Q&A: practice questions with answers

Concept: A satellite whose period equals Earth's rotation period stays above one spot.

1. Earth rotates once in about 24 hours.
2. A satellite with a 24-hour period (in the equatorial plane, moving eastward) keeps pace with the ground.
3. So it appears fixed over the same point – a geostationary satellite.

Yaad rakhein: Geostationary orbit height ≈ 35,786 km above the equator; used for communication and weather (e.g. INSAT, GSAT).

Answer: (B) Remains fixed over the same point on Earth

Concept: Pension scheme for small and marginal farmers (launched 2019).

1. Voluntary, contributory scheme for farmers aged 18–40.
2. After 60 years, a fixed pension of ₹3,000 per month.
3. Centre contributes an amount equal to the farmer's contribution.

Yaad rakhein: PM-SYM (unorganised workers) and PM-KMY both give ₹3,000/month after 60 – remember '3000 at 60'.

Answer: (C) ₹3,000

Concept: World Bank indices and what they measure.

1. LPI measures how efficiently a country moves goods – customs, infrastructure, shipments, tracking and timeliness.
2. So it is a benchmark for trade and transport logistics, not finance, farming or cybersecurity.

Yaad rakhein: India ranked 38th out of 139 countries in LPI 2023.

Answer: (B) Managing trade and transportation logistics efficiently

Concept: Different deficits compare different parts of the budget.

1. Revenue Deficit = Revenue expenditure − Revenue receipts.
2. Fiscal Deficit = Total expenditure − (Revenue receipts + non-debt capital receipts), i.e. total borrowing.
3. Primary Deficit = Fiscal deficit − Interest payments.

Trick: The word in the name tells you the account: 'Revenue' deficit uses only revenue items on both sides.

Answer: (A) Revenue expenditure over Revenue receipts

Concept: Regional folk theatre forms of India.

1. Tamasha is the folk theatre of Maharashtra, performed in villages, often around Shimga (Holi) – Statement 1 correct.
2. Communities like the Kolhati have traditionally formed Tamasha troupes – Statement 2 correct.

Yaad rakhein: Lavani (song-dance with dholki) is the heart of Tamasha; other folk theatres: Nautanki (UP), Jatra (Bengal), Bhavai (Gujarat).

Answer: (C) Both 1 and 2

Concept: Personalities behind national symbols.

1. Pingali Venkayya designed a flag and presented it to Gandhiji at Vijayawada in 1921.
2. His design became the base for the Tiranga adopted on 22 July 1947.
3. National Anthem – Rabindranath Tagore.

Yaad rakhein: National Flag adopted 22 July 1947; Flag Code of India 2002; Har Ghar Tiranga campaign began 2022 (Venkayya's 146th birth anniversary year).

Answer: (C) National Flag of India

Concept: Heads of India's space programme.

1. K. Sivan was Chairman of ISRO (2018–2022).
2. The ISRO Chairman is also Secretary, Department of Space and Chairman of the Space Commission.
3. He led Chandrayaan-2 and is called the 'Rocket Man' for cryogenic engine work; he never headed DRDO or HAL.

Yaad rakhein: ISRO chiefs after him: S. Somanath (2022–25), V. Narayanan (from January 2025).

Answer: (D) Led ISRO and its parent department (Department of Space)

Concept: Breaks in India's planning cycle.

1. After the Third Plan (1961–66), war with Pakistan (1965) and droughts strained resources.
2. From 1966 to 1969 no Five-Year Plan was launched; three Annual Plans were run instead – the 'Plan Holiday'.
3. The Fourth Plan started in 1969.

Yaad rakhein: Another gap: 1990–92 (two Annual Plans) before the Eighth Plan (1992–97).

Answer: (C) A break in the continuity of Five-Year Planning

Concept: AMOC carries warm tropical water north in the Atlantic; weakening it reduces northward heat transport.

1. Less heat to the north ⇒ North Atlantic cools (option b is an outcome).
2. Shift of the tropical rain belt ⇒ monsoons disrupted (a is an outcome); sea level rises on the US east coast (d is an outcome).
3. Extra Arctic warming is not caused by AMOC slowdown – it would reduce heat reaching the north.

Trick: 'NOT' questions: an AMOC slowdown means less heat going north, so any option claiming more northern warming is the misfit.

Answer: (C) Increased warming of the Arctic region

Concept: Doctrine of pleasure and its constitutional limits.

1. Art. 310: civil servants hold office during the pleasure of the President/Governor – borrowed from British practice. Statement 1 ✓
2. Art. 311: no dismissal/removal/reduction in rank without inquiry and a reasonable hearing; not by an authority subordinate to the appointing one. Statement 3 ✓
3. Hence the power under Art. 310 is not unrestricted – Statement 2 ✗

Trick: Statements 2 and 3 contradict each other – both cannot be true, so options (c) and (d) go out immediately.

