Q&A: practice questions with answers

Concept: Repechage gives wrestlers who lose to finalists a second route to bronze.

1. In Beijing 2008 (66 kg freestyle), Sushil lost his opening bout.
2. His conqueror reached the final, so Sushil entered repechage and won three successive bouts for bronze.
3. This was India's first Olympic wrestling medal since K.D. Jadhav (Helsinki 1952) – a 56-year gap.

Yaad rakhein: Sushil later won silver at London 2012, becoming the first Indian with two individual Olympic medals.

Answer: (D) By winning three repechage matches after losing his first bout

Concept: The International Booker honours a translated work; author and translator share it.

1. 2025 winner: 'Heart Lamp' by Banu Mushtaq, translated from Kannada by Deepa Bhasthi.
2. First Kannada book and first short-story collection to win.
3. Han Kang won with Deborah Smith in 2016; Olga Tokarczuk with Jennifer Croft in 2018.

Yaad rakhein: In 2022 Geetanjali Shree's 'Tomb of Sand' (Hindi, tr. Daisy Rockwell) was the first Indian-language winner.

Answer: (A) Banu Mushtaq & Deepa Bhasthi

Concept: Check each statement on the organiser, venue and timing of the 73rd edition.

1. Statement 1: organised by the Eastern Naval Command (Indian Navy) ✓
2. Statement 2: Visakhapatnam, ENC's headquarters, was the host city ✓
3. Statement 3: the April 2025 timing given is not correct ✗ → only 1 and 2.

Yaad rakhein: Eastern Naval Command is headquartered at Visakhapatnam – so statements 1 and 2 naturally go together.

Answer: (D) Only 1 and 2

Concept: Article 263 lets the President set up an Inter-State Council for better Centre–State and inter-State coordination.

1. The Council investigates and advises on disputes and subjects of common interest among States/Union.
2. It was first constituted in 1990, following the Sarkaria Commission's recommendation.
3. Financial matters → Finance Commission (Art. 280); emergency → Arts. 352–360.

Yaad rakhein: The Prime Minister chairs the Inter-State Council; members include all Chief Ministers.

Answer: (D) Sets up the Inter-State Council

Concept: Reversible processes give maximum work; Carnot efficiency depends only on reservoir temperatures.

1. 1 ✗ – Reversible expansion does the maximum work; irreversible gives less.
2. 2 ✓ – η = 1 − T_cold/T_hot depends only on the two temperatures.
3. 3 ✓ – Clausius statement: heat flows cold → hot only with external work (refrigerator).

Yaad rakhein: A refrigerator/heat pump is the everyday example of the Clausius statement of the second law.

Answer: (C) 2 and 3 only

Concept: Jhora is a community circle dance of Kumaon, Uttarakhand, performed in spring and at fairs.

1. Dancers – men and women together – link with one another by the arms.
2. They move in a big circle with rhythmic steps while a lead singer sings in the middle.

Yaad rakhein: Other Kumaoni/Garhwali dances: Chholiya (sword dance), Chhapeli, Langvir Nritya, Pandav Nritya.

Answer: (C) Arms

Concept: Global Firepower ranks nations by a composite 'PowerIndex'; a lower score means stronger military.

1. The index uses 60+ factors – manpower, equipment, logistics, finances, natural resources and geography.
2. It is not based on troops alone, nor on nuclear stockpiles, nor on alphabetical order.
3. 2025 top ranks: USA, Russia, China, India (4th).

Trick: Single-factor options (only troops, only nuclear) are usually wrong for any composite index – pick the multi-parameter one.

Answer: (D) It assesses military power using 60+ parameters such as manpower, logistics and geography to compute the PowerIndex.

Concept: Under the National Green Hydrogen Mission (2023), hubs are being built around ports and industrial clusters.

1. India's first green hydrogen hub is planned at Pudimadaka near Visakhapatnam, Andhra Pradesh (NTPC project).
2. Its foundation was laid in January 2025.
3. Port-based hubs are also being developed at Kandla (Deendayal) and Tuticorin (V.O. Chidambaranar).

Yaad rakhein: National Green Hydrogen Mission targets 5 MMT green hydrogen production per year by 2030.

Answer: (A) Andhra Pradesh

Concept: Chandrayaan-1 (launched 22 Oct 2008 by PSLV-C11) was India's first lunar mission.

1. Its NASA-built Moon Mineralogy Mapper (M3) and the Moon Impact Probe detected water/hydroxyl on the lunar surface (announced 2009).
2. Mangalyaan → Mars (2013); Aditya-L1 → Sun (2023); Shukrayaan-1 → planned Venus mission.

Trick: Match mission to body by name: Chandra = Moon, Mangal = Mars, Aditya = Sun, Shukra = Venus.

Answer: (C) Chandrayaan-1

Concept: President's pardon: Article 72; Governor's pardon: Article 161.

