Q&A: practice questions with answers

Concept: Match each awardee with the right field.

1. M.T. Vasudevan Nair – Malayalam writer, Kerala, Literature & Education (posthumous) ✓.
2. D. Nageshwar Reddy – gastroenterologist → Medicine, not Public Affairs.
3. Kumudini Lakhia – Kathak dancer → Art; Justice J.S. Khehar – former CJI → Public Affairs.

Trick: A dancer under "Medicine" and a judge under "Art" are obvious mismatches – only (A) survives.

Answer: (A) Shri M.T. Vasudevan Nair (Posthumous) — Literature and Education — Kerala

Concept: Safeguards for a person arrested without warrant.

1. The officer must tell the full grounds/reason of arrest at once.
2. For a bailable offence, he must also say that the person can be released on bail.
3. This flows from Article 22(1) of the Constitution.

Trick: The other options are irrelevant (family, list of stations, foreign language) – only (B) is a legal right.

Answer: (B) Reason for arrest and right to bail (if applicable)

Concept: PM-KISAN is a direct income-support scheme.

1. Farmers get ₹6,000 a year in 3 instalments of ₹2,000 via DBT.
2. The app lets them check beneficiary status, e-KYC and instalment payments.
3. Crop-insurance claims belong to PMFBY, not PM-KISAN.

Yaad rakhein: PM-KISAN was launched in February 2019 (Gorakhpur) with effect from December 2018.

Answer: (D) Tracking instalment payments to beneficiaries

Concept: Annual ranking of world cities by the Economist Intelligence Unit (EIU).

1. In the 2025 index Copenhagen (Denmark) ranked first.
2. Vienna, the winner of the previous three years, slipped to joint second.

Yaad rakhein: EIU judges 5 areas: stability, healthcare, culture & environment, education, infrastructure.

Answer: (A) Copenhagen

Concept: Break-even = no profit, no loss.

1. Profit = TR − TC; it is zero when TR = TC.
2. MR = MC is the profit-maximising condition, not break-even.
3. TC < TR means profit, not break-even.

Trick: "Break-even" = "even" → revenue and cost are equal.

Answer: (C) When total revenue equals total cost

Concept: Gap between the Third and Fourth Five-Year Plans.

1. Third Plan ended in 1966; Fourth began only in 1969.
2. 1966–69 had three Annual Plans instead – called the "Plan Holiday".
3. Reasons: 1962 and 1965 wars, droughts, 1966 rupee devaluation.

Yaad rakhein: Another break: 1990–92 (two annual plans) before the Eighth Plan.

Answer: (B) 1966-1969

Concept: Early women freedom fighters of Karnataka.

1. Rani Chennamma ruled Kittur (now in Belagavi district).
2. In 1824 she fought the British who refused to accept her adopted son – decades before 1857.

Yaad rakhein: Kittur Utsav is held every October in her memory; Mysore was ruled by the Wodeyars.

Answer: (C) Kittur

Concept: Otto von Bismarck unified Germany; the Indian parallel unified princely states.

1. As Home Minister, Sardar Patel merged 560+ princely states into India (with V.P. Menon).
2. Hence "Bismarck of India" and also "Iron Man of India".

Yaad rakhein: Statue of Unity (182 m) on the Narmada in Gujarat honours Patel; 31 October is National Unity Day.

Answer: (B) Sardar Vallabhbhai Patel

Concept: Location and status of the sugar industry (NCERT facts).

1. 1 wrong: sugarcane is heavy, bulky and perishable – a weight-losing raw material, so mills sit near farms.
2. 2 wrong: mills are spread over UP, Bihar, Maharashtra, Karnataka, TN etc.; UP–Bihar do not hold ~75%.
3. 3 ✓ India is first in gur and khandsari; 4 ✓ India is listed second in sugar (after Brazil) in NCERT.

Trick: Statement 1 is clearly false → drop (A), (B), (D) at once.

Answer: (C) Only 3 and 4

Concept: The licence-permit raj limited competition before 1991.

1. A is false: licensing restricted entry and capacity, so it discouraged innovation.
2. R is true: it created entry barriers and encouraged rent-seeking (bribes for licences).

Yaad rakhein: Industrial licensing was largely abolished by the New Industrial Policy of July 1991 (LPG reforms).

Answer: (C) A is false but R is true

Concept: Take the LCM, then make every prime power even.