Answer: (B) 1 and 3 only

Concept: If $\frac{a+b}{a-b}=\frac{k}{1}$, then $\frac{a}{b}=\frac{k+1}{k-1}$.

1. Here $a=\sqrt{8+x}$, $b=\sqrt{8-x}$, $k=5$.
2. $\frac{a}{b}=\frac{5+1}{5-1}=\frac{6}{4}=\frac{3}{2}$
3. Square: $\frac{8+x}{8-x}=\frac{9}{4}\Rightarrow 32+4x=72-9x$
4. $13x=40\Rightarrow x=\frac{40}{13}$

Trick: Componendo-dividendo turns the whole fraction into a simple ratio in one step – then just square.

Answer: (C) $\frac{40}{13}$

Concept: Quarterly: rate ÷ 4, number of periods = quarters.

1. Rate per quarter = $\frac{20}{4}=5\%$; 9 months = 3 quarters.
2. $(1.05{)}^3=1.157625$ ⇒ growth factor over 9 months
3. CI = $24,000\times 0.157625=$ ₹3,783

Trick: Effective rate for 3 periods at 5% = 15.7625% $(5+5+5+0.25\times 3+0.0125)$. 15.7625% of 24,000 = ₹3,783.

Answer: (D) ₹3,783

Concept: Same work ⇒ (persons × days) × efficiency is equal.

1. 15 women × 14 days = 210 woman-days.
2. 30 men × 10 days = 300 man-days.
3. $210W=300M\Rightarrow \frac{M}{W}=\frac{210}{300}=\frac{7}{10}$

Trick: Efficiency is inversely proportional to the person-days needed: M : W = 210 : 300 = 7 : 10.

Answer: (A) 7 : 10

Concept: Natural numbers: 1, 2, 3, …; integers: …, −2, −1, 0, 1, 2, ….

1. 2, 7, 9 are natural numbers (and integers).
2. 0 is an integer but natural numbers start from 1.
3. So 0 is the required number.

Yaad rakhein: Whole numbers = 0 + natural numbers. So 0 is whole and integer, but not natural.

Answer: (B) 0

Concept: Equal distances at speeds a and b ⇒ average = $\frac{2ab}{a+b}$.

1. $a=18$, $b=9$
2. Average = $\frac{2\times 18\times 9}{18+9}=\frac{324}{27}$
3. = 12 km/h

Trick: Take the half-distance as 18 km: times 1 h + 2 h = 3 h for 36 km ⇒ 12 km/h.

Answer: (A) 12 km/h

Concept: Largest hemisphere in a cube: flat face on a cube face, diameter = side.

1. Diameter = 12 cm ⇒ r = 6 cm
2. Volume = $(\frac{2}{3})\pi r^3=(\frac{2}{3})\times 3.14\times 216$
3. = $3.14\times 144=452.16$ cm³

Trick: $(\frac{2}{3})\times 216=144$, so just multiply $144\times 3.14$ – the decimal .16 matches only option (d).

Answer: (D) 452.16 cm³

Concept: Distance per litre = total distance ÷ fuel used.

1. Mileage = $11.9÷1.4$
2. = $119÷14$
3. = 8.5 km per litre

Trick: Check backwards: $1.4\times 8.5=11.9$ ✓.

Answer: (B) 8.5 km

Concept: Give R's fixed share first; split the rest in the capital ratio.

1. R = 30% of 3,50,000 = ₹1,05,000
2. Remaining = ₹2,45,000; P : Q = $60:40=3:2$
3. Q = $(\frac{2}{5})\times 2,45,000=$ ₹98,000

Trick: Q's share = $70\%\times 40\%=28\%$ of total ⇒ $0.28\times 3,50,000=$ ₹98,000.

Answer: (C) ₹98,000

Concept: Write milk and water as multiples of x and form the new ratio.

1. Milk = 6x, water = 5x
2. $\frac{6x-10}{5x+9}=\frac{2}{3}$
3. $18x-30=10x+18\Rightarrow 8x=48\Rightarrow x=6$
4. Total = $11x=66$ L

Trick: Total must be a multiple of 11 (6 + 5) – only 66 among the options.

Answer: (B) 66 L

Concept: Area of triangle = $\frac{1}{2}\times$ base $\times$ height.

1. Triangle area = 35% of 300 = 105 m²
2. $\frac{1}{2}\times 20\times h=105\Rightarrow 10h=105$
3. $h=10.5$ m

Trick: $h=2\times$ Area $÷$ base $=210÷20=10.5$.

Answer: (C) 10.5 m