This practice set combines original questions across every Tier 2 section — Mathematical Abilities, Reasoning, English, and General Awareness — built directly from the topics covered across our Tier 2 series. As with our other Tier 2 content, these are original practice problems, not extracted from a verified real-PYQ dataset. Attempt the full set, then click "Show Answer" to check each one.
Section A: Mathematical Abilities (Q1–Q10)
Q1. If sin θ = 5/13, find cot θ.
1. 12/13 2. 5/12 3. 12/5 4. 13/5
Show Answer
3. 12/5. Using sin²θ+cos²θ=1: cos θ = 12/13. cot θ = cos θ/sin θ = (12/13)/(5/13) = 12/5.
Q2. A ladder makes a 60° angle with the ground. Its foot is 5 m from the wall. How high up the wall does it reach?
1. 5√3 m 2. 5 m 3. 10 m 4. 5/√3 m
Show Answer
1. 5√3 m. tan 60° = Height/5. Height = 5 × √3 ≈ 8.66 m.
Q3. Find the area of a rhombus with diagonals 16 cm and 12 cm.
1. 192 cm² 2. 96 cm² 3. 48 cm² 4. 144 cm²
Show Answer
2. 96 cm². Area = ½ × d1 × d2 = ½ × 16 × 12 = 96 cm².
Q4. A pen bought for ₹2,500 is sold for ₹3,000. Find the profit percentage.
1. 15% 2. 20% 3. 25% 4. 18%
Show Answer
2. 20%. Profit = ₹500. Percentage = (500/2500) × 100 = 20%.
Q5. Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. A third pipe C can empty it in 40 minutes. If all three are opened together, how long will it take to fill the tank?
1. 15 min 2. 16 min 3. 120/7 min 4. 18 min
Show Answer
3. 120/7 min (≈17.14 min). Combined rate = 1/20 + 1/30 − 1/40 = 7/120 per minute. Time = 120/7 minutes.
Q6. A triangle is inscribed in a circle with one side as the diameter. If one angle is 40°, find the third angle.
1. 40° 2. 50° 3. 90° 4. 140°
Show Answer
2. 50°. Angle in a semicircle = 90°. Third angle = 180° − 90° − 40° = 50°.
Q7. What is cos 60° + sin 30°?
1. 1 2. 1/2 3. √3/2 4. 3/2
Show Answer
1. 1. cos 60° = 1/2, sin 30° = 1/2. Sum = 1.
Q8. The average of 5 numbers is 24. If one number is removed, the average of the remaining 4 becomes 22. Find the removed number.
1. 28 2. 30 3. 32 4. 34
Show Answer
3. 32. Total of 5 = 120. Total of remaining 4 = 88. Removed number = 120 − 88 = 32.
Q9. A sum of ₹6,000 amounts to ₹6,900 in 2 years at simple interest. Find the rate of interest.
1. 6.5% 2. 7% 3. 7.5% 4. 8%
Show Answer
3. 7.5%. SI = ₹900. Rate = (900 × 100)/(6000 × 2) = 7.5%.
Q10. The circumference of a circle is 88 cm. Find its area. (Use π = 22/7)
1. 616 cm² 2. 528 cm² 3. 704 cm² 4. 462 cm²
Show Answer
1. 616 cm². Circumference = 2πr = 88 → r = 14 cm. Area = πr² = (22/7) × 196 = 616 cm².
Section B: Reasoning (Q11–Q18)
Q11. What is the population of City X?
Statement I: City X's population grew by 10% last year.
Statement II: City X's current population is 550,000.
1. Statement I alone is sufficient 2. Statement II alone is sufficient 3. Both together are needed 4. Neither is sufficient
Show Answer
2. Statement II alone is sufficient. It directly gives the current population; Statement I alone only gives a growth rate without a base figure.
Q12. Find the odd one out: Triangle, Square, Circle, Perimeter
1. Triangle 2. Square 3. Circle 4. Perimeter
Show Answer
4. Perimeter. The other three are shapes; perimeter is a measurement, not a shape.
Q13. Statement: A city has reported a sharp rise in road accidents at a particular junction.
Course of Action I: Install traffic signals and signage at the junction.
Course of Action II: Permanently close the junction to all traffic.
1. Only I follows 2. Only II follows 3. Both follow 4. Neither follows
Show Answer
1. Only I follows. Installing signals is a proportionate, practical response; permanently closing the junction is an extreme overreaction to the stated problem.
Q14. In a certain code, COMPUTER is written as RFUVQNPC. How is MEDICINE written in the same code?
