Q&A: practice questions with answers

Concept: Kudremukh (Chikkamagaluru, Karnataka) in the Western Ghats is an iron-ore belt.

1. It has large magnetite iron-ore deposits, mined by KIOCL.
2. Ore slurry was sent by pipeline to Mangaluru port for export.
3. Mining stopped in 2005 to protect Kudremukh National Park.

Yaad rakhein: Other Karnataka iron-ore areas: Bellary–Hospet and Bababudan Hills.

Answer: (B) Iron ore

Concept: Article 279A(9): every decision needs at least three-fourths of the weighted votes present and voting.

1. Centre's vote = one-third (1/3) of total votes cast.
2. All States together = two-thirds (2/3).
3. 2/3 is twice 1/3 → States collectively have twice the Centre's weight.

Yaad rakhein: Neither side alone reaches 3/4: Centre (33%) has a veto, and States need the Centre to pass anything.

Answer: (D) The States collectively have twice the voting weight of the Centre in the GST Council.

Concept: An ideal gas assumes tiny, non-interacting molecules.

1. Volume of molecules is negligible compared to the container → 1 correct.
2. Collisions are perfectly elastic (no loss of kinetic energy) → 2 correct.
3. No intermolecular attraction exists in an ideal gas → 3 wrong.

Yaad rakhein: Real gases behave nearly ideal at high temperature and low pressure.

Answer: (A) 1 and 2 only

Concept: Default (statutory) bail arises when the investigation is not completed within the legal time limit.

1. Under Section 187 BNSS (old Sec 167 CrPC), the Magistrate authorises detention up to 60 or 90 days.
2. Once that limit passes without a charge-sheet, the accused (if ready to furnish bail) gets an indefeasible right to release, granted by the Magistrate.

Yaad rakhein: BNSS replaced the CrPC from 1 July 2024, along with BNS (for IPC) and BSA (for Evidence Act).

Answer: (B) Magistrate

Concept: Group schemes by the sector they mainly serve.

1. NSWS (National Single Window System), PM Gati Shakti and LEADS (logistics ease index) all target industry, infrastructure and logistics.
2. PMFBY (Pradhan Mantri Fasal Bima Yojana, 2016) is crop insurance for farmers → agriculture, the odd one.

Yaad rakhein: PMFBY farmer premium: 2% for Kharif, 1.5% for Rabi, 5% for commercial/horticultural crops.

Answer: (B) PMFBY

Concept: Ghoomar is a women's folk dance of Rajasthan known for its graceful twirls.

1. In 2013 it was placed among the world's top local dances in an international travel listing.
2. Dancers in long flowing ghagras spin in circles; it began with the Bhil community and was adopted by Rajput royals.

Yaad rakhein: Ghoomar is performed on occasions like Teej, Gangaur and weddings.

Answer: (C) 2013

Concept: Citizenship-by-investment ("golden passport") and residency-by-investment ("golden visa") schemes sell legal status for investment.

1. Transparency International's concern: weak background checks let corrupt people and money launderers buy residency or citizenship.
2. This gives them EU-wide travel rights and a safe haven for illicit money.

Yaad rakhein: Transparency International publishes the Corruption Perceptions Index (CPI); it is headquartered in Berlin.

Answer: (C) They allow corrupt individuals to misuse residency or citizenship schemes for personal benefit

Concept: Swachh Vayu Survekshan ranks NCAP cities on steps taken to improve air quality.

1. In the 2024 edition, Indore ranked first among cities with population above 10 lakh.
2. The survey is conducted by the Ministry of Environment, Forest and Climate Change under the National Clean Air Programme (NCAP, 2019).

Yaad rakhein: Indore has also topped the cleanliness survey (Swachh Survekshan) many years in a row.

Answer: (C) Indore

Concept: Lagrangian points are positions where a small body stays balanced relative to the Sun and Earth.

1. Aditya-L1 is in a halo orbit around Sun–Earth L1, about 1.5 million km from Earth.
2. From L1 the Sun is seen continuously without eclipse or occultation.
3. Polar, sun-synchronous and geostationary are Earth orbits, not stable points.

Yaad rakhein: Aditya-L1 was launched on 2 September 2023 by PSLV-C57 and reached L1 on 6 January 2024.

Answer: (A) Lagrangian

Concept: Check each statement against the Constitution and the Supreme Court's view.

1. Supreme Court (Mohit Minerals, 2022): GST Council recommendations are persuasive, not binding → Statement 1 incorrect.
2. Article 246A(1) lets Parliament and every State Legislature legislate on GST; States therefore can tax supplies within their own territory → Statement 2 incorrect.

Yaad rakhein: Inter-state supply is taxed only by Parliament (IGST) under Art. 246A(2); GST came via the 101st Amendment (2016).

Answer: (C) Both 1 and 2

Concept: $(a+b{)}^2=a^2+b^2+2ab$.

