Q&A: practice questions with answers

Concept: Surface area of sphere $=4\pi r^2$.

1. $4\times \frac{22}{7}\times r^2=528$.
2. $r^2=\frac{528\times 7}{88}=42\Rightarrow r=\sqrt{42}\text{cm}$.

Trick: $\frac{528}{88}=6$, then $6\times 7=42$.

Answer: (B) $\sqrt{42}\text{cm}$

Concept: A diameter perpendicular to a chord bisects it; also $PC·CQ=AC·CB$.

1. $AB=14$, $AC:BC=4:3\Rightarrow AC=8$, $BC=6$.
2. $P{C}^2=AC\times CB=48\Rightarrow PC=4\sqrt{3}$.
3. $PQ=2\times 4\sqrt{3}=8\sqrt{3}\text{cm}$.

Trick: Intersecting chords: $PC·CQ=AC·CB$ with $PC=CQ$.

Answer: (D) $8\sqrt{3}$

Concept: Average speed $=\frac{\text{Total distance}}{\text{Total time}}$.

1. Times: $\frac{1200}{80}=15$, $\frac{1600}{40}=40$, $\frac{1000}{400}=2.5$, $\frac{200}{50}=4$; total $=61.5$ h.
2. Distance $=4000$ km.
3. Average $=\frac{4000}{61.5}=65.04\text{km/h}$.

Trick: The slow ship leg (40 h) dominates, pulling the average down.

Answer: (A) $65.04\text{km/h}$

Concept: Brackets first, then divide.

1. $9\times 81=729$, $142÷2=71$ → $800$.
2. $800+350-155+5=1000$.
3. $(25\times 25)-125=500$; $1000÷500=2$.

Trick: Numerator $=1000$, denominator $=500$ – neat round numbers.

Answer: (D) $2$

Concept: Required $\%=\frac{\text{Total}-\text{Pop}}{\text{Total}}\times 100$ for age 31-50.

1. Total $=62$, Pop $=16$ → others $=46$.
2. $\frac{46}{62}\times 100=74.19\%$.

Trick: $\frac{23}{31}\approx 0.742$.

Answer: (C) 74.19%

Concept: Total work = LCM$(21,28,15)=420$ units.

1. Efficiencies: Manish $20$, Nakul $15$, Pintoo $28$ units/day.
2. First 5 days (M + P): $5\times 48=240$; left $=180$.
3. All three: $63$/day → $\frac{180}{63}=\frac{20}{7}=2\frac{6}{7}$ days.

Trick: Nakul works only for the remaining part – divide remainder by combined rate.

Answer: (B) $2\frac{6}{7}$

Concept: $\tan \theta ·\cot \theta =1$, so $(\tan \theta +\cot \theta {)}^2={\tan }^2\theta +{\cot }^2\theta +2$.

1. $6^2=36={\tan }^2\theta +{\cot }^2\theta +2$.
2. ${\tan }^2\theta +{\cot }^2\theta =34$.

Trick: If $x+\frac{1}{x}=k$ then $x^2+\frac{1}{x^2}=k^2-2$.

Answer: (C) $34$

Concept: $|a-b|<x<a+b$.

1. $12-7<x<12+7\Rightarrow 5<x<19$.
2. Integers: $6,7,\dots ,18$ → $18-6+1=13$ values.

Yaad rakhein: Count $=(a+b)-(a-b)-1=2b-1=2\times 7-1=13$ (b = smaller side).

Answer: (A) $13$

Concept: Net change $=a+b+\frac{ab}{100}$ (decrease negative).

1. $a=-3.125$, $b=+7.4$.
2. $-3.125+7.4-\frac{3.125\times 7.4}{100}=4.275-0.23125=4.04375$.
3. ≈ $4.04\%$ more.

Trick: Multiplier: $0.96875\times 1.074=1.0404$.

Answer: (B) 4.04% more

Concept: Final SP $=$ tag price after discount $-$ cashback $=$ CP $\times 1.1$.

1. SP $=1200\times 1.1=₹1320$.
2. $0.9T-250=1320\Rightarrow 0.9T=1570$.
3. $T=\frac{1570}{0.9}=₹1744.44$.

Trick: Add the cashback back before dividing by $0.9$.

