Q&A: practice questions with answers

Concept: The International Criminal Court (ICC), The Hague, was set up under the Rome Statute (2002).

1. Judge Tomoko Akane of Japan was elected ICC President in March 2024 – the first Japanese to hold the post.
2. Piotr Hofmański was the previous President; Karim A.A. Khan is the Prosecutor, not a judge-President.

Yaad rakhein: ICC: President – Tomoko Akane; Prosecutor – Karim Khan.

Answer: (A) Judge Tomoko Akane

Concept: The Citizenship Act, 1955 gives five ways: birth, descent, registration, naturalisation and incorporation of territory.

1. A foreigner (not of Indian origin) can apply for naturalisation after ordinarily residing in India for 12 years (11 of the last 14 years plus the last 12 months).
2. Registration is mainly for persons of Indian origin or spouses of Indian citizens; birth and descent do not apply to a foreigner.

Yaad rakhein: Foreigner + 12 years' residence = Naturalisation.

Answer: (B) By naturalisation

Concept: In Unix/Linux, touch updates a file's timestamps and creates an empty file if it does not exist.

1. Example: touch notes.txt creates an empty notes.txt.
2. mkdir creates a directory, cp copies files; mkfile exists only on some systems (e.g. Solaris/macOS) and creates a file of a given size.

Yaad rakhein: touch = new empty file; mkdir = new folder.

Answer: (C) touch

Concept: Volume of a hemisphere $=\frac{2}{3}\pi r^3$.

1. $r=33.6\text{cm}$, so $r^3={33.6}^3=37933.056$.
2. $V=\frac{2}{3}\times 37933.056\pi =25288.704\pi$.
3. Rounded: $25288.70\pi {\text{cm}}^3$.

Trick: $33.6=\frac{168}{5}$; only the last option ends near $\mathrm{.70}$, matching $\frac{2}{3}\times \dots 056$ — quick check by last digits.

Answer: (C) $25288.70\pi$

Concept: Rent takes 12%, so everything else is 88% of salary.

1. Other amounts: $407+8657+924=9988$.
2. $88\%$ of salary $=9988$.
3. Salary $=\frac{9988\times 100}{88}=11350$.

Trick: $\frac{9988}{88}=113.5$ → salary ₹11,350.

Answer: (A) ₹11,350

Concept: $\frac{a^m}{a^n}=a^{m-n}$.

1. $\frac{{31}^{10}}{{31}^9}=31$, $\frac{2^{15}}{2^{14}}=2$, $\frac{{84}^6}{{84}^5}=84$.
2. Value $=31\times 2\times 84$.
3. $=62\times 84=5208$.

Trick: Each power drops by exactly 1 → just multiply the bases: $31\times 2\times 84$.

Answer: (B) 5208

Concept: New salary = old salary × (1 + increase%).

1. X: $10\times 1.82=18.2$.
2. Y: $20\times 1.50=30$.
3. Z: $20\times 1.19=23.8$.
4. Ratio $=18.2:30:23.8=182:300:238=91:150:119$.

Trick: Old ratio $1:2:2$ → new $182:300:238$; divide by 2.

Answer: (B) $91:150:119$

Concept: $(a+b{)}^3=a^3+3a^{2}b+3a{b}^2+b^3$.

1. $216x^3=(6x{)}^3$ and $27y^3=(3y{)}^3$ → $a=6x$, $b=3y$.
2. $3a^{2}b=3\times 36x^2\times 3y=324x^{2}y$ ✓.
3. $3a{b}^2=3\times 6x\times 9y^2=162x{y}^2$ ✓.
4. So the expression $=(6x+3y{)}^3$.

Trick: Take cube roots of the first and last terms: $\sqrt[3]{216}=6$, $\sqrt[3]{27}=3$.

Answer: (A) $(6x+3y{)}^3$

Concept: $\sec \theta -\tan \theta =\frac{1-\sin \theta }{\cos \theta }$ and $(1-\sin \theta )(1+\sin \theta )={\cos }^2\theta$.

1. $(\sec \theta -\tan \theta )(1+\sin \theta )=\frac{(1-\sin \theta )(1+\sin \theta )}{\cos \theta }=\frac{{\cos }^2\theta }{\cos \theta }=\cos \theta$.
2. Squaring: $(\sec \theta -\tan \theta {)}^2(1+\sin \theta {)}^2={\cos }^2\theta$.
3. Divide by ${\cos }^2\theta$: value $=1$.

Trick: Put $\theta =0^{\circ }$: $(1-0{)}^2(1+0{)}^2÷1=1$.

Answer: (D) 1

Concept: Assume all 45 kg were apples, then adjust for the extra price of mangoes.

1. If all were apples: $45\times 25=1125$.
2. Extra paid $=1240-1125=115$; each kg of mango costs ₹5 more.
3. Mangoes $=\frac{115}{5}=23\text{kg}$ (apples 22 kg).
4. Spent on mangoes $=23\times 30=690$.

