Q&A: practice questions with answers

Concept: Average $=\frac{\text{sum of the three increments}}{3}$.

1. Kamal: May ₹65, June ₹55, July ₹75
2. Sum $=195$
3. Average $=\frac{195}{3}=65$

Trick: Deviations from 65: $0,-10,+10$ cancel, so average $=65$.

Answer: (D) ₹65

Concept: Volume of material $=\pi (R^2-r^2)h$, inner radius = outer radius − thickness.

1. $R=10$, $r=10-3=7$, $h=49$
2. $V=\frac{22}{7}(100-49)\times 49=\frac{22}{7}\times 51\times 49$
3. $=22\times 51\times 7=7854{\text{cm}}^3$

Trick: $R^2-r^2=(R+r)(R-r)=17\times 3=51$.

Answer: (D) $7854{\text{cm}}^3$

Concept: Use standard values $\tan {45}^{\circ }=1$, $\cos {30}^{\circ }=\sin {60}^{\circ }=\frac{\sqrt{3}}{2}$.

1. $2{\tan }^2{45}^{\circ }=2$
2. ${\cos }^2{30}^{\circ }-{\sin }^2{60}^{\circ }=\frac{3}{4}-\frac{3}{4}=0$
3. Value $=2$

Trick: $\cos {30}^{\circ }=\sin {60}^{\circ }$ (complementary angles), so those terms cancel.

Answer: (A) $2$

Concept: Compare the money received with the cost of the quantity actually given.

1. Gives $800\text{g}$ for ₹40
2. Cost of $800\text{g}=0.8\times 36=28.8$
3. Profit $\%=\frac{40-28.8}{28.8}\times 100=\frac{11.2}{28.8}\times 100\approx 38.89\%$

Trick: $(\frac{40}{36}\times \frac{1000}{800}-1)\times 100=(\frac{25}{18}-1)\times 100=38.89\%$.

Answer: (D) $38.89\%$

Concept: Apply Pythagoras: $P{R}^2=P{Q}^2+Q{R}^2$ to relate $x$ and $y$.

1. $(x+y{)}^2=(x-y{)}^2+x^2\Rightarrow 4xy=x^2\Rightarrow x=4y$
2. $PQ=3y$, $QR=4y$
3. $QS=PQ=3y$, $SR=4y-3y=y$
4. $QS:SR=3:1$

Trick: Sides become $3y,4y,5y$ – the 3-4-5 triangle.

Answer: (A) $3:1$

Concept: Add the required cells and simplify the ratio.

1. A + B in January $=212+168=380$
2. D + E in March $=255+245=500$
3. $380:500=19:25$

Trick: Divide both by 20.

Answer: (D) $19:25$

Concept: Average speed $=\frac{\text{total distance}}{\text{total time}}$; take total distance $=100\text{km}$.

1. $\frac{25}{25}=1\text{h}$, $\frac{50}{50}=1\text{h}$, $\frac{25}{12.5}=2\text{h}$
2. Total time $=4\text{h}$
3. Average $=\frac{100}{4}=25\text{km/h}$

Trick: Choose 100 km for percentage distances.

Answer: (C) $25\text{km/h}$

Concept: $\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}$ and $ab=\text{HCF}\times \text{LCM}$.

1. $ab=5\times 60=300$
2. $\frac{1}{a}+\frac{1}{b}=\frac{60}{300}=\frac{1}{5}$

Trick: Sum of reciprocals $=\frac{\text{sum}}{\text{HCF}\times \text{LCM}}$.

Answer: (D) $\frac{1}{5}$

Concept: Values are in hundreds – convert the difference to actual numbers.

1. 7AH in 2021 $=40$, in 2022 $=45$ (hundreds)
2. Difference $=5$ hundreds $=500$

Trick: Always apply the unit ('in hundreds') at the end.

Answer: (D) $500$

Concept: Numbers in ratio $2:7$ with HCF $9$ are $2\times 9$ and $7\times 9$.

1. Numbers: $18$ and $63$
2. Check LCM: $9\times 2\times 7=126$ ✓
3. Larger $=63$

Trick: HCF × ratio terms gives the numbers directly.

Answer: (B) $63$

Concept: ‘Rapt’ means completely absorbed or fascinated; giving full attention.

1. ‘Rapt listeners’ = listeners who are totally absorbed in the music.
2. ‘Fully attentive’ carries exactly this sense.
3. ‘Really fashionable’, ‘boldly dressed’ describe looks; ‘truly energetic’ describes activity – none means absorbed attention.

Yaad rakhein: rapt = rapt attention = full attention (do not confuse with ‘wrapped’).

