Q&A: practice questions with answers

Concept: Volume of a cube $=a^3$.

1. $a=8\text{cm}$
2. $V=8^3=512{\text{cm}}^3$

Trick: $8^3=2^9=512$.

Answer: (C) $512{\text{cm}}^3$

Concept: Extra quantity $\times$ new price $=$ money saved by the reduction.

1. Saving $=7.5\%$ of $7400=555$
2. New price $=\frac{555}{15}=37$ per kg
3. Original price $=\frac{37}{0.925}=40$ per kg
4. SP $=40\times 1.325=53$ per kg

Trick: Reduced price $=\frac{\text{saving}}{\text{extra kg}}$ — no equation needed.

Answer: (D) $53$

Concept: Make the common term (Praveen) equal in both ratios.

1. J : P $=5:8=15:24$; P : K $=3:2=24:16$
2. J : P : K $=15:24:16$, sum $=55$
3. J $=\frac{15}{55}\times 17600=4800$

Trick: One part $=\frac{17600}{55}=320$; J $=15\times 320$.

Answer: (C) ₹$4,800$

Concept: Percentage higher $=\frac{\text{difference}}{\text{base}}\times 100$, base $=2018$.

1. 2018: $25$ crore; 2020: $30$ crore
2. $\frac{30-25}{25}\times 100=20\%$

Trick: Base is the value after “than”.

Answer: (A) $20\%$

Concept: Budget share $=$ percentage $\times$ total.

1. Grocery $+$ Electricity $=20\%+19\%=39\%$
2. Budget $=39\%$ of $58000=22620$
3. Difference $=22620-18875=3745$

Trick: $1\%$ of $58000=580$; $39\times 580=22620$.

Answer: (C) ₹$3,745$

Concept: Passing in Q $=$ candidates of Q $\times \frac{3}{3+7}$.

1. Q passing $=2.26\times \frac{3}{10}=0.678$ lakh
2. Total $=1.10+2.26+2.12+1.46=6.94$ lakh
3. $\frac{0.678}{6.94}\times 100\approx 9.77\%$

Trick: Pass share of Q is $30\%$; $2.26$ is about one-third of $6.94$, so answer $\approx 10\%$.

Answer: (D) $9.77\%$

Concept: Inner brackets first, then $\times$, then $+$/$-$.

1. $48÷12=4$; $8÷4+4=6$
2. $4+2\times 6=16$
3. $29-16=13$

Trick: Never add before multiplying: $4+2\times 6\ne 36$.

Answer: (D) $13$

Concept: Treat it as a quadratic in $\cos A$ and factorise.

1. $2{\cos }^{2}A+4\cos A-\cos A-2=0$
2. $(2\cos A-1)(\cos A+2)=0$
3. $\cos A=-2$ is impossible, so $\cos A=\frac{1}{2}$
4. $A={60}^{\circ }$

Trick: Put options: $\cos {60}^{\circ }=\frac{1}{2}$ gives $2·\frac{1}{4}+\frac{3}{2}-2=0$.

Answer: (B) ${60}^{\circ }$

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

1. $\frac{60}{360}=\frac{1}{6}$
2. $\pi r^2=\frac{22}{7}\times 441=1386$
3. Area $=\frac{1386}{6}=231{\text{cm}}^2$

Trick: A ${60}^{\circ }$ sector is one-sixth of the circle.

Answer: (C) $231$

Concept: Divide by $\cos {13}^{\circ }$: $\frac{1+\tan {13}^{\circ }}{1-\tan {13}^{\circ }}=\tan ({45}^{\circ }+{13}^{\circ })$.

1. $\frac{\cos {13}^{\circ }+\sin {13}^{\circ }}{\cos {13}^{\circ }-\sin {13}^{\circ }}=\frac{1+\tan {13}^{\circ }}{1-\tan {13}^{\circ }}$
2. $=\frac{\tan {45}^{\circ }+\tan {13}^{\circ }}{1-\tan {45}^{\circ }\tan {13}^{\circ }}=\tan {58}^{\circ }$

Trick: $\frac{\cos x+\sin x}{\cos x-\sin x}=\tan ({45}^{\circ }+x)$ always.

Answer: (D) $\tan {58}^{\circ }$

Concept: The stage of life between childhood and adulthood, when a person is developing into an adult, is called adolescence.

