Q&A: practice questions with answers

Concept: Brackets first (inner to outer), then ×, then +.

1. $(5+7)=12$; $12÷2=6$
2. $[7+6]=13$
3. $3+2\times 13=3+26=29$

Trick: Never add $3+2$ first – multiplication comes before addition.

Answer: (A) $29$

Concept: Central angle $=\frac{\text{percentage}}{100}\times {360}^{\circ }$.

1. Store S $=34\%$
2. Angle $=\frac{34}{100}\times {360}^{\circ }={122.4}^{\circ }$

Trick: $1\%={3.6}^{\circ }$, so $34\%=34\times 3.6={122.4}^{\circ }$ (total 6500 not needed).

Answer: (B) ${122.4}^{\circ }$

Concept: Under SI, each instalment earns interest from its payment date till the due date; total must equal the debt due.

1. Let instalment $=x$. 1st earns 2 years: $x(1+0.2)=1.2x$
2. 2nd earns 1 year: $1.1x$; 3rd earns none: $x$
3. $1.2x+1.1x+x=3.3x=10192\Rightarrow x=\frac{10192}{3.3}=3088.48$

Trick: Formula: $x=\frac{100A}{100n+\frac{n(n-1)}{2}R}=\frac{1019200}{300+30}$.

Answer: (B) ₹3,088.48

Concept: Cube volume $a^3$, TSA $6a^2$; cuboid volume $lbh$, TSA $2(lb+bh+hl)$.

1. Cuboid volume $=32\times 8\times 4=1024$; cube volume $=4\times 1024=4096\Rightarrow a=16$
2. Cube TSA $=6\times {16}^2=1536$
3. Cuboid TSA $=2(256+32+128)=832$
4. Ratio $=1536:832=24:13$

Trick: Divide both by $64$: $1536÷64=24$, $832÷64=13$.

Answer: (A) 24 : 13

Concept: BODMAS: ÷ and × left to right before + and −.

1. $4.5÷0.9=5$; $5\times 1.2=6$
2. $8.2+2.6+3.2=14$
3. $14-6=8$

Trick: $4.5÷0.9$ is the same as $45÷9$.

Answer: (D) $8$

Concept: A median divides a triangle into two triangles of equal area (equal bases, same height).

1. XL is a median since L is the mid-point of YZ.
2. Area $△XYL=$ Area $△XLZ=13{\text{cm}}^2$
3. Area $△XYZ=2\times 13=26{\text{cm}}^2$

Yaad rakhein: Median → two equal halves.

Answer: (D) $26$

Concept: Difference of times for the same distance: $\frac{d}{s_1}-\frac{d}{s_2}=\Delta t$.

1. $40$ min $=\frac{2}{3}$ h
2. $\frac{d}{45}-\frac{d}{55}=\frac{2}{3}\Rightarrow d·\frac{10}{2475}=\frac{2}{3}$
3. $d=\frac{2\times 2475}{30}=165\text{km}$

Trick: $d=\frac{s_1{s}_2}{s_2-s_1}\times \Delta t=\frac{45\times 55}{10}\times \frac{2}{3}=165$.

Answer: (B) $165$

Concept: Each decrease multiplies the remaining population: $P\times 0.95\times 0.80$.

1. $P\times 0.95\times 0.8=0.76P$
2. $0.76P=4655\Rightarrow P=\frac{4655}{0.76}=6125$

Trick: Check options backwards: $6125\times 0.95=5818.75$, $\times 0.8=4655$ ✓.

Answer: (B) $6125$

Concept: Square and add the two given equations; use ${\sin }^2+{\cos }^2=1$.

1. $a^2={\sin }^{2}x+{\sin }^{2}y+2\sin x\sin y$
2. $b^2={\cos }^{2}x+{\cos }^{2}y+2\cos x\cos y$
3. $a^2+b^2=2+2(\sin x\sin y+\cos x\cos y)$
4. $\sin x\sin y+\cos x\cos y=\frac{a^2+b^2-2}{2}$

Trick: Put $x=y=0$: $a=0,b=2$ → value $1=\frac{0+4-2}{2}$ ✓.

Answer: (C) $\frac{a^2+b^2-2}{2}$

Concept: Apply the first discount on the marked price, then find the second discount on the reduced price.