Answer: (D) fully attentive

Concept: ‘Decline’ (verb) means to go down, decrease or sink.

1. Opposite of going down = going up.
2. ‘Ascend’ means to rise or climb up – the exact antonym.
3. ‘Escape’ (get away), ‘Demonstrate’ (show), ‘Traverse’ (travel across) are unrelated.

Yaad rakhein: Decline ↔ Ascend, Descend ↔ Ascend – think ‘down vs up’.

Answer: (B) Ascend

Concept: ‘Quite’ is an adverb (= fairly/completely); ‘quiet’ is an adjective (= calm, silent). An adjective is needed before the noun ‘afternoon’.

1. ‘a quite afternoon’ is wrong – ‘quite’ cannot describe a noun.
2. Use the adjective ‘quiet’: a calm, silent afternoon.
3. ‘quiet’ begins with a consonant sound /kw/, so the article is ‘a’, not ‘an’.

Yaad rakhein: quiet = silent (adjective); quite = very/fairly (adverb).

Answer: (D) a quiet

Concept: ‘An’ is used before a word beginning with a vowel sound; a singular countable noun (‘list’) needs an article.

1. The blank comes before ‘exhaustive’, which starts with the vowel sound /ɪg/.
2. ‘list’ is singular countable, so an indefinite article is needed – ‘an’.
3. ‘many’ needs a plural noun; ‘a’ does not suit a vowel sound; ‘no word’ leaves the singular noun without an article.

Yaad rakhein: The article depends on the sound of the very next word (exhaustive → an).

Answer: (B) an

Concept: A ‘left-handed compliment’ is a remark that looks like praise but is actually an insult.

1. She seemed to praise the hair (‘liked my hair’), but ‘it turned out’ signals a hidden meaning.
2. So the remark was really an insult disguised as praise.
3. ‘A praise’ and ‘a flattery’ are the surface meaning only; ‘a joke’ is not the sense.

Yaad rakhein: Left-handed compliment = backhanded compliment = taunt dressed as praise.

Answer: (C) An insult

Concept: ‘Redemption’ means being saved or delivered from sin or evil; deliverance.

1. Its religious opposite is an act of disrespect towards God or sacred things.
2. ‘Blasphemy’ = speaking irreverently of God/sacred things – the opposite of spiritual salvation.
3. ‘Salvation’ is a synonym; ‘Corrugation’ (folds/ridges) and ‘Conjunction’ (joining) are unrelated.

Yaad rakhein: Redemption ≈ Salvation; opposite side = Blasphemy (sin against the sacred).

Answer: (B) Blasphemy

Concept: Present perfect continuous tense: has/have + been + verb-ing.

1. The question is in the present perfect continuous: ‘Have they been … for several years?’
2. After ‘been’ the verb must take the ‘-ing’ form: ‘working’, not ‘work’.
3. Correct: Have they been working in that particular shop for several years?

Yaad rakhein: have/has been + V-ing + for/since → continuing action.

Answer: (A) work

Concept: Adverbs from adjectives ending in ‘-ous’ add ‘-ly’: ridiculous → ridiculously.

1. ‘jovial’ in the sentence is spelt correctly.
2. ‘ridiculusly’ is wrong – the adjective is ‘ridiculous’ (r-i-d-i-c-u-l-o-u-s).
3. Adding ‘-ly’ gives ‘ridiculously’; ‘ridicolusly’, ‘jouvial’, ‘juvial’ are all wrong spellings.

Yaad rakhein: ridicule → ridiculous → ridiculously (keep the ‘-ous’).

Answer: (D) ridiculously

Concept: ‘Unless’ already means ‘if … not’, so the clause with ‘unless’ is positive and in the simple present (for a future condition).

1. ‘Unless you do not prepare’ would be a double negative – wrong.
2. Rule: Unless + simple present, main clause + will + V1.
3. So: Unless you prepare well, you will not perform well.
4. ‘will prepare’ / ‘will do not prepare’ use ‘will’ in the condition clause; ‘would not prepare’ is negative and wrong tense.

Yaad rakhein: Unless = if not → never add ‘not’ or ‘will’ after unless.

Answer: (B) prepare

Concept: ‘Bite the bullet’ means to face an unpleasant but unavoidable situation bravely.

1. The idiom comes from patients biting a bullet to bear pain during surgery.
2. So it means deciding to do the difficult/inevitable thing you had been putting off.
3. ‘Decide to take the easier way out’ is the opposite; ‘bite something hard’ is literal.

Yaad rakhein: Bite the bullet = stop avoiding it, face it.

Answer: (C) Decide to do the inevitable which you were avoiding