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
Two cards are drawn at random from a standard deck without replacement. What is the probability that both cards are red and from the same suit?
Correct
Answer: (b)
Solution:
Red suits: Hearts (13) and Diamonds (13).
Favourable outcomes = ⁽¹³C₂⁾ (both Hearts) + ⁽¹³C₂⁾ (both Diamonds) = 78 + 78 = 156.
Total outcomes = ⁵²C₂ = 1326.
Probability = 156/1326 = 26/221.Incorrect
Answer: (b)
Solution:
Red suits: Hearts (13) and Diamonds (13).
Favourable outcomes = ⁽¹³C₂⁾ (both Hearts) + ⁽¹³C₂⁾ (both Diamonds) = 78 + 78 = 156.
Total outcomes = ⁵²C₂ = 1326.
Probability = 156/1326 = 26/221. -
Question 2 of 5
2. Question
Two factories, Factory A and Factory B, produce an equal number of units daily. Factory A reports 10 defective units per 100, while Factory B reports 8 per 100. However, when machine-related defects are excluded, Factory A has 2 fewer defective units per 100 than Factory B.
Correct
Answer: (b)
Explanation:
• Factory A has more total defects (10 vs. 8).
• When machine faults are removed, Factory A has fewer (−2 difference).
→ Hence, machine faults contribute more to Factory A’s defect rate.
Therefore, (b) is correct.Incorrect
Answer: (b)
Explanation:
• Factory A has more total defects (10 vs. 8).
• When machine faults are removed, Factory A has fewer (−2 difference).
→ Hence, machine faults contribute more to Factory A’s defect rate.
Therefore, (b) is correct. -
Question 3 of 5
3. Question
In a college, students who chose Arts, Commerce, and Science are in the ratio 7 : 9 : 11. The number of Science students exceeds Arts students by a number that is a multiple of both 20 and 30. What is the minimum number of students?
Correct
Answer: (c)
Solution:Let the numbers be 7x, 9x, 11x.
Difference (Science – Arts) = 11x – 7x = 4x. We need 4x = LCM(20, 30) = 60 ⇒ x = 15.
Total = (7 + 9 + 11) × 15 = 27 × 15 = 405.
Incorrect
Answer: (c)
Solution:Let the numbers be 7x, 9x, 11x.
Difference (Science – Arts) = 11x – 7x = 4x. We need 4x = LCM(20, 30) = 60 ⇒ x = 15.
Total = (7 + 9 + 11) × 15 = 27 × 15 = 405.
-
Question 4 of 5
4. Question
A cube of side 12 cm is painted on all its faces and then cut into small cubes of side 3 cm.
Statement I: The number of cubes with exactly two faces painted is 28.
Statement II: The number of cubes with no face painted is 8.
Which statement(s) is/are correct?Correct
Answer: (b)
Solution:
• Side of original cube = 12 cm ⇒ 12/3 = 4 divisions per edge
• Total small cubes = 4³ = 64
Cubes with Exactly Two Faces Painted:
• Edge (excluding corners): per edge = 4 − 2 = 2
• Total = 12 × 2 = 24 (not 28) → Statement I incorrect
Cubes with No Face Painted (interior):
• (4 − 2)³ = 2³ = 8 → Statement II correctIncorrect
Answer: (b)
Solution:
• Side of original cube = 12 cm ⇒ 12/3 = 4 divisions per edge
• Total small cubes = 4³ = 64
Cubes with Exactly Two Faces Painted:
• Edge (excluding corners): per edge = 4 − 2 = 2
• Total = 12 × 2 = 24 (not 28) → Statement I incorrect
Cubes with No Face Painted (interior):
• (4 − 2)³ = 2³ = 8 → Statement II correct -
Question 5 of 5
5. Question
X and Y start a business with capitals in the ratio 5 : 8. After 4 months, X doubles his capital while Y withdraws half of his capital. If the total profit at the end of the year is ₹20,500, what is Y’s share in the profit?
Correct
Answer: (b)
Solution:
Let initial capital of X = 5x, Y = 8x
For first 4 months:
• X = 5x × 4
• Y = 8x × 4
For next 8 months:
• X = (10x) × 8
• Y = (4x) × 8
Total:
• X = 20x + 80x = 100x
• Y = 32x + 32x = 64x
Ratio = 100x : 64x = 25 : 16
Total parts = 41
Y’s share = (16/41) × 20,500 = ₹8,000Incorrect
Answer: (b)
Solution:
Let initial capital of X = 5x, Y = 8x
For first 4 months:
• X = 5x × 4
• Y = 8x × 4
For next 8 months:
• X = (10x) × 8
• Y = (4x) × 8
Total:
• X = 20x + 80x = 100x
• Y = 32x + 32x = 64x
Ratio = 100x : 64x = 25 : 16
Total parts = 41
Y’s share = (16/41) × 20,500 = ₹8,000