1. After 10%: $2500\times 0.9=₹2250$
2. Second discount $=2250-1800=₹450$
3. Rate $=\frac{450}{2250}\times 100=20\%$

Trick: $\frac{1800}{2500}=0.72=0.9\times 0.8$ → second discount 20%.

Answer: (B) 20%

Concept: An idiom has a fixed figurative meaning; go down in flames means to fail suddenly, completely and in a very public, dramatic way.

1. Picture a plane falling in flames – the failure is total and everyone sees it.
2. E.g. His campaign went down in flames after the scandal. = it failed spectacularly.
3. (B) and (D) describe literal burning/destruction; (C) crash and burn is just another idiom, not a meaning.

Yaad rakhein: Go down in flames = fail badly and visibly (spectacular failure).

Answer: (A) To fail spectacularly

Concept: Blue blood means noble or aristocratic birth – belonging to a royal or upper-class family.

1. In the sentence, only people of noble birth can dethrone the autocrat – this matches royal lineage.
2. The phrase comes from Spanish nobles whose pale skin showed bluish veins.
3. Political ideology, vigilant nature and bitter relations have no link with birth or family.

Yaad rakhein: Blue blood = royal/noble family (aristocracy).

Answer: (C) Aristocratic lineage

Concept: Sequence of tenses: when the main action is in the past (past continuous were driving), the sudden interrupting action is in the simple past.

1. We were driving home – past continuous, background action.
2. The interrupting action must also be past: a deer ran across the road, not runs.
3. Correct: We were driving home when suddenly a deer ran across the road.

Yaad rakhein: Past continuous + when + simple past (was doing … when X happened).

Answer: (C) a deer runs across the road

Concept: Condemn means to express strong disapproval of something publicly; its synonym is denounce.

1. E.g. Leaders condemned/denounced the attack.
2. Uphold (support) and tolerate (put up with) are nearly opposite.
3. Elevate means to raise – unrelated.

Yaad rakhein: Condemn = denounce = criticise strongly.

Answer: (D) Denounce

Concept: Demography is the statistical study of human populations – births, deaths, age groups, migration.

1. The underlined phrase a study of statistics (of population) is best replaced by Demography.
2. Choreography – designing dance steps; Cartography – map-making.
3. Cinematography – the art of film camera work.

Yaad rakhein: Demo = people, -graphy = writing/record → statistical record of people.

Answer: (A) Demography

Concept: The correct spelling is Entrepreneur (French entreprendre, to undertake) – entre, not enter.

1. Enterpreneur ✗ → Entrepreneur ✓.
2. Disseminate (double s), Dilemma (double m) and Accommodate (double c, double m) are all correct.

Yaad rakhein: ENTRE-PRE-NEUR: starts like entrance in French – e-n-t-r-e.

Answer: (B) Enterpreneur

Concept: An adverb of manner normally comes after an intransitive verb: slept soundly, not soundly slept, especially in perfect tenses (had slept soundly).

1. had soundly slept sounds unnatural; the idiomatic order is had slept soundly.
2. Correct: His energetic attitude showed that he had slept soundly the previous night.
3. Other segments are grammatically fine.

Yaad rakhein: Verb + adverb of manner: slept soundly, ran fast, spoke clearly.

Answer: (D) soundly slept

Concept: Cacophony means a harsh, unpleasant mixture of loud sounds – i.e. noise.

1. Greek kakos = bad + phone = sound.
2. The cacophony in the theatre = the loud noise in the theatre.
3. Silence is its opposite; smell and laughter do not match.

Yaad rakhein: Caco = bad, phony = sound → bad sound = noise.

Answer: (C) noise

Concept: Wicked means evil or morally wrong; its opposite is righteous (morally good, virtuous).

1. Evil and improper are close to wicked (synonyms), so they are wrong.
2. Clean refers to dirt/physical state, not morality.
3. Righteous = just, upright – the moral opposite.

Yaad rakhein: Wicked ↔ Righteous (bad ↔ morally good).

Answer: (C) Righteous

Concept: Take it with a grain of salt means to accept a statement with some doubt, not believing it completely.

1. Kalpana listened carefully but knew she should not trust every word – she was sceptical.
2. Hence: regard it as exaggerated and not completely true.
3. (A) is the opposite; (B) is unrelated; (D) is ungrammatical and literal.

Yaad rakhein: Grain of salt = a bit of doubt.

Answer: (C) regard it as exaggerated and not completely true