Logical & analytical reasoning

Answer: (d) Neither Conclusion-I nor Conclusion-II

The only link to watches is 'some computers', and those computers need not include any mobile or radio. A diagram with the watches placed away from the mobiles fits every statement, so neither 'certainly' conclusion is forced.

1. Some radios are mobiles and all mobiles are computers, so some radios are computers.
2. 'Some computers are watches' does not say which computers.
3. Draw the watches overlapping only the part of 'computers' that has no mobile and no radio — all three statements still hold.
4. In that diagram no radio and no mobile is a watch, so neither conclusion is certain.

• ✗ Conclusion-I Radios reach watches only through two 'some' links; a radio being a watch is possible but not certain.
• ✗ Conclusion-II All mobiles are computers, but the computers that are watches may be the ones that are not mobiles.

Remember · A 'certainly' conclusion must hold in every possible diagram — try to draw one where it fails.

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) Both Conclusion-I and Conclusion-II

The almirahs that are chairs are also tables, so Conclusion-I is certain. Conclusion-II only claims a possibility ('may not'), and since nothing fixes how cats relate to chairs, that possibility is open — so both follow.

1. Some almirahs are chairs and all chairs are tables, so those almirahs are tables — 'some almirahs are tables' is certain.
2. Cats connect to chairs only through 'some almirahs', a particular link, so there is no definite relation between cats and chairs.
3. With no definite relation, a diagram where some cats are not chairs is allowed — so 'some cats may not be chairs' follows.

• ✓ Conclusion-I 'Some almirahs are chairs' + 'All chairs are tables' gives 'some almirahs are tables' with certainty.
• ✓ Conclusion-II It states only a possibility; since the statements do not force every cat to be a chair, the possibility holds.

Remember · 'Some A are B' + 'All B are C' gives 'some A are C'. A 'may / may not' conclusion follows when no definite relation rules it out.

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: (b) 25 km

Tracking the turns, the north–south legs cancel out (10 south, 40 north, 30 south) and the east legs add to 20 + 5 = 25 km. The bank is 25 km due East of the house.

1. Place the house at (0, 0), East as +x and North as +y.
2. 10 km South → (0, −10). Facing South, a left turn faces East: 20 km → (20, −10).
3. Left again faces North: 40 km → (20, 30). Right faces East: 5 km → (25, 30).
4. Right again faces South: 30 km → (25, 0), the bank.
5. The bank is 25 km due East of the house, so the shortest distance is 25 km.

Remember · Add the net East–West and North–South movements separately; use Pythagoras only if both are non-zero.

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: (b) An angle less than 45° North of East

She ends 6 km North and 8 km East of the start. Because the northward part (6) is smaller than the eastward part (8), she is North of East at an angle below 45°.

1. Net North = 12 − 6 = 6 km; East = 8 km.
2. She is 8 km East and 6 km North of the start.
3. tan θ = 6/8 = 0.75, which is less than 1, so the angle from East towards North is less than 45° (about 36.9°).

Remember · Compare the two net components: the direction lies within 45° of the axis with the larger component.

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: (b) Some villagers under 25 years of age are literate.

Fractions of the same village that add up to more than 1 must overlap. Under-25s (4/5) and literates (1/3) together make 17/15, so at least 2/15 of the villagers are both — some under-25s are certainly literate.

1. Under 25: 4/5 of the villagers; literate: 1/3.
2. 4/5 + 1/3 = 12/15 + 5/15 = 17/15, which is more than the whole village.
3. So at least 17/15 − 1 = 2/15 of the villagers are both under 25 and literate — (b) is certain.
4. Check the rest: house-owners (1/2) outnumber literates (1/3), so (a) is impossible; house-owners and under-25s (1/2 + 4/5 = 13/10) must overlap, so (d) is false; (c) cannot be fixed from the data.

• ✗ (a) Half the villagers own houses but only a third are literate, so not all house-owners can be literate.
• ✓ (b) 4/5 + 1/3 exceeds 1, so at least 2/15 of the villagers are both under 25 and literate.
• ✗ (c) Nothing tells us how literacy is spread among paddy growers.
• ✗ (d) 1/2 + 4/5 = 13/10 exceeds 1, so at least 3/10 of the villagers are under 25 and own a house.

Remember · If two fractions of one group add to more than 1, the excess over 1 is the guaranteed minimum overlap.

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) Neither Conclusion 1 nor 2 nor 3 nor 4

Two 'some' statements joined only through blues give no definite link between greens and blacks. None of the four conclusions follows on its own; at most, 1 and 2 form an either-or pair, which no option offers.

1. Both statements are particular ('some') and meet only in blues, so no definite relation between greens and blacks can be drawn.
2. Conclusion-1 and Conclusion-2 are each possible, but neither is certain.
3. Conclusions 3 and 4 ('all') cannot come from 'some' premises.
4. None follows. (1 and 2 together make an either-or pair, but option (a) claims both follow, which is impossible.)

• ✗ Conclusion-1 Greens and blacks may or may not overlap; nothing forces it.
• ✗ Conclusion-2 A diagram with some greens being blacks fits the statements, so 'no green is black' is not certain.
• ✗ Conclusion-3 An 'all' conclusion cannot follow from two 'some' statements.
• ✗ Conclusion-4 Likewise, nothing says every black is green.

Remember · Two particular ('some') premises never give a definite conclusion; use the either-or rule only when an option offers 'either … or'.

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: (b) BIDNHTSSX

The code moves letters alternately one step back and one step forward (M→L, A→B, T→S, H→I …). Applied to CHEMISTRY, this gives BIDNHTSSX.

1. MATHEMATICS → LBSIDNZUHDR: M−1 = L, A+1 = B, T−1 = S, H+1 = I, E−1 = D, M+1 = N, A−1 = Z … — alternately −1 and +1.
2. CHEMISTRY: C−1 = B, H+1 = I, E−1 = D, M+1 = N, I−1 = H, S+1 = T, T−1 = S, R+1 = S, Y−1 = X.
3. Code: BIDNHTSSX.
4. Check: (c) BIDLHTSSX differs only in the 4th letter — M+1 is N, not L.

Remember · In letter codes, write the shift under each letter; alternating shifts (−1, +1) are common. Compare options only where they differ.

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