📘 UGC NET Paper 1 – Mathematical Reasoning
Top 20 MCQs with Answers & Explanations
1. If 20% of a number is 40, what is the number?
A) 100
B) 150
C) 200
D) 250
Answer: C) 200
Explanation: 20% of x = 40 → x = 40 × 100/20 = 200.
2. A number is increased by 20% and then decreased by 20%. What is the net change?
A) No change
B) 4% increase
C) 4% decrease
D) 2% decrease
Answer: C) 4% decrease
Explanation: Let the number be 100. After increase = 120. After 20% decrease = 96. Net decrease = 4%.
3. The ratio of two numbers is 3 : 5 and their sum is 64. The smaller number is:
A) 20
B) 24
C) 30
D) 40
Answer: B) 24
Explanation: Total parts = 8. Smaller number = 64 × 3/8 = 24.
4. The average of 5 numbers is 28. If one number is removed, the average of the remaining 4 numbers becomes 25. The removed number is:
A) 35
B) 38
C) 40
D) 42
Answer: C) 40
Explanation: Total = 5 × 28 = 140. Remaining total = 4 × 25 = 100. Removed number = 40.
5. If 3 : 4 = x : 20, then x is:
A) 12
B) 15
C) 16
D) 18
Answer: B) 15
Explanation: x/20 = 3/4 → x = 15.
6. A shopkeeper buys an article for ₹800 and sells it for ₹960. His profit percentage is:
A) 15%
B) 18%
C) 20%
D) 25%
Answer: C) 20%
Explanation: Profit = 960 − 800 = ₹160. Profit% = 160/800 × 100 = 20%.
7. A man travels 120 km in 3 hours. His average speed is:
A) 30 km/h
B) 40 km/h
C) 45 km/h
D) 60 km/h
Answer: B) 40 km/h
Explanation: Speed = Distance/Time = 120/3 = 40 km/h.
8. If x + 5 = 17, then x² is:
A) 100
B) 121
C) 144
D) 169
Answer: C) 144
Explanation: x = 12, therefore x² = 144.
9. What is the next number in the series?
2, 6, 12, 20, 30, ?
A) 36
B) 40
C) 42
D) 44
Answer: C) 42
Explanation: Differences are 4, 6, 8, 10, so next difference = 12. Thus 30 + 12 = 42.
10. If 5 workers can complete a task in 12 days, how many days will 10 workers take, assuming equal efficiency?
A) 3
B) 5
C) 6
D) 8
Answer: C) 6
Explanation: Workers × Days = constant. 5 × 12 = 10 × x → x = 6 days.
11. The simple interest on ₹5,000 at 8% per annum for 2 years is:
A) ₹400
B) ₹600
C) ₹800
D) ₹1,000
Answer: C) ₹800
Explanation: SI = PRT/100 = 5000 × 8 × 2/100 = ₹800.
12. If the HCF of two numbers is 6 and their LCM is 72, and one number is 18, the other number is:
A) 12
B) 18
C) 24
D) 36
Answer: C) 24
Explanation: Product of two numbers = HCF × LCM = 6 × 72 = 432. Other number = 432/18 = 24.
13. A train covers 360 km in 4.5 hours. Its speed is:
A) 70 km/h
B) 75 km/h
C) 80 km/h
D) 90 km/h
Answer: C) 80 km/h
Explanation: Speed = 360/4.5 = 80 km/h.
14. What is 25% of 240?
A) 40
B) 50
C) 60
D) 80
Answer: C) 60
Explanation: 25% = 1/4. Therefore 240/4 = 60.
15. If the cost price of an article is ₹1,000 and it is sold at a loss of 15%, the selling price is:
A) ₹750
B) ₹800
C) ₹850
D) ₹900
Answer: C) ₹850
Explanation: Loss = 15% of 1000 = ₹150. SP = 1000 − 150 = ₹850.
16. A sum of ₹600 is divided between A and B in the ratio 2 : 3. B's share is:
A) ₹200
B) ₹240
C) ₹300
D) ₹360
Answer: D) ₹360
Explanation: B's share = 600 × 3/5 = ₹360.
17. The probability of getting an even number when a fair die is thrown once is:
A) 1/6
B) 1/3
C) 1/2
D) 2/3
Answer: C) 1/2
Explanation: Even outcomes = 2, 4, 6 → 3 favourable outcomes out of 6. Probability = 3/6 = 1/2.
18. If 2x − 7 = 15, then x is:
A) 9
B) 10
C) 11
D) 12
Answer: C) 11
Explanation: 2x = 22 → x = 11.
19. The perimeter of a square is 48 cm. Its area is:
A) 121 cm²
B) 144 cm²
C) 169 cm²
D) 196 cm²
Answer: B) 144 cm²
Explanation: Side = 48/4 = 12 cm. Area = 12² = 144 cm².
20. A number is divisible by both 6 and 8. Which of the following must it be divisible by?
A) 12
B) 18
C) 24
D) 36
Answer: C) 24
Explanation: LCM of 6 and 8 = 24. Therefore, any number divisible by both must be divisible by 24.
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