JIPMAT 2021 · Question Paper & Solutions

Floor area $\pi r^2=346.5\Rightarrow r^2=346.5\times \frac{7}{22}=110.25$, so $r=10.5$ m.

Slant height $l=\sqrt{14^2+10.5^2}=\sqrt{306.25}=17.5$ m.

Canvas area = curved surface $=\pi rl=\frac{22}{7}\times 10.5\times 17.5=577.5$ m².

Length $=\frac{577.5}{1.1}=525$ m.

Total age $=11\times 28=308$.

The three groups total $3(25+28+30)=249$, so the remaining two players (captain and youngest) total $308-249=59$.

$C+Y=59$ and $C-Y=11\Rightarrow C=35$ years.

$$\theta =\left|30H-\frac{11}{2}M\right|=\left|30(5)-5.5(15)\right|=|150-82.5|=67.5^{\circ }$$

Price $=40R$, annual income $=R$.

Rate $=\frac{R}{40R}\times 100=2.5\%$.

Diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs 20 and 15:

$$s=\sqrt{20^2+15^2}=25\text{ m}$$

Perimeter $=4\times 25=100$ m.

$$\text{HCF of fractions}=\frac{\text{HCF of numerators}}{\text{LCM of denominators}}$$

HCF$(9,12,18,21)=3$.

LCM$(10,25,35,40)=2^3\times 5^2\times 7=1400$.

HCF $=\frac{3}{1400}$.

Rule: multiply by $k$ and add $k$ for $k=1,2,3,\dots$

• $15\times 1+1=16$
• $16\times 2+2=34$
• $34\times 3+3=105$
• $105\times 4+4=424$
• $424\times 5+5=2125$ (not 2124)
• $2125\times 6+6=12756$ ✓

The last term confirms 2125 was intended, so 2124 is the odd term.

Let the pole be $L$. In mud: $\frac{4}{7}L$. Pulling out $\frac{1}{3}L$ leaves

$$\frac{4}{7}L-\frac{1}{3}L=\frac{12-7}{21}L=\frac{5}{21}L=250$$

$L=250\times \frac{21}{5}=1050$ cm.

Management share for A $=10\%$ of 9600 $=960$.

Remaining $8640$ is split in $12000:20000=3:5$, so A gets $\frac{3}{8}\times 8640=3240$.

A's total $=960+3240=\text{Rs. }4200$.

Let filling rate $=f$ m³/min. Then

$$\frac{2400}{f}-\frac{2400}{f+10}=8\Rightarrow \frac{24000}{f(f+10)}=8\Rightarrow f^2+10f-3000=0$$

$(f+60)(f-50)=0\Rightarrow f=50$ m³/min.

Check: $2400/50=48$ min, $2400/60=40$ min, difference 8 ✓.

Rationalise: $\frac{1}{\sqrt{n+1}-\sqrt{n}}=\sqrt{n+1}+\sqrt{n}$.

$$(3+\sqrt{8})-(\sqrt{8}+\sqrt{7})+(\sqrt{7}+\sqrt{6})-(\sqrt{6}+\sqrt{5})+(\sqrt{5}+2)$$

All surds cancel, leaving $3+2=5$.

Let maximum marks $=T$. Pass mark is the same in both cases:

$$0.25T+30=0.5T-20\Rightarrow 0.25T=50\Rightarrow T=200$$

Pass mark $=50+30=80$, i.e. $\frac{80}{200}=40\%$.

Take the first sum as 130 units, so the second is 260 units (130 is divisible by both $4+3+2+1=10$ and $5+6+7+8=26$).

• First (4:3:2:1 of 130): Naresh 52, Vipin 39, Bhupesh 26, Yogesh 13
• Second (5:6:7:8 of 260, each part 10): Naresh 50, Vipin 60, Bhupesh 70, Yogesh 80

Totals: Naresh 102, Vipin 99, Bhupesh 96, Yogesh 93. Naresh receives the most.

The line through $(-2,6)$ and $(3,1)$ has slope $\frac{1-6}{3+2}=-1$, so its equation is $y=-x+4$.

$(t,2t)$ lies on it: $2t=-t+4\Rightarrow t=\frac{4}{3}$.

$$a^2-b^2=(a-b)(a+b)=(10)(41.464)=414.64$$

Total work $=100\times 35+200\times 5=4500$ man-days.

With only 100 men: $\frac{4500}{100}=45$ days, i.e. $45-40=5$ days behind schedule.

Let daily work of a man $=m$, a woman $=w$.

$$4m+6w=\frac{1}{8},3m+7w=\frac{1}{10}$$

Multiply the first by 3 and the second by 4: $12m+18w=\frac{3}{8}$, $12m+28w=\frac{2}{5}$.

