Q&A: practice questions with answers

Concept: Frequency is decided by the source, not by the medium.

1. In a new medium, speed changes (v = c/n).
2. Since v = f × λ and f is fixed, the wavelength changes along with speed.
3. Amplitude also drops a little as part of the light is reflected — so only frequency is unchanged.

Trick: Colour depends on frequency — light does not change colour when it enters water, so frequency is constant.

Answer: (A) Frequency

Concept: BSA is one of the three new criminal laws that came into force on 1 July 2024.

1. It replaced the Indian Evidence Act, 1872.
2. Electronic/digital records (emails, server logs, smartphone data) are treated as documents and can be primary evidence; forensic and technological evidence is given a wider role.

Yaad rakhein: Other two new laws: Bharatiya Nyaya Sanhita (replaces IPC) and Bharatiya Nagarik Suraksha Sanhita (replaces CrPC).

Answer: (A) Forensic science and digital technology

Concept: Check the award's nature and the ministry behind it.

1. A ✓: it is the top national honour for scientists, technologists and innovators, first given in 2024.
2. R ✗: it is run by the Ministry of Science & Technology, not the Ministry of Culture.
3. Categories: Vigyan Ratna, Vigyan Shri, Vigyan Yuva–SSB, Vigyan Team.

Yaad rakhein: Prof. G. Padmanabhan received the first Vigyan Ratna (2024).

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

Concept: Published by the World Economic Forum since 2006.

1. Four sub-indices: Economic Participation & Opportunity, Educational Attainment, Health & Survival, Political Empowerment.
2. These map to Economy, Education, Health and Politics — option (a).

Trick: Mnemonic 'PEHE' – Politics, Economy, Health, Education.

Answer: (A) Politics, Economy, Health, and Education

Concept: Each North-Eastern state has its own traditional combat art.

1. Thang-Ta ('thang' = sword, 'ta' = spear) is the armed martial art of the Meitei people of Manipur.
2. Its full system is Huyen Langlon; it is also staged as a ritual dance.

Yaad rakhein: Sarit Sarak is Manipur's unarmed martial art; Kalaripayattu is from Kerala.

Answer: (A) Manipur

Concept: Heavy industry: bulky raw materials (steel), big capital, heavy finished goods.

1. Shipbuilding and automobiles use large amounts of steel and machinery → heavy industries.
2. Watches, paint brushes, bulbs, fuse wires and sewing machines are small consumer goods → light industries.

Trick: Ask: 'Can one person carry the product?' If yes, it is usually a light industry.

Answer: (B) Shipbuilding and Automobile

Concept: Indian Governors are appointed, not elected (Canadian model).

1. Article 155: the President appoints the Governor by warrant under hand and seal.
2. Article 156: he holds office during the pleasure of the President, normally for 5 years.

Yaad rakhein: Minimum age for a Governor is 35 years (Article 157).

Answer: (B) Appointed by the President

Concept: The question asks for the main risk 'beyond' habitat loss.

1. Roads, dams and mining are themselves forms of habitat loss, so (a) is excluded by the wording.
2. Invasive alien plants such as Lantana camara, Chromolaena and Acacia spread fast and crowd out native, narrowly adapted endemic species.
3. Hence invasive species are the key additional threat.

Trick: Read the qualifier: 'beyond habitat loss' removes every option that is just another way of destroying habitat.

Answer: (B) Spread of invasive alien species

Concept: Earth-imaging satellites need repeat coverage under the same sunlight.

1. NISAR, the NASA–ISRO radar mission, was launched by GSLV-F16 on 30 July 2025.
2. It flies in a near-polar Sun-synchronous orbit, mapping almost all land and ice every 12 days with L-band and S-band radar.

Trick: Remote-sensing / Earth-observation satellite ⇒ think Sun-synchronous polar orbit first.

Answer: (C) Polar Sun-synchronous Orbit

Concept: Both heads have the power to dissolve the elected House (on ministerial advice).

1. 1 ✓: Article 174(2)(b) – the Governor may dissolve the Legislative Assembly.
2. 2 ✗: Article 85(2)(b) – the President may dissolve the Lok Sabha.
3. Rajya Sabha and Legislative Councils are permanent and cannot be dissolved.

Yaad rakhein: Article 85 = President summons/prorogues/dissolves Parliament; Article 174 = same powers of the Governor for the State.

Answer: (A) 1 only

Concept: Numbers made of one repeated digit d can be written as $d\times (11\dots 1)$.

1. $7+77+777+7777+77777=7\times (1+11+111+1111+11111)$.
2. $1+11+111+1111+11111=12345$.
3. $7\times 12345=86415$.

