Q&A: practice questions with answers

Concept: Eₙ = −13.6/n² eV for hydrogen, so levels crowd together as n rises.

1. E₁ = −13.6, E₂ = −3.4, E₃ = −1.51, E₄ = −0.85 eV.
2. Gaps: 10.2 → 1.89 → 0.66 eV – getting smaller.
3. So the spacing decreases with each higher level.

Trick: 1/n² falls fast: 1, 1/4, 1/9, 1/16 – the steps between them shrink.

Answer: (A) It becomes smaller with each higher level

Concept: NBHM promotes scientific beekeeping as part of farm income growth.

1. Launched in 2020 under the Atmanirbhar Bharat package.
2. Implementing agency: National Bee Board, working under the Agriculture & Farmers Welfare ministry.
3. Linked to the “Sweet Revolution” (Meethi Kranti).

Trick: Bees are farm allies (pollination) → Agriculture ministry.

Answer: (C) Ministry of Agriculture and Farmers Welfare

Concept: The WEF Global Gender Gap Report scores how much of the gap each region has closed.

1. In the 2025 edition Northern America has the highest regional score (about 75.8%), just ahead of Europe (≈75.1%).
2. Southern Asia (≈64.6%) is near the bottom; MENA is last.

Yaad rakhein: Iceland tops the country ranking again in 2025; India ranks 131st.

Answer: (B) Northern America

Concept: GDP counts only final goods and services: C + I + G + (X − M).

1. Household consumption (C), government spending (G) and net exports (X − M) are all parts of GDP.
2. Intermediate goods are already inside the price of the final product.
3. Adding them again would cause double counting – so they are excluded.

Trick: Use the value-added method in mind: only the extra value at each stage counts.

Answer: (D) Value of intermediate goods used in manufacturing

Concept: Paika is a war dance of Odisha that mimics a battle from call to victory.

1. Start: the shankha (war conch) is blown – the call to battle (3).
2. Main part: sword-and-shield fighting moves (4).
3. Then acrobatic flips and somersaults (1), ending with the group chant “Jai Jagannath” (2).
4. Order: 3-4-1-2.

Trick: Think of a real battle: call → fight → display of skill → victory cry.

Answer: (C) 3-4-1-2

Concept: An early Indian national flag was hoisted abroad in 1907.

1. Madam Bhikaji Cama raised it at the International Socialist Congress, Stuttgart (Germany), on 22 Aug 1907.
2. The flag bore “Vande Mataram” and had green, saffron and red bands.

Yaad rakhein: Bhikaji Cama is called the “Mother of the Indian Revolution”.

Answer: (C) Madam Bhikaji Cama

Concept: An inclusive park lets children of every ability play together.

1. Visakhapatnam’s All-Abilities Park is built for children with disabilities, with accessible ramps and sensory/play equipment.
2. The other options are not projects of this kind in the city.

Trick: The phrase “children with disabilities” matches the name “All-Abilities”.

Answer: (B) All-Abilities Park

Concept: She is India’s best-known biotech entrepreneur.

1. Founded Biocon in Bengaluru in 1978 – a pioneer private biotech firm, now a large biopharma company.
2. Infosys was co-founded by N.R. Narayana Murthy and others – not her.
3. She is a Padma Shri and Padma Bhushan awardee.

Trick: Bio-con ↔ biotechnology – the company name links to the sector.

Answer: (A) She established India's first private biotech firm, Biocon Limited.

Concept: Structural transformation = labour shifting from farming to industry and services.

1. From 1950 to 1990 agriculture’s share in GDP fell, but its share of workforce stayed around 65%.
2. So people did not move out of farming – the structure hardly changed.
3. Services did not become the main employer, and mechanisation stayed uneven.

Trick: For “structural change”, always look at the employment share, not output.

Answer: (B) Share of workforce in agriculture stayed around 65%

Concept: The Inter-State Council is a recommendatory body under Article 263.

1. Set up in 1990 by Presidential order after the Sarkaria Commission’s advice → 1 correct.
2. Its basis is Article 263 → 2 correct.
3. It only advises; it has no power to enforce → 3 wrong.