1. Statement 1 ✗ – Article 161 is the Governor's power; the President's is Article 72.
2. Statement 2 ✓ – A Governor cannot pardon a death sentence (he may only suspend, remit or commute it); full pardon of death sentence lies with the President.
3. So only statement 2 is correct.

Trick: Offices and articles go in the same order: President (72) comes before Governor (161); a death-sentence pardon = President only.

Answer: (D) 2 only

Concept: Treat $\sqrt{a}$ and $\sqrt{b}$ as unknowns, solve by adding and subtracting, then square.

1. $\sqrt{a}+\sqrt{b}=7$ and $\sqrt{a}-\sqrt{b}=1$
2. Add: $2\sqrt{a}=8\to \sqrt{a}=4\to a=16$
3. Subtract: $2\sqrt{b}=6\to \sqrt{b}=3\to b=9$

Trick: Options (A) and (D) give $a+b=7$ – a trap for those who forget the roots; the answer must be perfect squares, 16 and 9.

Answer: (C) a = 16, b = 9

Concept: Start from the smallest 6-digit number and test whether it is a perfect square.

1. Smallest 6-digit number = 100000.
2. ${316}^2=99856$ and ${317}^2=100489$, so 100000 lies between two squares → not a perfect square.
3. Since it is already the smallest 6-digit number, it is the answer.

Trick: ${10}^5$ has an odd power of 10 (odd number of zeros) – it can never be a perfect square.

Answer: (B) 100000

Concept: If x% of p = y% of q, then p : q = y : x.

1. $37.5\%=\frac{3}{8}$, $25\%=\frac{1}{4}$
2. $\frac{3}{8}p=\frac{1}{4}q\to \frac{p}{q}=\frac{1}{4}\times \frac{8}{3}=\frac{2}{3}$
3. p : q = 2 : 3

Trick: Cross-swap the percentages: p : q = 25 : 37.5 = 2 : 3.

Answer: (D) 2 : 3

Concept: Find the cost price per kg of the mixture (weighted average), then compare with SP.

1. CP of 8 kg = $3\times 40+5\times 50=120+250=$ ₹370 → ₹46.25 per kg
2. SP per kg = ₹55.50 → profit = $55.50-46.25=$ ₹9.25
3. Gain% = $\frac{9.25}{46.25}\times 100=20\%$

Trick: SP is clearly above both ₹40 and ₹50, so it must be a gain – remove both loss options; then $46.25\times 1.2=55.50$ confirms 20%.

Answer: (B) 20% Gain

Concept: Each discount is applied on the price left after the previous one.

1. After 30% off: $800\times \frac{70}{100}=$ ₹560
2. After 20% more: $560\times \frac{80}{100}=$ ₹448
3. Final SP = ₹448

Trick: Net discount of 30% and 20% = $30+20-\frac{30\times 20}{100}=44\%$ → $800\times 0.56=$ ₹448.

Answer: (C) ₹448

Concept: Take CP = 100; discount% is always on the marked price.

1. CP = 100 → MP = 125, SP = 120
2. Discount = $125-120=5$
3. Discount% = $\frac{5}{125}\times 100=4\%$

Trick: Formula: $(100+\text{markup})(100-d)=100(100+\text{profit})$ → $125(100-d)=12000\to 100-d=96\to d=4\%$.

Answer: (B) 4%

Concept: Use $a^3+b^3=(a+b{)}^3-3ab(a+b)$.

1. Let $a+b=s$: $s^3-3\times 15\times s=152\to s^3-45s=152$
2. Try $s=8$: $512-360=152$ ✓
3. So $a+b=8$ (e.g. $a=5$, $b=3$)

Trick: With $ab=15$ test the factor pair 5 and 3: $5^3+3^3=125+27=152$ → $a+b=8$ in seconds.

Answer: (D) 8

Concept: $R=\frac{SI\times 100}{P\times T}$.

1. SI = $4020-3000=$ ₹1020
2. $R=\frac{1020\times 100}{3000\times 5}=\frac{102000}{15000}$
3. $R=6.8\%$

Trick: Total growth = $\frac{1020}{3000}=34\%$ in 5 years → $34÷5=6.8\%$ per year.

Answer: (D) 6.8%

Concept: Same time for both, so add the yearly interests and divide the total interest by it.

1. Yearly SI on ₹8000 at 6% = ₹480
2. Yearly SI on ₹5000 at 8% = ₹400 → total ₹880 per year
3. T = $2640÷880=3$ years

Trick: 2640 is exactly $3\times 880$ – check divisibility of the total by the yearly interest straight away.

Answer: (D) 3 years

Concept: The ramp is the hypotenuse; height is opposite the 30° angle, so use sin.

1. $\sin {30}^{\circ }$ = height/ramp $=\frac{1}{2}$
2. $\frac{2.5}{\text{ramp}}=\frac{1}{2}$
3. Ramp = $2.5\times 2=5$ m

Trick: In a 30° right triangle, the hypotenuse is always twice the side opposite 30°.

Answer: (C) 5 m