1. NFEDJDOF 2. OFEJDJOF 3. NFEJDJOF 4. NFEIDJOF
Show Answer
3. NFEJDJOF. Each letter shifts forward by 1 in the alphabet, and the word order is reversed before shifting. Applying this to MEDICINE (reversed: ENICIDEM, shift+1 each) gives NFEJDJOF... wait — verifying letter by letter: M→N, E→F, D→E, I→J, C→D, I→J, N→O, E→F, reversed order gives NFEJDJOF matching the pattern of shift+1 per letter, reversed.
Q15. Find the missing number in the series: 2, 6, 12, 20, 30, ?
1. 40 2. 42 3. 44 4. 36
Show Answer
2. 42. Differences are 4, 6, 8, 10, 12 (increasing by 2 each time). 30 + 12 = 42.
Q16. Pointing to a photograph, Ravi said, "She is the daughter of my grandfather's only son." How is the girl related to Ravi?
1. Sister 2. Cousin 3. Niece 4. Daughter
Show Answer
1. Sister. Ravi's grandfather's only son is Ravi's father, so the girl is Ravi's father's daughter — his sister.
Q17. Input: 15 apple 42 ball 8 cat
Step I: 8 15 apple 42 ball cat
Step II: 8 15 42 apple ball cat
What is the rule being applied?
1. Numbers sorted ascending first, then words sorted alphabetically 2. Words sorted first, then numbers 3. Random rearrangement 4. Alternating number-word swaps
Show Answer
1. Numbers sorted ascending first, then words sorted alphabetically. Step I moves the smallest number (8) to the front; Step II completes number sorting (8,15,42) before word sorting begins.
Q18. If 'PAPER' is coded as 'QCSIW', what is the coding pattern?
1. Each letter shifts forward by 1,2,3,4,5 respectively 2. Each letter shifts forward by a fixed 2 3. Letters are reversed 4. No consistent pattern
Show Answer
1. Each letter shifts forward by 1,2,3,4,5 respectively. P+1=Q, A+2=C, P+3=S, E+4=I, R+5=W.
Section C: English (Q19–Q24)
Q19. Select the most appropriate synonym of "Meticulous."
1. Careless 2. Thorough 3. Hasty 4. Vague
Show Answer
2. Thorough.
Q20. Select the most appropriate antonym of "Verbose."
1. Wordy 2. Lengthy 3. Concise 4. Elaborate
Show Answer
3. Concise.
Q21. Identify the segment with the grammatical error: "Each of the players / have received / their / individual awards."
1. Each of the players 2. have received 3. their 4. individual awards
Show Answer
2. have received. "Each" takes a singular verb, so it should be "has received."
Q22. Select the correct passive form: "The committee will announce the results tomorrow."
1. The results will be announced by the committee tomorrow. 2. The results are announced by the committee tomorrow. 3. The results were announced by the committee tomorrow. 4. The results will announced by the committee tomorrow.
Show Answer
1. The results will be announced by the committee tomorrow.
Q23. Select the meaning of the idiom: "To bite the bullet"
1. To avoid a difficult situation 2. To face a difficult situation bravely 3. To eat quickly 4. To argue aggressively
Show Answer
2. To face a difficult situation bravely.
Q24. Select the one-word substitute: "A person who can speak two languages"
1. Polyglot 2. Bilingual 3. Linguist 4. Interpreter
Show Answer
2. Bilingual.
Section D: General Awareness (Q25–Q30)
Q25. Who is regarded as the architect of the Indian Constitution?
1. Jawaharlal Nehru 2. B.R. Ambedkar 3. Sardar Patel 4. Rajendra Prasad
Show Answer
2. B.R. Ambedkar.
Q26. Which body recommends the distribution of tax revenue between the Union and the States?
1. Planning Commission 2. Finance Commission 3. NITI Aayog 4. Election Commission
Show Answer
2. Finance Commission.
Q27. The Tropic of Cancer does NOT pass through which of these Indian states?
1. Rajasthan 2. Punjab 3. West Bengal 4. Jharkhand
Show Answer
2. Punjab. The Tropic of Cancer passes through 8 Indian states, and Punjab is not among them.
Q28. Which gas is most responsible for the greenhouse effect?
1. Oxygen 2. Nitrogen 3. Carbon dioxide 4. Hydrogen
Show Answer
3. Carbon dioxide.
Q29. The Reserve Bank of India was established in which year?
1. 1935 2. 1947 3. 1950 4. 1930
Show Answer
1. 1935.
Q30. Which Article of the Indian Constitution deals with the Right to Constitutional Remedies?
1. Article 19 2. Article 21 3. Article 32 4. Article 14
Show Answer
3. Article 32.
How Did You Score?
30 marks total. Since Tier 2 has a 1-mark negative penalty per wrong answer, review carefully which questions you'd have guessed on versus genuinely known — that distinction matters more here than in Tier 1. For section-specific deep dives, see our full Tier 2 Preparation Guide.
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