Subtract: $10w=\frac{2}{5}-\frac{3}{8}=\frac{1}{40}$.

So 10 women do $\frac{1}{40}$ of the job per day and need 40 days.

$6\frac{18}{47}\%=\frac{300}{47}\%$. If he gives $w$ g for 1000 g:

$$\frac{1000-w}{w}=\frac{300}{47\times 100}=\frac{3}{47}\Rightarrow 47000-47w=3w\Rightarrow w=940\text{ g}$$

Check: $\frac{60}{940}=\frac{3}{47}=6\frac{18}{47}\%$ ✓.

Let still-water speed $=x$ km/h.

$$\frac{20}{x-2}+\frac{20}{x+2}=\frac{110}{60}=\frac{11}{6}\Rightarrow \frac{40x}{x^2-4}=\frac{11}{6}$$

$11x^2-240x-44=0\Rightarrow x=\frac{240+244}{22}=22$ km/h.

Check: $\frac{20}{20}+\frac{20}{24}=1\frac{5}{6}$ h $=110$ min ✓.

Number $=10a+b$ with $a+b=8$.

$10a+b+18=10b+a\Rightarrow 9(b-a)=18\Rightarrow b-a=2$.

So $a=3,b=5$: the number is 35 (and $35+18=53$ ✓).

90 km/h $=25$ m/s, so train + bridge $=25\times 36=900$ m.

Second train + bridge $=900-100=800$ m, at 45 km/h $=12.5$ m/s.

Time $=\frac{800}{12.5}=64$ s.

Let the initial number be $x$.

After station 1: $\frac{2x}{3}+280$.

After station 2: $\frac{1}{2}\left(\frac{2x}{3}+280\right)+12=\frac{x}{3}+152=248$.

$\frac{x}{3}=96\Rightarrow x=288$.

Alcohol $=35$ g; new total $=125$ g.

$$\frac{35}{125}\times 100=28\%$$

Outer radius $0.06$ m, inner radius $0.05$ m, length 4 m.

$$V=\pi (0.06^2-0.05^2)\times 4=\pi \times 0.0044\approx 0.013823{\text{ m}}^3$$

Iron's density is about 7800 kg/m³ (the printed "7.800 kg" is 7,800 written with a thousands point), so

$$\text{Weight}\approx 0.013823\times 7800\approx 107.8\text{ kg}\approx 108\text{ kg}$$

This matches option A. The official key, however, lists E, which is not a printed option. That usually means the question was dropped or treated as having no valid option, most likely because of the ambiguous "7.800 kg" (read literally it gives about 0.108 kg, which matches nothing).

Units digits of powers of 7 cycle with period 4: $7,9,3,1$.

• $95=4\times 23+3\Rightarrow 7^{95}$ ends in 3
• $58=4\times 14+2\Rightarrow 7^{58}$ ends in 9

Since $7^{95}>7^{58}$, borrow: $13-9=4$. The units digit is 4.

$a+(m-1)d=\frac{1}{n}$ and $a+(n-1)d=\frac{1}{m}$.

Subtract: $(m-n)d=\frac{1}{n}-\frac{1}{m}=\frac{m-n}{mn}\Rightarrow d=\frac{1}{mn}$.

Then $a=\frac{1}{n}-\frac{m-1}{mn}=\frac{1}{mn}$.

$$T_{mn}=a+(mn-1)d=\frac{1}{mn}+\frac{mn-1}{mn}=1$$

$(1+r{)}^2=1.44\Rightarrow 1+r=1.2\Rightarrow r=20\%$.

Doubling at simple interest needs interest $=100\%$ of principal: $\frac{100}{20}=5$ years.

Extend BD to meet the larger circle at E (as in the figure).

• $OD\perp BE$ (radius ⟂ tangent), so $BD=\sqrt{13^2-8^2}=\sqrt{105}$. A perpendicular from the centre bisects the chord, so $DE=\sqrt{105}$.
• AB is a diameter, so $\angle AEB=90^{\circ }$.
• O and D are midpoints of BA and BE, so $AE=2\cdot OD=16$ (midpoint theorem).

In right triangle ADE:

$$AD=\sqrt{A{E}^2+D{E}^2}=\sqrt{256+105}=\sqrt{361}=19\text{ cm}$$

Write the area two ways:

$$\frac{1}{2}ab=\frac{1}{2}cp\Rightarrow cp=ab$$

$$2{\sin }^2\theta +3{\cos }^2\theta =2({\sin }^2\theta +{\cos }^2\theta )+{\cos }^2\theta =2+{\cos }^2\theta$$

Since ${\cos }^2\theta \ge 0$, the minimum is 2 (at $\theta =90^{\circ }$).

Let speed $=s$, distance $=d$.

