Q&A: practice questions with answers

Concept: Pick the two values carefully (Neem 2021, Birch 2022).

1. Neem 2021 $=5000$
2. Birch 2022 $=9000$
3. Ratio $=5000:9000=5:9$

Trick: Read row and column twice – $5:7$ (Birch 2021) is the trap.

Answer: (A) $5:9$

Concept: Second discount is on the price after the first discount.

1. After $18\%$: $26000\times 0.82=21320$
2. Season discount $=21320-16000=5320$
3. $\frac{5320}{21320}\times 100\approx 24.95\%$

Trick: Never take the second discount on the marked price.

Answer: (B) $24.95\%$

Concept: In a right triangle, the altitude to the hypotenuse makes $\angle QPS=\angle R$.

1. $\angle Q={180}^{\circ }-{90}^{\circ }-{47}^{\circ }={43}^{\circ }$
2. In $△PQS$: $\angle QPS={90}^{\circ }-{43}^{\circ }={47}^{\circ }$

Trick: Altitude from the right angle swaps the acute angles.

Answer: (B) ${47}^{\circ }$

Concept: Take total work = LCM $(8,12)=24$ units: Sanjay $3$/day, Rohan $2$/day.

1. Every 2 days: $5$ units → 8 days: $20$ units
2. Day 9 (Sanjay): $23$ units
3. Remaining $1$ unit by Rohan: $\frac{1}{2}$ day
4. Total $=9\frac{1}{2}$ days

Trick: Stop at the last full cycle that leaves work less than one pair.

Answer: (B) $9\frac{1}{2}$

Concept: Above poverty line $=100\%-$ below; then split by the male : female ratio.

1. Above poverty line in R $=76\%$ of $26000=19760$
2. Ratio $3:3$ → females $=\frac{19760}{2}=9880$

Trick: $26000\times 0.76\times \frac{1}{2}=13000\times 0.76=9880$.

Answer: (B) $9,880$

Concept: Perpendicular from the centre bisects the chord.

1. Half chord $=\sqrt{{1.7}^2-{0.8}^2}=\sqrt{2.89-0.64}=\sqrt{2.25}=1.5$
2. AB $=2\times 1.5=3\text{cm}$

Trick: $(8,15,17)$ triplet scaled by $0.1$: $0.8,1.5,1.7$.

Answer: (C) $3$

Concept: Share $\%=\frac{\text{part}}{\text{total}}\times 100$.

1. Total $=8000+2000+6000+4000=20000$
2. Clothing $=\frac{2000}{20000}\times 100=10\%$

Trick: $2000$ is $\frac{1}{10}$ of $20000$.

Answer: (A) $10\%$

Concept: Find the HCF, then solve for $m$.

1. HCF of $45$ and $55=5$
2. $55\times 5+45m=5\Rightarrow 275+45m=5$
3. $45m=-270\Rightarrow m=-6$

Trick: HCF is small, so $m$ must be negative to cancel $275$.

Answer: (A) $-6$

Concept: Savings % = $100\%-$ total spending %.

1. Spending $=40\%+25\%+15\%=80\%$
2. Monthly saving $=20\%$ of $50000=10000$
3. Yearly $=10000\times 12=120000$

Trick: Don't forget to multiply by $12$ for a year.

Answer: (C) ₹1,20,000

Concept: Overall gain factor = (price gain factor) × (weight gain factor).

1. CP $=0.88$SP → price factor $=\frac{1}{0.88}=\frac{25}{22}$
2. Needed factor $=1.25=\frac{5}{4}$
3. Weight factor $=\frac{5}{4}÷\frac{25}{22}=\frac{22}{20}=1.1$
4. So the machine shows $10\%$ more weight.

Trick: $\frac{1.25}{1.136}\approx 1.1$ → $10\%$.

Answer: (C) $10\%$

Concept: An archive is a collection of historical documents or records about a place, institution or group of people (also the place where they are kept).

1. Museum – a building displaying objects of historical, artistic or scientific interest, not mainly records.
2. Apostate – a person who abandons his religion or belief.
3. Asylum – shelter or protection given to a refugee; also an old word for a mental hospital.
4. Only Archive fits 'collection of historical documents or records'.

Trick: Archive = records/documents; Museum = objects/artefacts.

Answer: (D) Archive

Concept: Grist to the mill means something that can be used to one's advantage or that is useful for a purpose. The underlined part 'provides useful advantage' matches it.

