: X → 4, total 16
Hour 6: Y → 2, total 18Remaining = 2 units. Next turn is X (4/hr).
Time = 2/4 hr = 15 min.Total = 6 hrs 15 min. Correct option = (a).
Incorrect
Answer: (a)
Solution:
Total work = LCM(5, 10, 20) = 20 units
Efficiency: X = 4 units/hr, Y = 2 units/hr, Z = 1 unit/hrStrategy: alternate X and Y.
Hour 1: X → 4
Hour 2: Y → 2, total 6
Hour 3: X → 4, total 10
Hour 4: Y → 2, total 12
Hour 5: X → 4, total 16
Hour 6: Y → 2, total 18Remaining = 2 units. Next turn is X (4/hr).
Time = 2/4 hr = 15 min.Total = 6 hrs 15 min. Correct option = (a).
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Question 3 of 5
3. Question
Consider the following questions and statements
Question: What is the total time required for A and B together to complete a job?
Statement I: A alone can complete the job in 15 days, and B alone can complete the job in 20 days.
Statement II: A and B together can complete 7/60 of the job in one day.Which of the following is correct with respect to above?
Correct
Answer: (b)
Explanation:
From Statement I:
Work/day of A = 1/15, B = 1/20.
Together = 1/15 + 1/20 = 7/60.
So total = 60/7 days. Sufficient.From Statement II:
Directly gives daily work = 7/60, so total = 60/7 days. Sufficient.Hence either alone is sufficient, correct option = (b).
Incorrect
Answer: (b)
Explanation:
From Statement I:
Work/day of A = 1/15, B = 1/20.
Together = 1/15 + 1/20 = 7/60.
So total = 60/7 days. Sufficient.From Statement II:
Directly gives daily work = 7/60, so total = 60/7 days. Sufficient.Hence either alone is sufficient, correct option = (b).
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Question 4 of 5
4. Question
The number of triangles that can be formed using 12 distinct points on a circle (no three points are collinear) is
Correct
Answer – A
Solution:
To form a triangle, we need to choose 3 points out of 12.
Number of triangles = 12C3 = (12×11×10)/(3×2×1) = 220.Hence, option (a) 220 is correct.
Incorrect
Answer – A
Solution:
To form a triangle, we need to choose 3 points out of 12.
Number of triangles = 12C3 = (12×11×10)/(3×2×1) = 220.Hence, option (a) 220 is correct.
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Question 5 of 5
5. Question
There are 4 horizontal and 6 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles that can be formed?
Correct
Answer – C
Solution:Given that,
There are 4 horizontal and 6 vertical lines, parallel and equidistant.
To form a rectangle, choose 2 of the vertical lines and 2 of the horizontal lines.
So,
4C2 × 6C2 = 6 × 15 = 90 rectangles.
Hence option (c) is correct
Incorrect
Answer – C
Solution:Given that,
There are 4 horizontal and 6 vertical lines, parallel and equidistant.
To form a rectangle, choose 2 of the vertical lines and 2 of the horizontal lines.
So,
4C2 × 6C2 = 6 × 15 = 90 rectangles.
Hence option (c) is correct
