Q&A: practice questions with answers

Concept: Lothal, on the Bhogavo river in Gujarat, is famous for the world's earliest known dockyard.

1. The brick dock linked Lothal to the Gulf of Khambhat (Cambay), supporting sea trade with Mesopotamia and the Persian Gulf.
2. Persian Gulf seals and bead-making workshops found there confirm its role as a port town.

Yaad rakhein: Lothal = Dockyard = Maritime trade.

Answer: (A) maritime trade

Concept: The Indian Councils Act 1892 was a response to Congress demands for more Indian participation.

1. It increased the number of non-official (Indian) members in the Imperial and provincial Legislative Councils, chosen through an indirect nomination/recommendation method.
2. Members could discuss the budget and ask questions.
3. Separate electorates for Muslims came in 1909; direct elections in 1919; provincial autonomy in 1935.

Yaad rakhein: 1892 = indirect election + budget discussion; 1909 = separate electorate.

Answer: (B) Provision for Indian representation in the Imperial Legislative Council

Concept: Archery World Cup 2025 Stage 1 was held in Auburndale, Florida (USA) in April 2025.

1. Dhiraj Bommadevara won the bronze medal in the men's individual recurve event.
2. India also won medals in compound events at the same stage.

Yaad rakhein: Dhiraj Bommadevara – Andhra Pradesh recurve archer, Olympic team member 2024.

Answer: (C) Dhiraj Bommadevara

Concept: Mendeleev arranged elements by atomic mass and grouped them by similar properties and formulae of oxides/hydrides.

1. Iodine is a halogen like F, Cl and Br.
2. Halogens were placed in Group VII of Mendeleev's table (oxide formula ${\text{R}}_2{\text{O}}_7$, hydride HR).
3. Group VIII held Fe, Co, Ni etc. (noble gases were added later as Group 0).

Yaad rakhein: Famous anomaly: Te (127.6) placed before I (126.9) so that iodine stays with halogens in Group VII.

Answer: (B) Group VII

Concept: Article 15 prohibits discrimination on grounds of religion, race, caste, sex or place of birth.

1. Article 15(2) bars restrictions on access to shops, restaurants, hotels and places of public entertainment, and on use of wells, tanks, bathing ghats, roads and public resorts.
2. Art. 16 = equality in public employment; Art. 17 = abolition of untouchability; Art. 18 = abolition of titles.

Yaad rakhein: Art. 14 to 18 = Right to Equality; 15 = no discrimination in public places.

Answer: (A) Article 15

Concept: Form two linear equations in A and B and solve by substitution.

1. $5A+B=95$ and $A+2.2B=63$.
2. From the second: $A=63-2.2B$.
3. $5(63-2.2B)+B=95\Rightarrow 315-11B+B=95\Rightarrow 10B=220$.
4. $B=22$ (and $A=14.6$).

Trick: Check options quickly: $B=22\Rightarrow A=63-48.4=14.6$, and $5\times 14.6+22=95$ ✓.

Answer: (A) 22

Concept: Net filling rate = filling rate − emptying rate.

1. Filling tap: $\frac{1}{14}$ tank per hour; emptying tap: $\frac{1}{18}$ tank per hour.
2. Net: $\frac{1}{14}-\frac{1}{18}=\frac{9-7}{126}=\frac{2}{126}=\frac{1}{63}$.
3. Time to fill $=63$ hours.

Trick: Two-pipe shortcut: $T=\frac{a\times b}{b-a}=\frac{14\times 18}{18-14}=\frac{252}{4}=63$.

Answer: (A) 63

Concept: Take total work = LCM of days; work in 2-day cycles, then finish the remainder.

1. Total work = LCM(24, 28) = 168 units; A = 7 units/day, B = 6 units/day.
2. One cycle (B then A) = 2 days = 13 units. $12$ cycles = 24 days → $156$ units.
3. Left: $12$ units. Day 25 (B): $6$ units → left $6$.
4. Day 26 (A): $\frac{6}{7}$ day.
5. Total $=25+\frac{6}{7}=25\frac{6}{7}$ days.

Trick: Never stop at $\frac{168}{13}$ — always finish the last part day by day with the correct person.

Answer: (A) $25\frac{6}{7}$

Concept: ${\sigma }^2=\frac{\sum x^2}{n}-{\overline{x}}^2$.

1. $9=\frac{\sum x^2}{100}-{50}^2$.
2. $\frac{\sum x^2}{100}=2500+9=2509$.
3. $\sum x^2=250900$, i.e. 2,50,900.

Trick: Sum of squares $=n({\sigma }^2+{\overline{x}}^2)=100(9+2500)$.

