Q&A: practice questions with answers

Concept: Net price $=\text{MP}\times \frac{100-\text{commission}\%}{100}$.

1. $\text{MP}\times 0.8=9080$.
2. $\text{MP}=\frac{9080}{0.8}=11350$.

Trick: Divide by 0.8 = multiply by $\frac{5}{4}$: $9080\times \frac{5}{4}=11350$.

Answer: (B) ₹11,350

Concept: Interest is charged on the unpaid balance: $R=\frac{SI\times 100}{P\times T}$.

1. Balance (principal) $=4400-2000=2400$; paid later $2440$, so $SI=40$.
2. $T=\frac{1}{12}$ year.
3. $R=\frac{40\times 100\times 12}{2400}=20\%$ per annum.

Trick: Monthly rate $=\frac{40}{2400}=\frac{1}{60}$; yearly $=\frac{12}{60}=20\%$.

Answer: (A) 20%

Concept: The bisectors of an interior angle and of the exterior angle at another vertex meet at an angle equal to half the third angle: $\angle QSR=\frac{\angle P}{2}$.

1. Exterior $\angle R=\angle P+\angle Q$, so $\frac{\angle P+\angle Q}{2}=\frac{\angle Q}{2}+\angle QSR$.
2. Hence $\angle QSR=\frac{\angle P}{2}$.
3. $\angle P=2\times {40}^{\circ }={80}^{\circ }$.

Yaad rakhein: Internal–external bisectors: $\frac{\angle P}{2}$; both internal: ${90}^{\circ }+\frac{\angle P}{2}$; both external: ${90}^{\circ }-\frac{\angle P}{2}$.

Answer: (C) ${80}^{\circ }$

Concept: $a^3+b^3=(a+b)(a^2-ab+b^2)$ with $a=x^2$, $b=y^2$.

1. $x^4+y^4=x^2{y}^2\Rightarrow x^4-x^2{y}^2+y^4=0$.
2. $x^6+y^6=(x^2+y^2)(x^4-x^2{y}^2+y^4)$.
3. $=(x^2+y^2)\times 0=0$.

Trick: Spot the factor $a^2-ab+b^2$ of a sum of cubes.

Answer: (B) 0

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

1. School B: girls $=846$, total $=1880$.
2. $\frac{846}{1880}\times 100=45\%$.

Trick: $10\%$ of $1880=188$; $846=188\times 4.5$, so $45\%$.

Answer: (B) 45%

Concept: Opposite angles of a cyclic quadrilateral are supplementary (sum ${180}^{\circ }$).

1. In EFGH, $\angle FGH$ (at G) and $\angle HEF$ (at E) are opposite.
2. $\angle HEF={180}^{\circ }-{57}^{\circ }={123}^{\circ }$.

Trick: ${33}^{\circ }$ is the complement (${90}^{\circ }-{57}^{\circ }$) – a trap.

Answer: (B) ${123}^{\circ }$

Concept: $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$; dividing by a fraction means multiplying by its reciprocal.

1. Expression $=\frac{1}{4\times 9\times 25\times 49}\times \frac{121}{36}$.
2. Square root $=\frac{1}{2\times 3\times 5\times 7}\times \frac{11}{6}$.
3. $=\frac{1}{210}\times \frac{11}{6}=\frac{11}{1260}$.

Trick: All are perfect squares – take roots term by term: $\frac{1}{2}·\frac{1}{3}·\frac{1}{5}·\frac{1}{7}·\frac{11}{6}$.

Answer: (A) $\frac{11}{1260}$

Concept: Surface area of a hemisphere ($2\pi r^2$ or $3\pi r^2$) is proportional to $r^2$.

1. Ratio $=\frac{7^2}{4^2}$.
2. $=\frac{49}{16}$, i.e. $49:16$ (new : original).

Trick: Area ratio $=$ (radius ratio)${}^2$; volume ratio $=$ (radius ratio)${}^3$.

Answer: (B) 49 : 16

Concept: Add each column over the seven years and compare.

1. 4AH $=676$; 7AH $=694$.
2. 32AH $=114+102+75+150+135+165+160=901$.
3. 35AH $=601$; 55AH $=799$.
4. Highest $=901$ (32AH).

Trick: Eyeball first: 32AH has three entries $\ge 150$ – it clearly leads.