Trick: Check: $22\times 25+690=550+690=1240$ ✓.

Answer: (C) ₹690

Concept: Take the third number as 100.

1. First number $=100+46=146$.
2. Second number $=100+54=154$.
3. Ratio $=146:154=73:77$.

Trick: Divide both by 2 directly.

Answer: (A) $73:77$

Concept: Opposite directions: relative speed = sum of speeds; distance covered = sum of lengths.

1. Relative speed $=72+63=135\text{km/h}=135\times \frac{5}{18}=37.5\text{m/s}$.
2. $L_A+L_B=37.5\times 24=900\text{m}$; with $L_B=1.5L_A$: $2.5L_A=900$, so $L_A=360$, $L_B=540\text{m}$.
3. B's speed $=63\times \frac{5}{18}=17.5\text{m/s}$; in 62 s it covers $17.5\times 62=1085\text{m}$.
4. Bridge $=1085-540=545\text{m}$.

Trick: Crossing a bridge: distance = train length + bridge length.

Answer: (D) 545

Concept: $\text{SP}=\text{CP}\times \frac{100-\text{loss}\%}{100}$.

1. $950=\text{CP}\times 0.95$ → $\text{CP}=1000$.
2. New SP $=1350$ → gain $=350$.
3. Gain% $=\frac{350}{1000}\times 100=35\%$.

Trick: 95% = 950 means 100% = 1000 instantly.

Answer: (B) 35

Concept: If 80% is spent, 20% is saved.

1. $20\%$ of income $=6738$ → income $=6738\times 5=33690$.
2. Expenses $=80\%=6738\times 4=26952$.

Trick: Expenses : savings $=80:20=4:1$ → expenses $=4\times 6738$.

Answer: (B) 26,952

Concept: Empirical formula: $\text{Mode}=3\text{Median}-2\text{Mean}$, i.e. $\text{Mode}-\text{Mean}=3(\text{Median}-\text{Mean})$.

1. $12.6=3(\text{Median}-\text{Mean})$ → $\text{Median}-\text{Mean}=4.2$.
2. $\text{Mode}-\text{Median}=12.6-4.2=8.4$.

Trick: Mode–Median is always $\frac{2}{3}$ of Mode–Mean: $\frac{2}{3}\times 12.6=8.4$.

Answer: (D) 8.4

Concept: Sum = average × number of items.

1. Sum of 9 numbers $=9\times 17=153$.
2. Sum of 7 numbers $=7\times 16=112$.
3. Remaining two $=153-112=41$; average $=\frac{41}{2}=20.5$.

Trick: Each of the 7 is 1 below 17 → deficit 7, shared by 2: $17+\frac{7}{2}=20.5$.

Answer: (B) 20.5

Concept: Bracket first, then multiplication, then addition.

1. $74+30=104$.
2. $\frac{88}{9}\times 104=\frac{9152}{9}$.
3. $\frac{9152}{9}+37=\frac{9152+333}{9}=\frac{9485}{9}$.

Trick: Answer must exceed $\frac{88}{9}\times 100\approx 978$ → only $\frac{9485}{9}\approx 1054$ fits.

Answer: (C) $\frac{9485}{9}$

Concept: Take total work = LCM of the days; find one-day work of each and count 2-day cycles.

1. Total work $=\text{LCM}(18,22)=198$ units. A $=\frac{198}{18}=11$ units/day, B $=\frac{198}{22}=9$ units/day.
2. One cycle (B then A) = 2 days = $9+11=20$ units. 9 cycles = 18 days = $180$ units; left $=18$ units.
3. Day 19 (B): $9$ units, left $9$. Day 20 (A): $\frac{9}{11}$ day.
4. Total $=19+\frac{9}{11}=19\frac{9}{11}$ days.

Trick: Do full cycles first, then let the starter work, then finish the remainder by the next person's fraction of a day.

Answer: (D) $19\frac{9}{11}$

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

1. SI $=2700-1440=₹1260$.
2. $1260=\frac{1440\times 10\times T}{100}=144T$.
3. $T=\frac{1260}{144}=8.75$ years.

Trick: 10% of 1440 = 144 per year; $\frac{1260}{144}=8.75$.

Answer: (D) $8.75$

Concept: $\text{SP}=\text{CP}\times \frac{100+\text{markup}\%}{100}\times \frac{100-\text{discount}\%}{100}$

1. MP $=1.5\text{CP}$; SP $=1.5\times 0.74\text{CP}=1.11\text{CP}$.
2. $1.11\text{CP}=86580$.
3. CP $=\frac{86580}{1.11}=₹78000$.

Trick: Net effect of +50% and −26%: 50 − 26 − 13 = +11% ⇒ SP = 111% of CP.

Answer: (D) 78,000