Trick: Words like “enforcement powers” for an advisory council are a red flag.

Answer: (D) 1 and 2 only

Concept: $A=P{(1+\frac{r}{100})}^n$; tripling in 3 years means ${(1+\frac{r}{100})}^3=3$.

1. ${(1+\frac{r}{100})}^3=3\Rightarrow 1+\frac{r}{100}=\sqrt[3]{3}$.
2. $\sqrt[3]{3}\approx 1.442$ (since ${1.44}^3\approx 2.99$).
3. $r\approx 0.442\times 100=44.2\%$.

Trick: Check options: ${1.442}^3\approx 3.00$, while ${1.5}^3=3.375$ – so 50% is too high.

Answer: (A) 44.2%

Concept: A fraction in lowest terms terminates only if its denominator has no prime factor other than 2 and 5.

1. $\frac{6}{16}=\frac{3}{8},8=2^3$ → 0.375 terminates.
2. $\frac{2}{12}=\frac{1}{6}$ (factor 3), $\frac{4}{14}=\frac{2}{7}$ (factor 7), $\frac{8}{18}=\frac{4}{9}$ (factor 3) → recurring.

Trick: Always reduce the fraction first, then check the denominator.

Answer: (A) $\frac{6}{16}$

Concept: Same direction: the faster walker pulls ahead by (fast − slow) every hour.

1. Sanjay gains $6-3=3$ km each hour.
2. In 2 hours: $3\times 2=6$ km apart.

Trick: Same direction → subtract speeds; opposite direction → add.

Answer: (C) 6 km

Concept: Surface area $\propto r^2$, so use successive % change: $a+b+\frac{ab}{100}$.

1. r rises 5% twice over $(r\times r)$.
2. Change = $5+5+\frac{5\times 5}{100}=10.25\%$.

Trick: ${1.05}^2=1.1025$ → 10.25% in one step.

Answer: (A) 10.25%

Concept: $1{\text{m}}^3=1000$ litres.

1. Tubs needed = $1000÷12.5$.
2. = $10000÷125=80$.

Trick: $12.5=\frac{100}{8}$, so $1000÷12.5=1000\times \frac{8}{100}=80$.

Answer: (A) 80

Concept: Profit is shared in the ratio of capital × time.

1. Months: P and Q 12 each, R only 9 (joined after 3).
2. In thousands: 720 : 360 : 405 = 16 : 8 : 9 (÷ 45). Total = 33.
3. $R=\frac{9}{33}\times 40,000=\frac{3}{11}\times 40,000\approx$ ₹10,909.

Trick: $\frac{9}{33}=\frac{3}{11}\approx 27.27\%$; 27.27% of 40,000 ≈ 10,909.

Answer: (A) ₹10,909

Concept: Ratio difference ($5-3=2$ parts) equals the actual difference.

1. 2 parts = 16 ⇒ 1 part = 8.
2. Numbers = $3\times 8=24$ and $5\times 8=40$.

Trick: Check options: only 24 and 40 have ratio 3 : 5 and difference 16.

Answer: (A) 24 and 40

Concept: Equal areas: side${}^2$ = length × breadth.

1. Area = $36\times 25=900$ m².
2. Side = $\sqrt{900}=30$ m.
3. Perimeter = $4\times 30=120$ m.

Trick: $\sqrt{36\times 25}=6\times 5=30$ directly.

Answer: (B) 120 m

Concept: Area $\propto$ side${}^2$, so $\text{new side factor}=\sqrt{\text{new area factor}}$.

1. New area = $121\%=1.21$ × old.
2. Side factor = $\sqrt{1.21}=1.1$.
3. Side increased by 10%.

Trick: $121={11}^2$ → 10% rise in side (${1.1}^2=1.21$).

Answer: (D) 10%

Concept: Difference of two percents of the same number = (difference)% of it.

1. $40\%-10\%=30\%$ of the number = 120.
2. Number = $120\times \frac{100}{30}=400$.

Trick: Check: 10% of 400 = 40, 40% = 160, gap 120 ✓.

Answer: (D) 400