Q&A: practice questions with answers

Concept: BODMAS: 'of', then $÷$/$\times$ left to right, then $+$/$-$.

1. $7.2\times 4.1=29.52$; $29.52÷12.3=2.4$
2. $22.5\text{ of }\frac{1}{25}=0.9$
3. $2.4+0.9-0.1=3.2$

Trick: $\frac{4.1}{12.3}=\frac{1}{3}$, so first term $=\frac{7.2}{3}=2.4$.

Answer: (D) $3.2$

Concept: $a^3+b^3+c^3-3abc=(a+b+c)[(a+b+c{)}^2-3(ab+bc+ca)]$.

1. $(a+b+c{)}^2=225$
2. $225-3\times 35=120$
3. $15\times 120=1800$

Yaad rakhein: $a^2+b^2+c^2-ab-bc-ca=(a+b+c{)}^2-3(ab+bc+ca)$.

Answer: (C) $1800$

Concept: Simplify each bracket, then $\times$ and $÷$ left to right.

1. $\frac{3}{4}+\frac{5}{4}=2$
2. $\frac{9}{5}-\frac{4}{5}=1$
3. $\frac{3}{2}+\frac{1}{2}=2$
4. $2\times 1÷2=1$

Trick: Each bracket gives a whole number – no LCM needed.

Answer: (A) $1$

Concept: SP $=\text{MP}\times (1-d_1)(1-d_2)$.

1. SP $=\text{MP}\times 0.76\times 0.70=0.532\text{MP}$
2. $0.532\text{MP}=7700.70$
3. MP $=\frac{7700.70}{0.532}=14475$

Trick: Option check: $14475\times 0.532=7700.70$ ✔

Answer: (C) ₹14475

Concept: Transverse (direct-crossing) common tangent $=\sqrt{d^2-(r_1+r_2{)}^2}$.

1. $d=13$, $r_1+r_2=5$
2. $\sqrt{169-25}=\sqrt{144}=12\text{cm}$

Yaad rakhein: Transverse uses $(r_1+r_2)$; direct common tangent uses $(r_1-r_2)$.

Answer: (D) $12\text{cm}$

Concept: $\%\text{ increase}=\frac{\text{increase}}{\text{old value}}\times 100$.

1. 2019: $32$ lakh, 2020: $34$ lakh
2. Increase $=2$
3. $\frac{2}{32}\times 100=6.25\%=6\frac{1}{4}\%$

Trick: $\frac{1}{16}=6.25\%$.

Answer: (A) $6\frac{1}{4}\%$

Concept: Remainder on dividing $p(x)$ by $(x-5)$ is $p(5)$; add its negative.

1. $p(5)=125-75+20-75=-5$
2. Add $5$ to make remainder $0$

Trick: Remainder $-5$ → add $+5$.

Answer: (D) $5$

Concept: Start with $D=100$ and move up the chain.

1. $C=120$
2. $B=120\times 0.7=84$
3. $A=84\times 1.25=105$
4. A is $5\%$ more than D

Trick: $1.2\times 0.7\times 1.25=1.05$.

Answer: (A) $5\%$

Concept: Volume of cone $=\frac{1}{3}\pi r^{2}h$.

1. $\frac{1}{3}\times \frac{22}{7}\times 7^2\times 9$
2. $=22\times 7\times 3=462$ cubic ft

Trick: Cone is one third of the cylinder: $\frac{1386}{3}=462$ (1386 is the cylinder trap).

Answer: (B) $462$ cubic ft.

Concept: Lateral (curved) surface area of a cone $=\pi rl$.

1. $\frac{22}{7}\times r\times 4.2=13.2$
2. $13.2r=13.2\Rightarrow r=1$

Trick: $\frac{22}{7}\times 4.2=13.2$ exactly, so $r=1$.

Answer: (D) 1 unit

Concept: The verb ask takes the preposition for when we request something: ask somebody for something.