1. Cost an arm and a leg – be very expensive.
2. Put something on ice – postpone or delay something.
3. Play it by ear – act according to the situation without a plan.
4. Statistics data being useful to players = grist to the mill.

Trick: Grist (grain) brought to a mill is always useful – so 'grist to the mill' = something useful/advantageous.

Answer: (B) Grist to the mill

Concept: 'Noise' is an uncountable noun here and begins with a consonant sound, so 'an' cannot be used before it.

1. 'An' is used only before a vowel sound (an apple, an hour). 'Noise' starts with the /n/ consonant sound.
2. As an uncountable noun 'noise' takes no article: 'not make noise' (or 'any noise').
3. Correct sentence: We should not make noise in the class.
4. Error lies in the part 'not make an noise'.

Trick: Before an article, check the sound of the next word: consonant sound → 'a', vowel sound → 'an'.

Answer: (D) not make an noise

Concept: Languid means slow, relaxed, lacking energy or spirit. Its opposite is animated – full of life, energy and excitement.

1. Look in the sentence for a word meaning 'lively/energetic'.
2. Animated infantry = lively, energetic soldiers → opposite of languid.
3. Infantry (foot soldiers), rehearsal (practice) and forward (direction) are not related to energy level.
4. Hence the antonym is animated.

Trick: Languid ≈ lazy, listless; Animated ≈ lively (think 'animation' = bringing to life).

Answer: (D) animated

Concept: Steer clear of someone or something means to avoid them, usually because they are dangerous or unpleasant.

1. 'Steer' = guide a vehicle; 'clear of' = away from – so you guide yourself away from danger.
2. Example: Steer clear of strangers who offer free gifts.
3. Losing temper, teaching someone a job, or being kind have no link with avoiding.
4. So the meaning is: avoid someone or something because it is dangerous for you.

Trick: Steer clear = 'steer' your boat 'clear' of the rocks → keep away.

Answer: (B) Avoid someone or something because it is dangerous for you

Concept: Malice means the intention or desire to harm others; ill will. Its opposite is goodwill or sympathy – feeling of care and concern for others.

1. Avarice – extreme greed for wealth (not opposite).
2. Oppression – cruel treatment; it is close to malice, not opposite.
3. Grace – elegance or courtesy; not the direct opposite of ill will.
4. Sympathy (kind feeling for others) is the best antonym.

Trick: Malice = ill will; Sympathy = good will.

Answer: (D) sympathy

Concept: 'Wish' is a main verb; it cannot be used with the base form after 'was'. Simple past of 'wish' is wished.

1. 'I was wish' combines the helping verb 'was' with the base form 'wish' – grammatically wrong.
2. Correct form: I wished to meet her on her birthday.
3. 'to meet her' (infinitive) and 'on her birthday' (preposition 'on' with a day) are correct.
4. So the error is in 'I was wish'.

Trick: 'Was/were' + verb needs -ing (continuous) or V3 (passive); never the base form.

Answer: (A) I was wish

Concept: With the dummy subject 'It' + time expression, we use the verb takes: 'It takes a couple of minutes…'. 'It is take' is wrong.

1. 'Is' (helping verb) cannot be followed by the base form 'take'.
2. Correct structure: It + takes + time + for someone + to do something.
3. Correct sentence: It takes a couple of minutes for the computer to boot up.
4. Error is in 'It is take'.

Trick: 'It takes' + time is a fixed pattern: It takes 10 minutes to reach school.

Answer: (D) It is take

Concept: The highlighted word is pervasive, meaning spreading widely through a group or area; present everywhere. Its synonym is widespread.

1. Retrospective – looking back at past events.
2. Longitudinal – running lengthwise, or a study done over a long time.
3. Equatorial – related to the equator.
4. 'A severe and widespread issue' keeps the meaning of 'pervasive'.

Trick: Pervade = spread through → pervasive = widespread.

Answer: (C) Widespread

Concept: The correct spelling is Abduct (to take someone away illegally by force). 'Abdact' is wrong.

1. Adjourn – to postpone a meeting: correct.
2. Addict – a person dependent on a substance: correct.
3. Advise – to give advice (verb): correct.
4. Abdact → correct form Abduct (ab + duct, as in 'conduct', 'product').

Trick: '-duct' family: conduct, product, deduct, abduct – always 'u'.

Answer: (C) Abdact