Q&A: practice questions with answers

Concept: Opposite directions: speeds add; same direction: speeds subtract. ($1\text{km/h}=\frac{5}{18}\text{m/s}$)

1. $9\text{km/h}=2.5\text{m/s}$; $\frac{234}{6}=39=v+2.5\Rightarrow v=36.5\text{m/s}$.
2. $23.4\text{km/h}=6.5\text{m/s}$; relative $=36.5-6.5=30\text{m/s}$.
3. Time $=\frac{234}{30}=7.8$ s.

Trick: Work in m/s throughout to avoid conversions twice.

Answer: (A) 7.8

Concept: Boat speed $=\frac{D+U}{2}$, stream $=\frac{D-U}{2}$.

1. $\frac{33+27}{2}=30\text{km/h}$.

Yaad rakhein: Half the sum = boat, half the difference = stream (3).

Answer: (A) 30 km/h

Concept: Work in percentages of income directly.

1. Savings $25\%$ ⇒ expenditure $=75\%$.
2. Education $=\frac{2}{5}\times 75\%=30\%$ of income.

Trick: Income ₹40,000 is not needed – everything is a % of income.

Answer: (A) 30%

Concept: Area of sector $=\frac{\theta }{{360}^{\circ }}\times \pi r^2$.

1. $\frac{72}{360}=\frac{1}{5}$; $\pi r^2=\frac{22}{7}\times 1225=3850$.
2. Area $=\frac{3850}{5}=770{\text{cm}}^2$.

Trick: ${72}^{\circ }$ = one-fifth of the circle.

Answer: (A) $770{\text{cm}}^2$

Concept: Brackets first, then 'of', then ÷/× left to right, then −.

1. $[16÷8\times 4]=8$; $(14÷7\times 28)=56$.
2. $4\text{ of }6=24$; $27÷24=\frac{9}{8}$; $\frac{9}{8}\times 8=9$.
3. $9-56=-47$.

Yaad rakhein: 'of' before ÷: $27÷(4\text{ of }6)$.

Answer: (C) $-47$

Concept: Three lengths form a triangle only if the sum of the two smaller ones exceeds the largest.

1. (2, 5, 7): $7=7$ ✗; (2, 5, 8): $7<8$ ✗.
2. (2, 7, 8): $9>8$ ✓; (5, 7, 8): $12>8$ ✓.
3. Triangles possible $=2$.

Yaad rakhein: Equality (2 + 5 = 7) does not make a triangle.

Answer: (D) 2

Concept: ÷ and × left to right, then + and −.

1. $264÷8=33$; $32\times 2=64$.
2. $80÷5\times 40÷20=16\times 40÷20=32$.
3. $33-1-64+32=0$.

Yaad rakhein: Do ÷/× strictly from left to right.

Answer: (A) 0

Concept: Read both values from the 1985 column and reduce.

1. P (1985) $=20$, T (1985) $=40$.
2. $20:40=1:2$.

Trick: Read the correct column – the year matters.

Answer: (B) 1 : 2

Concept: SP $=\text{MP}\times \frac{100-d}{100}$.

1. $900\times 0.88=792$.

Trick: $12\%$ of $900=108$; $900-108=792$.

Answer: (D) 792

Concept: Work = efficiency × time.

1. Efficiency Sapna : Rakesh $=2:1$; together $=3$ units/day.
2. Total work $=3\times 48=144$ units.
3. Sapna alone $=\frac{144}{2}=72$ days.

Trick: Sapna's share of combined efficiency $=\frac{2}{3}$ ⇒ $48\times \frac{3}{2}=72$.

Answer: (B) 72

Concept: An antonym is a word with the opposite meaning. Diligent means hard-working, careful and persistent in effort.

1. The sentence praises the student's diligent work and consistent effort – a positive quality of hard work.
2. Opposite of hard-working = lazy (unwilling to work).
3. Persistent is a synonym; frazzle (to exhaust/fray) and squander (to waste) are not opposites of diligent.

Trick: Diligent ↔ Lazy; Diligent ≈ Industrious, Hard-working.