1. 'When Ramu was working' – past continuous, correct.
2. 'as a clerk' – correct use of 'as' for a role.
3. 'he asked me money' – the object 'money' needs 'for': he asked me for money.

Yaad rakhein: ask for (request) money/help/permission; ask a question (no 'for').

Answer: (D) he asked me money

Concept: A lagoon is a stretch of salt water separated from the sea by a low sandbank, rocks or a coral reef.

1. The description 'saltwater lake separated from the sea by rocks and sand' exactly defines a lagoon.
2. A river flows (fresh water); a ditch is a narrow trench; the sea is not separated from itself.

Yaad rakhein: Lagoon = sea-water lake behind a sand bar, e.g. Chilika Lake (Odisha).

Answer: (A) lagoon

Concept: The correct spelling is Bureaucracy (bu-reau-cra-cy), from French bureau (office) + -cracy (rule).

1. Rhinoceros, Acquaintance and Miscellaneous are spelt correctly.
2. 'Bueraucracy' swaps the letters: it must be bu-REAU, not bu-ERAU.

Trick: Think of 'bureau' (a desk/office) + 'cracy' → bureaucracy.

Answer: (B) Bueraucracy

Concept: Choose 'a/an' by the first sound, not the first letter. 'SDO' is read 'es-dee-o' – it begins with a vowel sound.

1. Blank 1: 'es' starts with a vowel sound → An SDO.
2. Blank 2: 'government' starts with the consonant sound /g/ → a government organisation.
3. So: 'An SDO is the head of the sub-division of a government organisation.'

Trick: Abbreviations like MLA, SDO, FIR, MP take 'an' because the letter name starts with a vowel sound.

Answer: (D) an; a

Concept: Conundrum means a confusing and difficult problem or question.

1. Looking after small children while working is a difficult problem for parents.
2. Peace, plan and pacification (calming) do not mean a puzzle or difficulty.

Yaad rakhein: Conundrum = puzzle / riddle / dilemma / problem.

Answer: (C) problem

Concept: The correct spelling is Withering (wither + -ing), meaning drying up or fading.

1. Notation, Gallantry and Vagabond are spelt correctly.
2. The base verb is 'wither' with an e, so the -ing form is withering, not 'witharing'.

Trick: Keep the root unchanged: wither → withering, like gather → gathering.

Answer: (B) Witharing

Concept: Before a word beginning with a vowel sound we use an, not 'a'.

1. 'international' begins with the vowel sound /ɪ/.
2. So 'a international' must be 'an international'.
3. Correct sentence: Mrs. Rani works for an international school.

Yaad rakhein: a + consonant sound, an + vowel sound (an apple, an hour, an international).

Answer: (C) a international

Concept: After the possessive 'His' and before 'of' we need a noun. 'Interpretation' (noun) is replaced by the noun/gerund understanding.

1. 'His understands', 'his understand', 'his understood' are verb forms – they cannot follow 'His' here.
2. 'Understanding of realities' = interpretation of the facts → 'His understanding of realities was impressive.'

Trick: Possessive (his/her/my) + noun + of … – pick the option that is a noun.

Answer: (D) understanding of realities

Concept: Nip in the bud = to stop something (usually bad) at an early stage, before it develops.

1. A bud is a flower before it opens; nipping it stops the flower from ever growing.
2. E.g. The police nipped the riot in the bud.
3. Option B talks about stopping something 'beyond limit' – the idea of the early stage is missing.

Yaad rakhein: Bud = beginning stage → nip in the bud = kill it at the start.

Answer: (D) To suppress something at an early stage

Concept: Future continuous tense = will be + V-ing. A modal + be is never followed by the base verb.

1. 'I will be drive' is wrong – it should be 'I will be driving'.
2. B (will be driving), C (might drive) and D (could be driving) are all grammatically correct.

Trick: will be / could be / might be → always V-ing after 'be'.

Answer: (A) I will be drive into town later on.