Q&A: practice questions with answers

Concept: For a dead heat, B is given a start equal to the distance B is short when A finishes.

1. Speed of A $=\frac{250}{25}=10\text{m/s}$ → A runs $1000\text{m}$ in $100\text{s}$.
2. Speed of B $=\frac{250}{30}=\frac{25}{3}\text{m/s}$ → in $100\text{s}$ B runs $\frac{2500}{3}=833.33\text{m}$.
3. Start $=1000-833.33=166.67\text{m}$.

Trick: Start $=1000\times (1-\frac{25}{30})=\frac{1000}{6}$.

Answer: (C) $166.67\text{m}$

Concept: Apply the loss and profit as successive multipliers.

1. Anju's CP $=75000\times 0.9=67500$.
2. Anju's SP $=67500\times 1.2=81000$.

Trick: $0.9\times 1.2=1.08$ → $75000\times 1.08=81000$.

Answer: (C) ₹$81000$

Concept: If HCF is divisible by both $x$ and $y$, it is a multiple of $\text{LCM}(x,y)$; so $23x$ must divide $a\times y$.

1. $x=224=2^5\times 7$, $y=322=2\times 7\times 23$.
2. $23x=2^5\times 7\times 23$ (this already equals $\text{LCM}(x,y)$).
3. $a\times y=2\times 7\times 23\times a$ must contain $2^5\times 7\times 23\Rightarrow a$ must contain $2^4=16$.
4. $a=16$ works: HCF $=2^5\times 7\times 23$, divisible by $x$ and $y$.

Trick: Compare powers of $2$: need $2^5$, $y$ gives only $2^1$ → $a$ supplies $2^4$.

Answer: (A) $16$

Concept: SP $=\text{MP}\times (1-0.10)\times (1-0.05)$.

1. $\text{MP}\times 0.9\times 0.95=342\Rightarrow \text{MP}\times 0.855=342$.
2. $\text{MP}=\frac{342}{0.855}=400$.

Trick: Equivalent discount $=10+5-\frac{10\times 5}{100}=14.5\%$; $85.5\%$ of $400=342$.

Answer: (A) ₹$400$

Concept: The perpendicular from the centre bisects the chord; use Pythagoras in $△OCA$.

1. $AC=\sqrt{O{A}^2-O{C}^2}=\sqrt{{13}^2-5^2}=\sqrt{144}=12\text{cm}$.
2. $AB=2\times AC=24\text{cm}$.

Trick: $5$-$12$-$13$ triplet → half chord $12$.

Answer: (A) $24\text{cm}$

Concept: Two quadratics have both roots common when their corresponding coefficients are proportional.

1. Compare $k(21x^2+24)+rx+\dots$ with $k(7x^2+8)+px+\dots$: the $k$-terms are in ratio $21:7=24:8=3:1$.
2. So the whole first equation is $3$ times the second; hence coefficients of $x$ also satisfy $r=3p$.
3. $\frac{p}{r}=\frac{1}{3}$.

Trick: Both roots common ⇒ $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$; read the constant ratio from the clean terms.

Answer: (A) $\frac{1}{3}$

Concept: If first : second $=7:8$, second $=\text{first}\times \frac{8}{7}$.

1. $7$ parts $=35\Rightarrow 1$ part $=5$.
2. Second $=8\times 5=40$.

Trick: Find one part, then multiply by the other ratio term.

Answer: (B) $40$

Concept: $(s-a)+(s-b)+(s-c)=3s-2s=s$; Area $=\sqrt{s(s-a)(s-b)(s-c)}$.

1. $s=18+17+25=60\text{cm}$.
2. Area $=\sqrt{60\times 18\times 17\times 25}=\sqrt{459000}$.
3. $=\sqrt{900\times 510}=30\sqrt{510}{\text{cm}}^2$.

Trick: Sum of the three differences directly gives $s$.

Answer: (C) $30\sqrt{510}{\text{cm}}^2$

Concept: New average $=\frac{\text{old total}-\text{leaving total}+\text{joining total}}{\text{new count}}$.

1. Old total $=45\times 52=2340$.
2. New total $=2340-6\times 40+8\times 43=2340-240+344=2444$.
3. New count $=45-6+8=47$; average $=\frac{2444}{47}=52$.

Trick: Deviation method: the $6$ leaving were $12$ below average (a deficit of $72$ removed); the $8$ joining are $9$ below (a deficit of $72$ added) → net $0$, average stays $52$.

Answer: (D) $52$

Concept: A number is divisible by $9$ if the sum of its digits is divisible by $9$.