1. $(\sqrt{5}+3{)}^2=(\sqrt{5}{)}^2+3^2+2\times \sqrt{5}\times 3$
2. $=5+9+6\sqrt{5}=14+6\sqrt{5}$
3. Compare with $?+6\sqrt{5}\to ?=14$

Trick: The rational part = sum of squares only: $5+9=14$; the 2ab term is the √ part.

Answer: (D) 14

Concept: Find each square root, subtract, then multiply by $\frac{1}{2}$.

1. $\sqrt{7396}=86$ (${86}^2=7396$)
2. $\sqrt{1156}=34$ (${34}^2=1156$)
3. $(86-34)\times \frac{1}{2}=52\times \frac{1}{2}=26$

Trick: 7396 ends in 6 → root ends in 4 or 6; ${85}^2=7225$, so root is 86.

Answer: (C) 26

Concept: Convert percentages to a simple equation and solve for $\frac{A}{B}$.

1. Divide both sides by 20%: $(A+B)=3\times (A-B)$.
2. Opening the bracket: $2A=4B$.
3. So A is twice B → 2 : 1.

Trick: Use componendo-dividendo: $\frac{A+B}{A-B}=\frac{3}{1}\to A:B=(3+1):(3-1)=4:2=2:1$.

Answer: (B) 2 : 1

Concept: Value of each type = number of coins × coin value.

1. Coins: 2x, 3x, 5x
2. Value: 5(2x) + 2(3x) + 1(5x) = 21x
3. 21x = 252 → x = 12
4. Coins: 24 of ₹5, 36 of ₹2, 60 of ₹1

Trick: Option check: (C) gives 120 + 72 + 60 = ₹252 ✓.

Answer: (C) 24 coins of ₹5, 36 of ₹2, and 60 of ₹1

Concept: $\text{SP}=\text{MP}\times \frac{100-d}{100}$ and $\text{CP}=\text{SP}\times \frac{100}{100+\text{profit}\%}$.

1. $\text{SP}=800\times \frac{85}{100}=$ ₹680
2. $\text{CP}=680\times \frac{100}{120}=680\times \frac{5}{6}$
3. CP = ₹566.67

Trick: $\text{MP}:\text{CP}=(100+P\%):(100-D\%)=120:85\to \text{CP}=800\times \frac{85}{120}=$ ₹566.67.

Answer: (C) ₹566.67

Concept: Find CP from profit, then MP from the first discount, then apply the new discount.

1. 8% of CP = ₹224 → CP = ₹2800; SP = ₹3024
2. SP = 80% of MP → $\text{MP}=3024\times \frac{100}{80}=$ ₹3780
3. $33.33\%=\frac{1}{3}$ discount → new SP = $3780\times \frac{2}{3}=$ ₹2520

Trick: Directly: new SP = old $\text{SP}\times \frac{\frac{2}{3}}{\frac{4}{5}}=3024\times \frac{5}{6}=$ ₹2520.

Answer: (C) ₹2520.00

Concept: For $a{x}^3+b{x}^2+cx+d=0$, sum of roots = $-\frac{b}{a}$.

1. Here $a=1,b=-8$.
2. $x+y+z=-\frac{-8}{1}=8$

Trick: Sum of roots = negative of the $a^2$ coefficient when the leading coefficient is 1; product = $-\frac{d}{a}=4$.

Answer: (D) 8

Concept: For dated loans, count days (exclude the first day, include the last) and use $\text{time}=\frac{\text{days}}{365}$.

1. Days: Mar 16 + Apr 30 + May 31 + Jun 30 + Jul 31 + Aug 31 + Sep 15 = 184
2. $\text{SI}=\frac{6000\times 12\times 184}{100\times 365}=\frac{720\times 184}{365}\approx$ ₹362.96
3. Amount = $6000+362.96=$ ₹6362.96

Trick: 6 months would give ₹360; 184 days is a little more than half a year, so SI is just above 360 → only ₹6362.96 fits.

Answer: (B) ₹6362.96

Concept: For equal SI over the same time, $\text{principal}\propto \frac{1}{\text{rate}}$.

1. $P_1:P_2:P_3=\frac{1}{4}:\frac{1}{5}:\frac{1}{10}=5:4:2$ (LCM 20)
2. Total 11 parts = ₹4400 → 1 part = ₹400
3. 5% scheme = 4 parts = ₹1600

Trick: Check: 4% of 2000 = 5% of 1600 = 10% of 800 = ₹80 each ✓.

Answer: (B) ₹1600

Concept: Horizontal distance = height ÷ tan(angle of depression).

1. 45°: distance = $\frac{150}{\tan {45}^{\circ }}=150$ m
2. 60°: distance = $\frac{150}{\tan {60}^{\circ }}=\frac{150}{\sqrt{3}}$ m
3. Gap = $150-\frac{150}{\sqrt{3}}=150(1-\frac{1}{\sqrt{3}})$ m

Trick: Larger angle = nearer car; gap = $h(\cot {45}^{\circ }-\cot {60}^{\circ })$.

Answer: (C) 150(1 − $\frac{1}{\sqrt{3}}$) m