Trick: Unit digit: five 7s → 35 → ends in 5. Only 86415 ends in 5.

Answer: (A) 86415

Concept: Turn mixed fractions into decimals: $1\frac{4}{5}=1.8$ and $1\frac{1}{4}=1.25$.

1. $(1\frac{4}{5}+3.2)-1\frac{1}{4}=(1.8+3.2)-1.25$.
2. Bracket = 5.
3. $5-1.25=3.75$.

Trick: Learn $\frac{1}{5}=0.2$ and $\frac{1}{4}=0.25$ — such sums then become one-line mental work.

Answer: (A) 3.75

Concept: $\frac{1}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a}+\sqrt{b}}{a-b}$; here every $a-b=1$.

1. Terms: $\frac{1}{4-\sqrt{15}},\frac{1}{\sqrt{15}-\sqrt{14}},\dots ,\frac{1}{\sqrt{10}-3}$ with alternating signs.
2. They become $(4+\sqrt{15})-(\sqrt{15}+\sqrt{14})+(\sqrt{14}+\sqrt{13})-\dots +(\sqrt{10}+3)$.
3. Each surd appears once with + and once with −, so all cancel: $x=4+3=7$.
4. $x+1=8$.

Trick: In such alternating chains only the first and last rational parts survive: $x=4+3$.

Answer: (A) 8

Concept: Total in a set = only that set + both.

1. Cricket = 55 (only) + 35 (both) = 90.
2. Badminton = 45 (only) + 35 (both) = 80.
3. 90 : 80 = 9 : 8. (Check: 35 + 55 + 45 + 25 = 160 ✓)

Trick: The 'both' group is common, so compare only-groups: 55 vs 45 → Cricket is larger by 10 → 90 : 80.

Answer: (C) 9 : 8

Concept: Profit share $\propto$ capital $\times$ time (in ₹ thousand for ease).

1. Komal: $120\times 6+(120-40)\times 6=720+480=1200$.
2. Koyal: $80\times 6+(80+40)\times 6=480+720=1200$.
3. Ratio = 1200 : 1200 = 1 : 1.

Trick: Both have the same two amounts (120 and 80) for 6 months each, just in reverse order — so the shares must be equal.

Answer: (A) 1 : 1

Concept: First remove the fee, then split the rest in the capital ratio.

1. Fee to Ankit = 25% of ₹80,000 = ₹20,000; balance ₹60,000.
2. Capital ratio 20 : 30 = 2 : 3 → Ankit gets $\frac{2}{5}\times 60,000$ = ₹24,000.
3. Ankit's total = $20,000+24,000$ = ₹44,000.

Trick: Ankit's share as a fraction of profit = $\frac{1}{4}+(\frac{3}{4}\times \frac{2}{5})=\frac{11}{20}$; $\frac{11}{20}\times 80,000$ = ₹44,000.

Answer: (B) ₹44,000

Concept: New score − new average = extra runs that lift every innings.

1. Next innings 144 is 72 above the new average 72.
2. These 72 extra runs raised each of the earlier n innings by $72-66=6$.
3. $n=72÷6=12$.

Trick: n = (new score − new avg) ÷ (rise in avg) $=(144-72)÷6=12$.

Answer: (B) 12

Concept: Sum = average × count; subtract known group sums from the total.

1. Sum of all 15 = $15\times 80=1200$.
2. First 6: $6\times 70=420$; next 6 average = $70\times 1.2=84$ → $6\times 84=504$.
3. Last 3 sum = $1200-924=276$ → average $276÷3=92$.

Trick: Deviation method from 80: first six −60, next six +24 → net −36, so last three need +36 → each +12 → 92.

Answer: (C) 92

Concept: Work backward through each percentage stage.

1. Winner's 16,200 = 60% of valid → valid votes = 27,000.
2. Valid = 90% of votes cast → cast = 30,000.
3. Cast = 80% of eligible → eligible = 37,500.

Trick: One line: $E\times 0.8\times 0.9\times 0.6=16,200$ → $E=16,200÷0.432=37,500$.

Answer: (C) 37,500

Concept: For $1\frac{1}{2}$ years compounded yearly: full rate for 1 year, half the rate for the extra half-year.

1. Amount factor = $1.12\times 1.06=1.1872$.
2. $\text{CI}=0.1872\times P=1872$.
3. $P=1872÷0.1872$ = ₹10,000.

Trick: The CI 1872 matches the digits of 18.72% — so P = ₹10,000 at once.

Answer: (A) ₹10,000