Section A – Mathematical Reasoning (Q1–Q25)
Q1. “Either it rains or it snows” is represented by
A) p ∧ q B) p ∨ q C) p → q D) ¬p → q
Answer: B
Solution: “Either…or” means disjunction (∨).
Q2. Negation of “Some students are honest” is
A) No student is honest B) All students are dishonest C) All students are not honest D) All students are dishonest
Answer: A
Solution: Negation of “Some A are B” → “No A are B.”
Q3. Which of the following is not a statement?
A) 5 + 7 = 12 B) Today is Monday C) Read this book D) Moon reflects light
Answer: C
Solution: Imperative sentence ≠ logical statement.
Q4. Truth value of (p ∧ q) when p = T, q = F is
A) T B) F C) Undefined D) Both
Answer: B
Q5. The compound statement “If 3 > 5 then 10 > 8” is
A) True B) False C) Cannot say D) Contradiction
Answer: A
Solution: Antecedent false ⇒ implication true.
Q6. “All cats are mammals” ⇒ Contrapositive is
A) If not mammal then not cat B) If mammal then cat C) If cat then mammal D) None
Answer: A
Q7. Identify the tautology:
A) p ∧ ¬p B) p ∨ ¬p C) ¬(p ∨ q) D) p → ¬p
Answer: B
Q8. Which of the following is a contradiction?
A) p ∨ ¬p B) p ∧ ¬p C) ¬(p ∧ ¬p) D) p → p
Answer: B
Q9. If p = T, q = F then ¬(p ∨ q) = ?
A) T B) F C) Both D) Undefined
Answer: A
Q10. “If it rains then I take umbrella” – converse is
A) If I take umbrella then it rains.
B) If it doesn’t rain then no umbrella.
C) I never use umbrella.
D) None.
Answer: A
Q11. Valid conclusion:
All A are B; Some B are C ⇒ ?
A) Some A are C B) All C are A C) Cannot be concluded D) No A is C
Answer: C
Q12. “Either the train is late or the driver is ill.” – when false?
A) Both true B) Both false C) Only one true D) Never
Answer: B
Q13. Which statement pair forms contradictory propositions?
A) All A are B & No A are B B) Some A are B & Some A are not B C) All A are B & Some A are not B D) No A are B & Some A are not B
Answer: C
Q14. “If p then q” and “¬p or q” are
A) Contradictory B) Equivalent C) Independent D) Inverse
Answer: B
Q15. If all statements are true except one, which cannot be true together?
A) p ∧ ¬p B) p ∨ q C) ¬p ∨ ¬q D) p → q
Answer: A
Q16. A valid argument is also called
A) Tautology B) Contradiction C) Deductive truth D) Inference
Answer: D
Q17. If “No books are pens” is true, then “Some books are pens” is
A) True B) False C) Uncertain D) Independent
Answer: B
Q18. “All students in the class are attentive.” – negation is
A) Some students in the class are not attentive.
Answer: A
Q19. A proposition that is always false is called a
A) Tautology B) Contradiction C) Contingency D) Negation
Answer: B
Q20. If a valid argument has true premises, then its conclusion is
A) True B) False C) Indeterminate D) Independent
Answer: A
Q21. Symbolic form of “If it is not cold then I go out.”
A) ¬p → q B) p → ¬q C) q → p D) ¬q → p
Answer: A
Q22. Inference rule “If p→q and q→r then p→r” is
A) Law of syllogism B) Law of identity C) Law of negation D) Law of equivalence
Answer: A
Q23. When a conclusion is probable but not certain, it is
A) Deduction B) Induction C) Fallacy D) Contradiction
Answer: B
Q24. “Either India wins or the match is drawn.” – if both false ⇒
A) Statement true B) Statement false C) Cannot say D) Partially true
Answer: B
Q25. Identify the fallacy:
If it rains, streets wet. Streets wet ⇒ it rained.
A) Denying antecedent B) Affirming consequent C) Inverse error D) Contrapositive
Answer: B
Section B – Quantitative Aptitude (Q26–Q50)
Q26. 20 % of a number = 60. Find the number.
→ N = 60 × 100 / 20 = 300.
Answer: 300
Q27. Find the mean of 10, 20, 30, 40, 50.
Sum = 150 → Avg = 150/5 = 30.
Answer: 30
Q28. A and B can finish a job in 12 and 18 days. Together?
Answer: 7.2 days
Q29. Compound interest on ₹ 800 at 5 % for 2 years = ?
Answer: ₹ 82
Q30. Ratio A:B = 4:5. If A = 80, B =?
B = 80 × 5/4 = 100.
Answer: 100
Q31. Two numbers have HCF 6 and LCM 72. If one is 18, the other =?
Answer: 24
Q32. A car runs 60 km at 30 km/h and 60 km at 90 km/h. Average speed = ?
Answer: 45 km/h
Q33. Discount 10 % on ₹ 2000 ⇒ SP = ?
= 2000 – 200 = 1800.
Answer: ₹ 1800
Q34. If SP = ₹ 600, loss = 25 %, CP = ?
Answer: ₹ 800
Q35. 15 % of x = 75. Find x.
Answer: 500
Q36. Find probability of odd number on dice.
= 3/6 = 1/2.
Answer: 0.5
Q37. If 10 workers finish job in 15 days, work done in 9 days by 10 workers = ?
= 9/15 = 3/5 = 60 %.
Answer: 60 % of work.
Q38. Find simple interest on ₹ 5000 at 12 % for 2 years.
Answer: ₹ 1200
Q39. Average of first n natural numbers = ?
Answer: (n + 1)/2
Q40. Number of factors of 36 = ?
36 = 2²×3² → (2+1)(2+1)=9.
Answer: 9
Q41. Find next term: 5, 11, 23, 47, ?
Pattern ×2 +1 ⇒ (47×2)+1 = 95.
Answer: 95
Q42. 8 men can build a wall in 20 days. How long for 10 men?
8×20 = 10×x ⇒ x = 16.
Answer: 16 days
Q43. Price of item ₹ 5000 increased by 8 %, then decreased by 8 %. Net effect =?
Loss = (8×8)/100 = 0.64 %.
Answer: 0.64 % loss.
Q44. Find median of 3, 7, 9, 11, 13.
= 9.
Answer: 9
Q45. Mean of first 5 even numbers = ?
(2+4+6+8+10)/5 = 6.
Answer: 6
Q46. If 2x + 3 = 11 ⇒ x =?
x = 4.
Answer: 4
Q47. Simplify:
= (1 + 2 + 1) = 4.
Answer: 4
Q48. A train 150 m long crosses a pole in 15 s. Speed = ?
= 150/15 = 10 m/s = 36 km/h.
Answer: 36 km/h
Q49. If sum of digits of a number is divisible by 9, the number is divisible by ?
A) 3 B) 6 C) 9 D) 12
Answer: C
Q50. Find value of √(144 + 25).
= √169 = 13.
Answer: 13