1. Known digits of $51\&918\#0$: $5+1+9+1+8+0=24$.
2. $24+\&+\#$ must be $27$ or $36$ → $\&+\#=3$ or $12$.
3. Options: $17,4,9,12$ → only $8+4=12$ works.

Trick: Find the remainder of the known digits ($24\to 6$); the missing pair must give remainder $3$.

Answer: (D) $8$ and $4$

Concept: In seventh heaven means being in a state of extreme happiness or bliss.

1. In some old beliefs the seventh heaven is the highest heaven, the place of greatest joy.
2. Example: She was in seventh heaven after topping the exam.
3. 'Extremely sad' is the opposite; the ceremony and God options are literal guesses.

Yaad rakhein: Seventh heaven = on cloud nine = over the moon (all mean very happy).

Answer: (D) Extremely happy

Concept: Bonhomie (French: bon = good, homme = man) means a cheerful, friendly nature; good fellowship.

1. Example: The bonhomie between the players was visible after the match.
2. 'Friendship' is closest to this warm friendliness.
3. 'Bad-natured', 'Enemy' and 'Disagreeable' all point to hostility — the opposite.

Trick: bon = good (as in bon voyage) → bonhomie = good-natured friendliness.

Answer: (C) Friendship

Concept: Partisan means strongly supporting one side, group or party, often without fair judgement — i.e. biased.

1. The sentence says the crowd was one-sided in nature.
2. 'Biased' = favouring one side unfairly — exact match.
3. 'Pitiful', 'Kind' and 'Destructive' do not relate to taking sides.

Yaad rakhein: Partisan ↔ impartial / neutral (antonyms); partisan = biased, one-sided.

Answer: (C) biased

Concept: Check each word letter by letter against its standard spelling.

1. Quarrelsome, Ecclesiastical (related to the church) and Bovine (related to cows) are correct.
2. The correct form is Calamitous (calamity → calamitous); there is no 'i' before 'ous'.
3. So 'Calamitious' is misspelt.

Trick: calamity drops 'y' and adds '-tous': calami + tous = calamitous (like 'momentous').

Answer: (D) Calamitious

Concept: Barbaric means savagely cruel, uncultured or primitive.

1. Its opposite is civilised = cultured, refined and humane.
2. 'Brutal' is a synonym of barbaric, not an antonym.
3. 'Indifferent' and 'Inquisitive' are unrelated in meaning.

Yaad rakhein: Barbaric / barbarous ↔ civilised / refined.

Answer: (D) Civilised

Concept: As good as gold is said (mostly of children) to mean very well-behaved and obedient.

1. Example: The kids were as good as gold while their parents were away.
2. Option (A) gives exactly this sense.
3. The other options take 'gold' literally.

Yaad rakhein: As good as gold = very well-behaved; 'good as one's word' = keeps promises (different idiom).

Answer: (A) A person who is obedient and well-behaved

Concept: Come up with = to produce or suggest an idea or plan.

1. 'Brought new ideas' means she produced or suggested new ideas → came up with.
2. It is also in past tense, matching the sentence.
3. 'Draw on' = make use of; 'Swept off' = carried away; 'Carry off' = win or manage successfully — none fit.

Yaad rakhein: Ideas, plans, solutions → come up with.

Answer: (C) Came up with

Concept: To judge a book by its cover = to form an opinion about someone or something only from outward appearance.

1. Usually used in the negative: Don't judge a book by its cover.
2. Option (C) states this exactly.
3. 'Good at evaluating people' is the opposite idea — the idiom warns against shallow judgement.

Yaad rakhein: Cover = outer look; the idiom = judging by looks alone.

Answer: (C) To evaluate people’s worth by their outward appearance

Concept: Like is followed by a gerund (like doing) or an infinitive (like to do); 'to meeting of people' mixes both wrongly.

1. 'like to meeting' is wrong — after 'to' (infinitive) we need the base verb, and 'of' is unnecessary.
2. 'like meeting people' — like + gerund + object — is correct.
3. 'like meet to', 'like to be meeting' and 'will like meeting with' are ungrammatical or change the meaning.

Yaad rakhein: like + V-ing or like + to + V1 — never 'like to + V-ing'.

Answer: (A) like meeting people

Concept: Two subjects joined by and form a plural subject and take a plural verb.

1. 'Vicky and Deepa' = plural → plural verb try (not 'tries').
2. 'their level best' is the correct fixed expression.
3. 'had tries' and 'have try' are wrong verb forms; 'tries their best level' has a singular verb and garbled idiom.

Yaad rakhein: A and B → plural verb (they try, not they tries).

Answer: (B) try their level best