1. Adolescence = the period of growth from puberty to adulthood – exactly the given description.
2. Teenage is an adjective/informal noun for ages 13–19 only; it does not name the developmental period precisely.
3. Childhood is the earlier stage; Adultery means a married person's unfaithfulness – totally unrelated.

Trick: Adolescent = 'growing up' (Latin adolescere = to grow up).

Answer: (A) Adolescence

Concept: A singular countable noun needs an article (a/an/the) before it.

1. 'Horse' is a singular countable noun used for the first time, so it needs the indefinite article 'a'.
2. Correct sentence: Mr. Thomas is going to buy a horse.
3. 'Mr. Thomas', 'is going' and 'to buy' are all correct.

Yaad rakhein: Singular countable noun can never stand alone – use a/an/the (a horse, an apple).

Answer: (D) horse

Concept: 'By the time' + subject needs a finite verb; with a past perfect main clause, the time clause takes the simple past.

1. 'I reaching' has no helping verb – a participle cannot act as the verb of a clause.
2. The main clause 'the train had departed' is past perfect, so the earlier-reference clause takes simple past: By the time I reached the metro station…
3. The other parts are correct.

Yaad rakhein: By the time + Simple Past, … Past Perfect (By the time I reached, the train had left).

Answer: (D) By the time I reaching

Concept: A single precise adjective is preferred over a weak 'adverb + adjective' phrase.

1. 'Extremely painful' = excruciating (intensely painful) – exact match.
2. Horrible = very unpleasant (not necessarily painful); extreme = very great (no idea of pain); devastating = destructive or shocking.
3. So 'caused excruciating headaches' keeps the meaning exactly.

Trick: Excruciating comes from Latin cruciare = to torture – pain of torture level.

Answer: (A) excruciating

Concept: Pacify means to calm someone who is angry or upset.

1. Soothe = to calm or comfort – same meaning as pacify.
2. Rebuke = scold; Blame = hold responsible; Strengthen = make strong – none means calming.
3. Example: The mother tried to pacify (soothe) the crying child.

Trick: Pacify has 'pax' (peace) – bring peace = soothe.

Answer: (D) Soothe

Concept: Choose the option that keeps the meaning of the underlined words: 'expand' = make larger.

1. Expand its business = make the business bigger = increase it.
2. 'To reduce', 'to contract' and 'to limit' all mean the opposite (make smaller).
3. Sentence: The company plans to increase its business to the international market.

Trick: Expand ↔ contract are opposites; expand ≈ increase/enlarge.

Answer: (C) to increase

Concept: Ephemeral means lasting for a very short time; the context 'bloom for only a short period' confirms it.

1. Opposite of short-lived = permanent (lasting for ever).
2. Transient is a synonym of ephemeral – a trap option.
3. Uniform = same throughout; Unwavering = steady/firm – not opposites of short-lived.

Yaad rakhein: Ephemeral = transient = fleeting ↔ permanent = eternal = everlasting.

Answer: (C) Permanent

Concept: Conservative = holding traditional values and disliking change.

1. Its opposite is liberal = open to new ideas and change.
2. Fantastic = wonderful; Determined = firm in purpose; Authentic = genuine – none is opposite.
3. Conservative vs liberal is a standard antonym pair (traditional vs progressive).

Yaad rakhein: Conservative ↔ Liberal / Progressive / Modern.

Answer: (A) Liberal

Concept: Nerves of steel describes a person who does not feel fear or nervousness even in difficult or dangerous situations.

1. Facing multiple obstacles without giving up shows she was not frightened or anxious – an absence of fear or anxiety.
2. Extraordinary beauty – unrelated; Relentless determination describes persistence, not freedom from fear.
3. Steel nerves = nerves that do not shake – no fear, no panic.

Trick: Nerves = anxiety; 'of steel' = unbreakable → fear cannot shake you.

Answer: (B) An absence of fear or anxiety

Concept: A substance that can be hammered or pressed into any desired shape without breaking is called malleable.

1. Tin (like gold, silver, aluminium) can be beaten into sheets – it is malleable.
2. Rigid = stiff, cannot bend; Immutable = unchangeable; Gullible = easily deceived (used for people).
3. Correct: Tin is malleable.

Yaad rakhein: Malleable (beaten into sheets) vs ductile (drawn into wires).

Answer: (A) malleable