Answer: (D) 2,50,900

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

1. $SI=\frac{1380\times 3\times 3}{100}=124.2$.
2. Amount $=1380+124.2=1504.2$.

Trick: Total rate $=3\times 3=9\%$; amount $=1380\times 1.09=1504.2$. Option (A) is only the interest.

Answer: (B) ₹1,504.2

Concept: Half-yearly: rate halves, periods double.

1. Rate $=\frac{18}{2}=9\%$ per half-year; periods $=2$.
2. $A=60000\times (1.09{)}^2=60000\times 1.1881$.
3. $A=71286$.

Trick: $9\%$ twice $=9+9+\frac{9\times 9}{100}=18.81\%$; $18.81\%$ of 60000 = 11286.

Answer: (B) ₹71,286

Concept: In $a:b::b:x$, $x$ is the third proportional: $x=\frac{b^2}{a}$.

1. $x=\frac{{3.7}^2}{7.4}=\frac{13.69}{7.4}$.
2. $x=1.85$.

Trick: Since $7.4=2\times 3.7$, $x=\frac{3.7}{2}=1.85$.

Answer: (C) 1.85

Concept: "of" means multiplication; solve innermost bracket first.

1. $\frac{3}{5}\text{ of }\frac{5}{9}=\frac{3}{5}\times \frac{5}{9}=\frac{1}{3}$.
2. $7\times \frac{1}{3}=\frac{7}{3}$.
3. $25÷\frac{7}{3}=25\times \frac{3}{7}=\frac{75}{7}$.

Trick: Dividing by a fraction = multiplying by its reciprocal.

Answer: (D) $\frac{75}{7}$

Concept: Correct total = wrong total − wrong values + correct values.

1. Wrong total $=50\times 45=2250$.
2. Correction: $-35+25=-10$ and $-28+30=+2$; net $-8$.
3. Correct total $=2242$; average $=\frac{2242}{50}=44.84$.

Trick: Change in average $=\frac{-8}{50}=-0.16$; $45-0.16=44.84$.

Answer: (D) 44.84

Concept: Expenditure = $100\%-$ savings%.

1. Expenditure $=55\%$ of 2580.
2. $\frac{55}{100}\times 2580=1419$.

Trick: $10\%=258$, $5\%=129$ → $55\%=5\times 258+129=1419$.

Answer: (D) ₹1,419

Concept: $SP=CP\times (1+\text{markup})\times (1-\text{discount})$.

1. $SP=CP\times 1.64\times 0.5=0.82CP$.
2. $0.82CP=59860$.
3. $CP=\frac{59860}{0.82}=73000$.

Trick: Only the round option 73,000 gives $0.82\times 73000=59860$.

Answer: (D) 73,000

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

1. $(a-b{)}^2=83-12=71$; since $a>b$, $a-b=\sqrt{71}$.
2. $(a+b{)}^2=83+12=95$, so $a+b=\sqrt{95}$ (here $a,b$ are positive since $ab>0$).
3. $\frac{a-b}{a+b}=\frac{\sqrt{71}}{\sqrt{95}}=\sqrt{\frac{71}{95}}$.

Trick: ${\left(\frac{a-b}{a+b}\right)}^2=\frac{a^2+b^2-2ab}{a^2+b^2+2ab}$ — then take the root.

Answer: (B) $\sqrt{\frac{71}{95}}$

Concept: Sum = average × count.

1. Total of 8 numbers $=8\times 15=120$.
2. Total of 5 numbers $=5\times 18=90$.
3. Remaining 3: $\frac{120-90}{3}=10$.

Trick: Deviation method: 5 numbers are $+3$ each $=+15$, so other 3 are $-5$ each → $15-5=10$.

Answer: (D) 10

Concept: TSA of cube $=6a^2$, volume $=a^3$.

1. $6a^2=216\Rightarrow a^2=36\Rightarrow a=6$ cm.
2. Volume $=6^3=216{\text{cm}}^3$.

Trick: For a cube with side 6, TSA and volume are numerically equal (216).

Answer: (C) $216{\text{cm}}^3$

Concept: Write everything in powers of 2 and 7.

1. $8^2=64$, $7^3=343$; $\sqrt{64}=8$, $\sqrt{2401}=49$.
2. $\frac{64\times 343}{8\times 49}=\frac{64}{8}\times \frac{343}{49}$.
3. $=8\times 7=56$.

Trick: $2401=7^4$, so $\sqrt{2401}=7^2$; then $\frac{8^2}{8}\times \frac{7^3}{7^2}=8\times 7$.

Answer: (B) 56