Answer: (C) lazy

Concept: A synonym has the same meaning. Strive means to make great efforts to achieve something.

1. "I will strive to win the race" = I will try hard to win.
2. Attempt (to try) carries this meaning.
3. Trouble, Support and Assume (to suppose) do not mean 'try hard'.

Trick: Strive = Try / Endeavour / Attempt / Struggle.

Answer: (D) Attempt

Concept: Pitiable means deserving pity; sad, miserable or wretched.

1. Pitiable describes a sorry, unhappy, distressing state.
2. The opposite quality is something agreeable and happy = Pleasant.
3. Grievous (serious, causing grief) is close to pitiable; Eradicate (remove completely) and Aggregate (total) are unrelated.

Trick: Pitiable = Miserable, Wretched ↔ Pleasant, Delightful.

Answer: (B) Pleasant

Concept: Efface means to erase, rub out or wipe away completely (e.g. a mark or memory).

1. To efface something is to remove it so that it no longer exists.
2. Among the options, Destroy (to put an end to / ruin completely) is closest.
3. Hidden means concealed (still existing); Makeup and Daily are unrelated (do not confuse 'face' inside efface with makeup).

Trick: Efface = Erase / Obliterate / Wipe out / Destroy.

Answer: (D) Destroy

Concept: Astonished means greatly surprised or amazed.

1. "I was astonished to know the truth" = I was shocked/greatly surprised.
2. Stunned means so surprised that one cannot react – same meaning.
3. Awesome describes a thing, not a feeling of a person; Blindsided means attacked unexpectedly; Sickened means disgusted.

Trick: Astonished = Amazed / Stunned / Astounded / Dumbfounded.

Answer: (A) Stunned

Concept: Jump at the opportunity/chance is a fixed idiom meaning to accept an opportunity eagerly and quickly.

1. The principal is leaving, so the speaker eagerly grabbed the chance to fill the job.
2. Played out means 'came to an end/happened' – wrong here.
3. Only jumped at the opportunity is the correct idiom; 'glided at', 'started at' and 'ran to' are not used with opportunity.

Trick: Jump at = seize eagerly. "She jumped at the offer."

Answer: (B) jumped at the opportunity

Concept: Phrasal verbs have fixed meanings. Fall out = to quarrel; fall off = to drop down from something or to decrease.

1. The sense is that the sons quarrelled after their father died ('breathed his last').
2. So the correct phrasal verb is fell out: "The sons of the old farmer fell out after their father breathed his last."
3. Hence the error is in the segment fell off after their father; the other segments are correct.

Trick: Fall out = quarrel; Fall off = decline / drop down; Breathe one's last = die.

Answer: (D) fell off after their father

Concept: To show that something is a part/component belonging to a whole, we use the preposition of (part of something).

1. Knowledge engineering, machine learning etc. are components belonging to AI.
2. So: "The core part of Artificial Intelligence is …"
3. in, on, from, with do not express this part–whole relation after 'part'.

Trick: Part of, member of, piece of, branch of – the whole always takes 'of'.

Answer: (B) The core part of Artificial Intelligence

Concept: Quaint means attractively unusual or old-fashioned; charmingly different.

1. A quaint village/cottage is one that is unusual and charming in an old-fashioned way.
2. The opposite of unusual/special is Ordinary (common, plain).
3. Distinct is close in sense (different); Brisk (quick) and Ridiculous (silly) are not opposites.

Trick: Quaint = Unusual, Picturesque ↔ Ordinary, Commonplace.

Answer: (C) Ordinary

Concept: Check each tricky word: professional, surpassing, expectations, achieving.

1. (A) 'profesional' and 'acheiving' are wrong.
2. (B) 'profesional', 'surpasing', 'expectasions' are wrong.
3. (C) 'surpasing' and 'acheving' are wrong.
4. (D) all four words are spelt correctly.

Trick: professional, surpassing, expectations, achieving ('i before e except after c').

Answer: (D) The professional athlete pushed her body to the limit, surpassing all expectations and achieving a new personal record.