Puzzles, arrangements & general mental ability

Answer: (b) 14

A capital letter looks unchanged in a mirror only if it is symmetric about a vertical line. Of the 21 consonants, only H, M, T, V, W, X and Y are, so 14 consonants look different.

1. The alphabet has 26 − 5 = 21 consonants (leaving out A, E, I, O, U).
2. A mirror flips left and right, so only letters symmetric about a vertical line look the same.
3. Such consonants: H, M, T, V, W, X, Y — 7 letters.
4. Consonants whose images look different: 21 − 7 = 14.
5. Check: B, C, D, F, G, J, K, L, N, P, Q, R, S, Z — 14 letters.

Remember · Mirror-symmetric capitals: A, H, I, M, O, T, U, V, W, X, Y — learn the list once.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) Q and T

Write the three sets — blue covers (Q, R, T), old books (all but S and U) and Gazetteers (all but P, R and S) — and take what is common. Only Q and T are in all three.

1. Blue covers: Q, R, T.
2. Old books: all except S and U → P, Q, R, T, V.
3. Gazetteers: all except the law reports P, R, S → Q, T, U, V.
4. Common to all three: Q and T (R is a law report; U is new and red).

Remember · For multi-attribute questions, list each set and intersect; one mismatch eliminates an option.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (a) 0

The odd-place terms rise by 4, 6, 8, 10, 12. The even-place terms follow the same steps only from 4 onwards, so their first term should be 4 − 4 = 0, not 2.

1. Odd places: 3, 7, 13, 21, 31, 43 — differences 4, 6, 8, 10, 12.
2. Even places: 2, 4, 10, 18, 28, 40 — differences 2, 6, 8, 10, 12.
3. Only the first even-place difference breaks the pattern; to match, the first even term must be 4 − 4 = 0.
4. So the incorrect term 2 should be replaced by 0.
5. Check: each even-place term is then 3 less than the odd-place term before it — 0, 4, 10, 18, 28, 40.

Remember · In an alternating series, split it into two sub-series and compare their differences; the misfit shows itself.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) 3B

In each row the third number is the second minus the first, and the letters A, B and C each appear once. Row 3 therefore needs 13 − 10 = 3 with the letter B: 3B.

1. Numbers, row 1: 10 − 7 = 3; row 2: 9 − 3 = 6 — the third number is the second minus the first.
2. Row 3: 13 − 10 = 3.
3. Letters: each row uses A, B and C once; row 3 already has A and C, so it needs B.
4. The missing entry is 3B.

Remember · In matrix puzzles treat numbers and letters as separate patterns, and check each rule against every row.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 1 Oct 2026 (how we verify). Permalink · Report an error

Answer: (c) 9.375

Sequence-I multiplies by 0.5, 1.5, 2.5, 3.5 and 4.5 in turn. Starting from 5, Sequence-II runs 2.5, 3.75, 9.375, so C = 9.375.

1. Sequence-I: 8 × 0.5 = 4, 4 × 1.5 = 6, 6 × 2.5 = 15, 15 × 3.5 = 52.5, 52.5 × 4.5 = 236.25 — the multiplier rises by 1 each time.
2. Sequence-II from 5: A = 5 × 0.5 = 2.5, B = 2.5 × 1.5 = 3.75.
3. C = 3.75 × 2.5 = 9.375.
4. Check: D = 9.375 × 3.5 = 32.8125 — option (d) is the next term, a trap; (a) is A.

Remember · When terms first fall and then shoot up, test multipliers; options often offer the neighbouring terms as traps.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 1 Oct 2026 (how we verify). Permalink · Report an error

Answer: (b) T

After reversing each block of four, the 13th place holds P (block PONM). Four places to its right is the 17th place, which starts the next block TSRQ — so the letter is T.

1. Reverse each block of four: DCBA HGFE LKJI PONM TSRQ XWVU, and then Y Z become Z Y.
2. Places 1–12 hold D C B A H G F E L K J I, so the 13th letter is P.
3. The fourth letter to its right is in the 17th place: places 13–17 are P, O, N, M, T.
4. The answer is T.

Remember · Work with positions: in reversed blocks of four, place 4k − 3 holds the letter numbered 4k.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (a) Sunday

Counting odd days gives 4 for the years 2001–2026 and 3 for 2027 up to 10 October — 7 in all, i.e. none left over, so the day is Sunday. A quicker route: this very paper was held on Sunday, 10 October 2021, and six years with one leap day add exactly 7 days.

1. Odd days up to the end of 2000: 0 (every 400 years has 0 odd days).
2. 2001–2026: 26 years with 6 leap years (2004, 2008, 2012, 2016, 2020, 2024), so 26 + 6 = 32 odd days; 32 = 4 × 7 + 4, leaving 4.
3. 2027 up to 10 October: Jan 3, Feb 0, Mar 3, Apr 2, May 3, Jun 2, Jul 3, Aug 3, Sep 2, Oct 3 — total 24, leaving 3.
4. Total = 4 + 3 = 7 odd days, i.e. 0, so 10 October 2027 is a Sunday.
5. Check: 10 October 2021 (the date of this paper) was a Sunday; 2022–2027 add 6 + 1 (for 29 February 2024) = 7 days — Sunday again.

Remember · Anchor on a date you know: each ordinary year moves the weekday on by 1 and each leap year by 2.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) 607

Every term is three times the previous one plus 1. So X = 202 × 3 + 1 = 607, and 607 × 3 + 1 = 1822 confirms it.

1. 2 × 3 + 1 = 7, 7 × 3 + 1 = 22, 22 × 3 + 1 = 67, 67 × 3 + 1 = 202 — each term is 3 × previous + 1.
2. X = 202 × 3 + 1 = 607.
3. Check: 607 × 3 + 1 = 1822, the next term.

Remember · When terms roughly triple, test '× 3 ± k', and always verify with the term after the blank.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) Between 7:05 hours and 7:10 hours

At 7:00 the hour hand is 210° ahead of the minute hand, and the minute hand gains 5.5° every minute. The gap falls to 180° after 30 ÷ 5.5 = 5 5/11 minutes — just after 7:05.

1. Angle between the hands = |30H − 5.5M| degrees (H = hour, M = minutes).
2. At 7:00 the angle is 30 × 7 = 210°, and it shrinks by 5.5° each minute.
3. 210 − 5.5M = 180 gives M = 30 ÷ 5.5 = 5 5/11 minutes.
4. The hands are opposite at 7:05 5/11, i.e. between 7:05 and 7:10.
5. Check: at 7:05 the angle is 210 − 27.5 = 182.5°, still above 180°.

Remember · Angle = |30H − 5.5M|; the minute hand gains 5.5° a minute on the hour hand.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) ababab

Filling the blanks with a, b, a, b, a, b turns the series into abbaab abbaab abbaab — one six-letter block repeated three times. None of the other choices produces a repeating block.

1. The series has 18 places, so look for a repeating block of 6 (or 3, 9).
2. Fill the blanks with a, b, a, b, a, b: abbaababbaababbaab.
3. This splits as abbaab | abbaab | abbaab — the same block three times.
4. Check: bababa gives bbaabbaabbababaaab, which has no repeating block.

Remember · For letter-series gaps, count the length and test whether the filled series splits into equal repeating blocks.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error