Answer: (A) 32 AH

Concept: Compare the column totals of the classes.

1. Totals: V $=917$, VI $=924$, VII $=904$.
2. VIII $=919$, IX $=903$, X $=910$.
3. Maximum $=924$ (class VI).

Trick: Use the given Total row – no need to re-add.

Answer: (C) VI

Concept: Spontaneous means done naturally, without planning or outside prompting.

1. Instinctive = arising from natural impulse, not from thought – same sense.
2. Attractive = pleasing; Exhaustive = complete/thorough; Acquisitive = eager to gain possessions – none fits.

Yaad rakhein: Spontaneous laughter = instinctive laughter – it just comes out by itself.

Answer: (C) Instinctive

Concept: Check each underlined word against its standard spelling.

1. rolling, beach, soothing – all correctly spelt.
2. ‘trainquil’ is wrong; the correct word is tranquil (calm, peaceful).

Yaad rakhein: tran-quil: only one ‘a’ and no ‘i’ after it – think ‘tranquility’.

Answer: (B) trainquil

Concept: An adjective (upset) is modified by an adverb, not by another adjective.

1. ‘extreme’ is an adjective; it cannot modify the adjective ‘upset’.
2. Correct: Rani was extremely upset with her results this year.
3. Other parts are correct.

Trick: Adjective ke pehle intensity batani ho to ‘-ly’ adverb lagao: extremely, highly, deeply.

Answer: (A) extreme upset

Concept: Check each underlined word against its standard spelling.

1. chains, circus, heed – correct.
2. ‘thrshed’ is wrong; the correct form is thrashed (moved violently, struggled).

Yaad rakhein: thrash → thr-a-sh; a word with no vowel between ‘thr’ and ‘sh’ is a red flag.

Answer: (A) thrshed

Concept: Sit up and take notice = to suddenly start paying serious attention to something and consider it seriously.

1. A strong protest letter will make them give the matter serious thought – i.e. consider it.
2. Follow = obey; Observe = merely watch; Attend = be present – they miss the idea of giving serious thought.

Yaad rakhein: Take notice of something = take it into consideration.

Answer: (D) Consider

Concept: Defunct means no longer existing or functioning.

1. Extant = still in existence, surviving – exact opposite.
2. Stoicism = endurance without complaint; Convoluted = complicated; Redundant = unnecessary (close to defunct, not opposite).

Yaad rakhein: Extant manuscripts = manuscripts that still exist; defunct company = closed company.

Answer: (B) Extant

Concept: The highlighted word is evolve = to develop gradually, to emerge/grow out of something.

1. Emanate = to come out from, originate and spread – the only option expressing emergence/development.
2. Censor = suppress; Demolish = destroy; Conceal = hide – all opposite in spirit.

Trick: Eliminate negative words (censor, demolish, conceal); the one ‘coming out/growing’ word is left.

Answer: (A) Emanate

Concept: Distance from a place is shown with away from / far from; ‘adjacent’, ‘near’ and ‘proximate’ take to and mean closeness.

1. 113 km is a large distance, so words of nearness (adjacent, near, proximate) are illogical; ‘near from’, ‘adjacent from’ are also wrong prepositions.
2. ‘city capital’ is wrong word order – it must be ‘capital city’.
3. Only ‘far from the capital city of MP, Bhopal’ keeps the correct sense and order.

Trick: near/adjacent/proximate + to, never ‘from’; far/away + from.

Answer: (B) far from the capital city of MP, Bhopal

Concept: Scan each sentence for a misspelt word.

1. Sentences with ‘essential’, ‘intricately’, ‘deteriorating’, ‘Mission’ are correctly spelt.
2. ‘hygeine’ is wrong – the correct spelling is hygiene.
3. So the sentence ‘Our health depends … personal hygeine …’ has the error.

Yaad rakhein: hyg-ie-ne: ‘i before e’ – h-y-g-i-e-n-e.

Answer: (D) Our health depends not just on our nutrition and personal hygeine but also on how we clean our cities and surroundings.

Concept: Amiable = having a pleasant, friendly manner.

1. Students like the professor for his amiable approach → a friendly approach.
2. Simple = plain; Strict = stern (opposite); Academic = scholarly – not the meaning.

Yaad rakhein: Amiable comes from Latin ‘amicus’ = friend (as in amicable).

Answer: (D) friendly