1. $\text{LCM}(3,5,12,15)=60=2^2\times 3\times 5$.
2. 3 and 5 have odd powers → multiply by $3\times 5=15$.
3. $60\times 15=900$ is the least such square; among options only 3600 ($={60}^2$) is a multiple of 60.

Trick: A square divisible by 5 must end in 25 or 00 – only 3600 qualifies.

Answer: (A) 3600

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

1. $T=\frac{3000\times 100}{8000\times 12.5}$
2. $=\frac{3,00,000}{1,00,000}=3$ years

Trick: $12.5\%=\frac{1}{8}$, so yearly SI = $\frac{8000}{8}=$ ₹1000; ₹3000 needs 3 years.

Answer: (C) 3 years

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

1. Rearrange: $(a+b{)}^3=a^3+b^3+3ab(a+b)$
2. $1331=407+33ab\Rightarrow 33ab=924$
3. $ab=924÷33=28$

Trick: Guess integers: $a+b=11$, $ab=28\Rightarrow a=7$, $b=4$; $343+64=407$ ✓.

Answer: (C) 28

Concept: $\text{SI}=\frac{PRT}{100}$; amount n times → interest = $(n-1)P$.

1. 1: $\frac{10000\times 15\times 3}{100}=$ ₹4500 ✓
2. 2: doubles in 5 yrs → $R=20\%$; in 3 yrs interest = 60% → 1.6 times, not 1.5 ✗
3. 3: 4.5 times → interest 350% in 7 yrs → $R=50\%$ ✓

Trick: Rate = $\frac{(n-1)\times 100}{T}$: statement 3 → $\frac{3.5\times 100}{7}=50$.

Answer: (C) 1 and 3 are correct

Concept: Horizontal distance = $h\times \cot (\text{angle})$; banks on opposite sides → add distances.

1. 45° side: distance = h.
2. 30° side: distance = $h\sqrt{3}$.
3. $h+h\sqrt{3}=50(\sqrt{3}+1)\Rightarrow h=50$ m

Trick: The width is already written as $k(\sqrt{3}+1)$, so $h=k$ directly.

Answer: (A) 50 m

Concept: Product of three adjacent face areas = $(lbh{)}^2=V^2$.

1. $V^2=48\times 54\times 72$
2. $48\times 72=3456=64\times 54\Rightarrow V^2=64\times {54}^2$
3. $V=8\times 54=432$ cm³

Trick: Find sides: $lb=48$, $bh=54$, $lh=72\Rightarrow l=8$, $b=6$, $h=9\Rightarrow 8\times 6\times 9=432$.

Answer: (B) 432 cm³

Concept: Volume stays the same when a solid is melted and recast.

1. Hemisphere = $\frac{2}{3}\pi \times 9^3=486\pi$
2. Cylinder = $\pi r^2\times 6$
3. $6r^2=486\Rightarrow r^2=81\Rightarrow r=9$ cm

Trick: $\frac{2}{3}{R}^3=r^{2}h\Rightarrow \frac{2}{3}\times 729=6r^2\Rightarrow r=9$ (same as R, since $h=\frac{2R}{3}$).

Answer: (A) 9 cm

Concept: Same base radius: cone height must be 3 times cylinder height for equal volume.

1. Cylinder = $\pi r^2\times 3h$
2. Cone = $\frac{1}{3}\pi r^{2}H$
3. $\frac{1}{3}H=3h\Rightarrow H=9h$

Yaad rakhein: Same radius & height: cone : cylinder volume = 1 : 3.

Answer: (A) 9h

Concept: Cuboid diagonal $\sqrt{l^2+b^2+h^2}$ = sphere diameter.

1. Diameter = $2\times 13=26\Rightarrow {26}^2=676$
2. $h^2=676-(81+225)=676-306=370$
3. $h=\sqrt{370}\approx 19.2$ cm

Trick: ${19}^2=361$ and ${20}^2=400$, so $\sqrt{370}$ lies just above 19 – only 19.2 fits.

Answer: (D) 19.2 cm

Concept: ${\text{Slant height}}^2={\text{height}}^2+(\text{half the base side}{)}^2$.

1. Half side = $\frac{10}{2}=5$ cm
2. $l=\sqrt{{12}^2+5^2}=\sqrt{169}$
3. $l=13$ cm

Trick: 5-12-13 is a Pythagorean triplet – no calculation needed.

Answer: (B) 13 cm