(50 MCQs with Solutions)

🔹 Section A: Logical & Mathematical Reasoning (Q1–Q20)

Q1. Which of the following is a statement in mathematical logic?
A) “Please open the door.”
B) “What a beautiful day!”
C) “5 is a prime number.”
D) “Close the window.”
Answer: C
Solution: Only declarative sentences that are either true or false are statements. “5 is a prime number” is true; the rest are commands or exclamations.

Q2. The negation of “All teachers are honest” is:
A) “No teacher is honest.”
B) “Some teachers are not honest.”
C) “All teachers are dishonest.”
D) “Some teachers are honest.”
Answer: B
Solution: Negation of “All A are B” = “Some A are not B.”

Q3. If p: “It is raining.” and q: “The ground is wet.”, then “If it is raining, then the ground is wet” is symbolically:
A) p ∧ q
B) p ∨ q
C) p → q
D) q → p
Answer: C
Solution: “If p then q” = p → q.

Q4. The contrapositive of p → q is:
A) q → p
B) ¬p → ¬q
C) ¬q → ¬p
D) p ↔ q
Answer: C
Solution: Contrapositive = reverse order + negation → ¬q → ¬p.

Q5. The converse of “If you study, you will pass” is:
A) If you do not study, you will not pass.
B) If you pass, you studied.
C) If you pass, you studied hard.
D) If you pass, you have not studied.
Answer: B
Solution: Converse reverses positions: p → q ⇒ q → p.

Q6. In a truth table for p ∨ q, when is it false?
A) When both p and q are true
B) When p true, q false
C) When both p and q are false
D) Never
Answer: C
Solution: Disjunction (∨) is false only when both statements are false.

Q7. For p = True, q = False, what is truth value of p → q?
A) True
B) False
C) Cannot say
D) Both
Answer: B
Solution: In implication, p→q is false only if p is true and q is false.

Q8. Identify the tautology.
A) p ∨ ¬p
B) p ∧ ¬p
C) ¬(p ∨ q)
D) ¬p ∨ ¬q
Answer: A
Solution: p ∨ ¬p is always true, hence a tautology.

Q9. “Some birds can swim.” is logically equivalent to:
A) All birds can swim.
B) There exists at least one bird that can swim.
C) No bird can swim.
D) Some birds cannot swim.
Answer: B
Solution: “Some” = “there exists at least one.”

Q10. Deductive reasoning example:
A) Observing several black crows and concluding all crows are black.
B) If all A are B, and X is A, then X is B.
C) Predicting future based on experience.
D) Assuming probability.
Answer: B

Q11. The conclusion follows logically from:
Premise 1: All roses are flowers.
Premise 2: All flowers are plants.
∴ ?
A) All roses are plants.
B) All plants are roses.
C) All flowers are roses.
D) No roses are plants.
Answer: A

Q12. In logic, Fallacy means:
A) Correct reasoning
B) False reasoning
C) True argument
D) Valid deduction
Answer: B

Q13. Inductive reasoning leads to:
A) Definite truth
B) Probable conclusion
C) Mathematical proof
D) Contradiction
Answer: B

Q14. “Either the meeting is today or tomorrow.” is a:
A) Conjunction
B) Disjunction
C) Implication
D) Negation
Answer: B

Q15. Identify invalid argument:
A) If p→q, q→r ⇒ p→r
B) If p→q and p true ⇒ q true
C) If p→q and q true ⇒ p true
D) If ¬q true ⇒ ¬p true (contrapositive)
Answer: C
Solution: q true does not guarantee p true (fallacy of affirming the consequent).

Q16. A valid argument’s conclusion:
A) Must be true
B) Must follow logically
C) Must be false
D) May be uncertain
Answer: B

Q17. In syllogism:
All dogs are animals.
Some animals are cats.
Conclusion: ?
A) Some cats are dogs.
B) All dogs are cats.
C) No cats are dogs.
D) Cannot be concluded.
Answer: D
Solution: No direct relationship between dogs and cats.

Q18. If “All men are mortal” is true, “Some mortals are men” is:
A) True
B) False
C) Indeterminate
D) Contradictory
Answer: A

Q19. If p and q are both false, then ¬(p ∨ q) is:
A) True
B) False
C) Indeterminate
D) Same as q
Answer: A
Solution: p∨q = False ⇒ ¬(False) = True.

Q20. “If 7 is even, then 2+2=5.” — what is truth value?
A) True
B) False
C) Unknown
D) Conditional
Answer: A
Solution: Antecedent (7 is even) is false → conditional p→q is automatically true.

🔹 Section B: Quantitative Aptitude (Q21–Q50)

Q21. Find average of 25, 35, 45, 55, 65.
Solution:
Sum = 225 → Average = 225/5 = 45
Answer: 45

Q22. If cost price = ₹80, selling price = ₹100, profit % = ?

$\frac{100 - 80}{80} \times 100 = 25 %$

Answer: 25%

Q23. Find simple interest on ₹2000 at 5% for 3 years.