Answer: (C) 1744.44

Concept: When an adjective ending in -ous becomes a noun, the 'u' is often dropped: generous → generosity.

1. The correct spelling is Generosity (no 'u' after 'o').
2. 'feature', 'godly' and 'individuals' are all spelt correctly.
3. Correct sentence: Generosity is a godly feature among many individuals on the earth.

Trick: Similar pattern: curious → curiosity, generous → generosity, famous → fame. The '-ous' + '-ity' combination becomes '-osity'.

Answer: (A) Generousity

Concept: Suspect (verb/noun) means to doubt someone's honesty or motives; as a noun it can mean a look or examination with doubt.

1. The definition stresses doubt about motives → suspect.
2. Introspect = examine one's own thoughts (no doubt involved).
3. Circumspect = cautious; Retrospect = looking back at the past.

Trick: Sus-pect = 'look from under' with doubt; intro- = inside, retro- = back, circum- = around.

Answer: (B) Suspect

Concept: Effervescent literally means bubbly (like soda); figuratively it describes a person who is vivacious and enthusiastic.

1. Vivacious + enthusiastic = lively and bubbly → effervescent.
2. Introverted = shy, reserved (opposite idea).
3. Rowdy = noisy and disorderly; Brazen = shameless, bold.

Trick: Think of a fizzing soft drink – full of bubbles and energy = effervescent person.

Answer: (B) Effervescent

Concept: Symphony (Greek syn = together + phone = sound) means a harmonious combination or consonance of sounds.

1. 'Consonance of sounds' = sounds agreeing together → symphony.
2. Troupe = a group of performers.
3. Woodwinds = a family of instruments; Orchestration = arranging music for an orchestra.

Trick: syn/sym = together, phone = sound (telephone, microphone) → symphony = sounds together.

Answer: (D) Symphony

Concept: Bonsai is the Japanese art of growing artificially dwarfed trees and shrubs in pots.

1. Dwarfed trees in pots → bonsai.
2. Bonafide = genuine; Orchard = a piece of land with fruit trees.
3. Botanical = related to plants in general.

Trick: Bon-sai = 'tray planting' in Japanese – a tree in a tray/pot.

Answer: (D) Bonsai

Concept: With the noun level (rank or tier in a hierarchy), the fixed preposition is at: at all levels, at the national level.

1. Correct: …to various government departments at all levels…
2. 'through', 'from' and 'in all levels' are not idiomatic for a position in a hierarchy.
3. The sentence also uses 'at the Centre', parallel to 'at all levels'.

Trick: at + level/stage/point: at all levels, at this stage, at that point.

Answer: (D) various government departments at all levels

Concept: Tighten one's belt = to spend less money because there is less available.

1. 'had to reduce spending' + 'frugal lifestyle' → tighten his belt.
2. Hit the nail on the head = say exactly the right thing.
3. Let the cat out of the bag = reveal a secret; kick the bucket = die.

Trick: Less food/money → tighter belt. Spending cut = belt tightened.

Answer: (A) tighten his belt

Concept: Black sheep = a member of a family or group who is regarded as a disgrace; i.e. disreputable.

1. The idiom describes someone with a bad reputation within a group → disreputable.
2. Miscreant (wrongdoer) is close but too strong; the idiom is about bringing shame, not committing crime.
3. Naive and Intelligent are unrelated.

Trick: 'Black sheep of the family' = the one who brings disgrace (bad name) to the family.

Answer: (C) Disreputable

Concept: In a time clause (when, before, after, until, as soon as) referring to the future, we use the simple present, not 'will'.

1. Main clause already has future: 'I will make sure'.
2. So the time clause should be: When my father comes.
3. The other parts are correct.

Trick: When/if/until clause → no 'will'. 'When he comes, I will…'

Answer: (C) When my father will come

Concept: The verb phrase is place trust in someone; after a preposition the object form of the relative pronoun, whom, is used.

1. 'has placed its trust in whom' → 'in whom the ruling government has placed its trust' – correct.
2. 'who' is a subject form, so 'in who', 'with who', 'on who' are wrong.
3. Also 'trust in' (not 'with/on') is the correct collocation.

Trick: Preposition + whom (never preposition + who).

Answer: (A) No substitution