$S I = \frac{2000 \times 5 \times 3}{100} = 300$

Answer: ₹300

Q24. Compound Interest on ₹1000 at 10% for 2 years

$C I = 1000 [(1 + 0.10)^{2} - 1] = 1000 (1.21 - 1) = 210$

Answer: ₹210

Q25. A and B can complete work in 10 and 15 days respectively. Time together = ?

$T = \frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6$

Answer: 6 days

Q26. Train covers 120 km in 3 hours. Find speed in km/hr.

$S p e e d = 120 / 3 = 40$

Answer: 40 km/h

Q27. Convert 54 km/hr into m/s.

$= 54 \times \frac{5}{18} = 15 m/s$

Answer: 15 m/s

Q28. Ratio of 2 quantities is 3:5 and their sum = 80. Find quantities.
Sum ratio parts = 8 → each part = 10.
Quantities = 30, 50.
Answer: 30 and 50

Q29. If 25% of a number is 20, find number.

$N = 20 \times \frac{100}{25} = 80$

Answer: 80

Q30. Find HCF of 24 and 36.
Factors: 24 (2³×3), 36 (2²×3²) → Common = 2²×3 = 12
Answer: 12

Q31. Find LCM of 15 and 20.
LCM = (15×20)/HCF(5) = 300/5 = 60
Answer: 60

Q32. A sells an article at 10% loss. If SP = ₹450, find CP.

$C P = \frac{S P \times 100}{100 - 10} = 450 \times \frac{100}{90} = 500$

Answer: ₹500

Q33. A’s salary increases from ₹20,000 to ₹22,000. % increase = ?

$\frac{2000}{20000} \times 100 = 10 %$

Answer: 10%

Q34. Average of first 5 odd numbers = ?
(1+3+5+7+9)/5 = 25/5 = 5
Answer: 5

Q35. If 12 workers can finish a job in 10 days, 8 workers will take?

$Man-days = 12 \times 10 = 120, Time = 120 / 8 = 15$

Answer: 15 days

Q36. A sum doubles in 8 years under simple interest. Rate = ?

$S I = P, T = 8 \Rightarrow P \times R \times 8 / 100 = P \Rightarrow R = 12.5 %$

Answer: 12.5%

Q37. Probability of getting head in a coin toss = ?

$1 / 2$

Answer: 0.5

Q38. In how many ways can letters of word “MATH” be arranged?

$4! = 24$

Answer: 24

Q39. From 5 persons, choose 2 for a committee.

$^{5} C_{2} = 10$

Answer: 10

Q40. Find next term: 2, 6, 12, 20, ?
Differences: 4, 6, 8 → next difference = 10 → next = 30
Answer: 30

Q41. In a class of 60, 40% are girls. How many boys?
Girls = 24 ⇒ Boys = 60 – 24 = 36
Answer: 36

Q42. Speed ratio of A and B = 2:3. If A takes 45 minutes, B takes ?
Time ∝ 1/Speed ⇒ ratio 3:2 ⇒ B = 45×(2/3)=30 min
Answer: 30 minutes

Q43. If selling price = ₹500, profit = 25%, then CP = ?

$C P = 500 \times 100 / 125 = 400$

Answer: ₹400

Q44. A shopkeeper allows 10% discount on ₹800. Selling price = ?
SP = 800 – 10% of 800 = 720
Answer: ₹720

Q45. Average of 8 numbers is 15. If one number 9 removed, new average = ?
Sum = 120 – 9 =111; Average =111/7=15.857≈15.86
Answer: 15.86

Q46. If A’s income is 20% more than B’s, then B’s income is how much less than A’s?

$\frac{20}{120} \times 100 = 16.67 %$

Answer: 16.67% less

Q47. If CP of 12 pens = SP of 8 pens, find profit %.
Profit on 8 pens = cost of 12 – cost of 8 = 4/8 = 50%
Answer: 50%

Q48. A travels 60 km at 30 km/h and 60 km at 60 km/h. Find average speed.

$= \frac{2 \times 30 \times 60}{30 + 60} = 40$

Answer: 40 km/h

Q49. The next term of series 1, 4, 9, 16, ?
Square numbers → 25
Answer: 25

Q50. If 4 workers complete job in 6 days, how many workers needed to finish in 3 days?
Work ∝ (Workers × Time) → 4×6= W×3 → W=8
Answer: 8 workers

UGC NET Paper – 1- UNIT 5 – MATHEMATICAL REASONING & APTITUDE

(50 MCQs with Solutions)

🔹 Section A: Logical & Mathematical Reasoning (Q1–Q20)

🔹 Section B: Quantitative Aptitude (Q21–Q50)

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UGC NET Paper – 1- UNIT 5 – MATHEMATICAL REASONING & APTITUDE

(50 MCQs with Solutions)

🔹 Section A: Logical & Mathematical Reasoning (Q1–Q20)

🔹 Section B: Quantitative Aptitude (Q21–Q50)

👋Subscribe to ProTeacher.in

Sign up to receive NewsLetters in your inbox.

👋Subscribe to
ProTeacher.in