$\frac{d}{s}-\frac{d}{s+4}=\frac{1}{2}\Rightarrow d=\frac{s(s+4)}{8}$

$\frac{d}{s-2}-\frac{d}{s}=\frac{1}{3}\Rightarrow d=\frac{s(s-2)}{6}$

Equate: $6(s+4)=8(s-2)\Rightarrow s=20$ km/h, so $d=\frac{20\times 24}{8}=60$ km.

Check: $3$ h at 20, $2.5$ h at 24, $3\frac{1}{3}$ h at 18 ✓.

Let the course be $L$. When A finishes, B has run $L-15$ and C has run $L-29$, so speed ratio $C:B=(L-29):(L-15)$.

When B runs $L$, C runs $L-15$, so $C:B=(L-15):L$.

$$\frac{L-29}{L-15}=\frac{L-15}{L}\Rightarrow L^2-29L=L^2-30L+225\Rightarrow L=225\text{ m}$$

Let $2^x=3^y=6^{-z}=k$ (with $k\ne 1$). Then

$$2=k^{1/x},3=k^{1/y},6=k^{-1/z}$$

Since $2\times 3=6$: $k^{1/x+1/y}=k^{-1/z}\Rightarrow \frac{1}{x}+\frac{1}{y}=-\frac{1}{z}$.

Hence $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$.

Differences alternate in sign and double: $+2,-4,+8,-16,+32$.

Next difference is $-64$: $39-64=-25$.

Each letter moves forward 6 places (wrapping Z → A):

• First letters: M(13) → S(19) → Y(25) → E(31 − 26 = 5)
• Second letters: O → U → A → G
• Third letters: Q → W → C → I

Within each term letters also step by 2 (E, G, I). Answer: EGI.

Filling with b, c, b, a gives

$$\text{abc}\mid \text{cba}\mid \text{bca}\mid \text{acb}$$

The blocks come in mirror pairs: cba is abc reversed, and acb is bca reversed. Each block is also a permutation of a, b, c.

The other options break this. For example, abcc gives "aac bba cca ccb", with repeated letters inside blocks.

$210=14\times 15$ and $380=19\times 20$, i.e. $n(n+1)\to (n+5)(n+6)$.

$182=13\times 14\Rightarrow 18\times 19=342$.

(Equivalently $210=15^2-15$, $380=20^2-20$; $182=14^2-14\to 19^2-19=342$.)

A drill is the tool used to bore (make holes). A sieve is the tool used to sift.

• *Pry* is done with a lever.
• *Rinse* is done with water.
• *Thresh* is done with a flail or thresher.

So the tool–function relationship gives Sift.

Check the day of the week each month begins on:

• 1 February 2021: Monday
• 1 March 2021: Monday (February 2021 has 28 days, exactly 4 weeks)
• 1 November 2021: Monday
• 1 December 2021: Wednesday

Three months start on Monday. December 2021 is the odd one.

With 3 colours and no two adjacent faces alike, each colour occupies a pair of opposite faces. Take red as top and bottom.

32 small + 4 big = 36 pieces fits a $4\times 4\times 4$ division: $4\times 8+32=64$ unit cubes, with each big cube being $2\times 2\times 2$.

The big cubes have no red face, so they fill the two middle layers (as four $2\times 2\times 2$ blocks). The 32 small cubes form the top and bottom layers of 16 each.

• In each $4\times 4$ red layer, only the central $2\times 2=4$ cubes have exactly one coloured face (red). Edge cubes also show blue or green.
• Each big cube sits at a corner of the middle layers and shows two faces (one blue, one green).

Cubes with only one side coloured $=4+4=8$.

MIRACULOUS contains M, I, R, A, C, U, L, O, U, S.

• LOCUS: L, O, C, U, S ✓
• MOLAR: M, O, L, A, R ✓
• SCAR: S, C, A, R ✓
• SOLACE needs an E, which MIRACULOUS lacks ✗

Substitute the symbols:

$$36-12÷4+6÷2\times 3$$

Apply BODMAS: $12÷4=3$ and $6÷2\times 3=9$.

$$36-3+9=42$$

Chain: $E<L=R<V\le F$, so $F>E$. Conclusion I is true.

For II, H connects to the rest only through $H>P\le E$. Since P is at most E, nothing fixes H relative to E, L or R. Conclusion II does not follow.

Only conclusion I is true.

• Games: A and B play football, D boxes, and the remaining friend C is the cricketer. That is 3 games.
• Subjects: C studies chemistry and biology. A and B both study mathematics, and one of them also studies physics. D studies mathematics and accounts.

Distinct subjects named: mathematics, physics, chemistry, biology, accounts, a total of 5. The second footballer's other subject must come from this set, since no sixth subject is mentioned and no option allows more.

Answer: 3 games and 5 subjects.

Q, P and R are siblings. S is R's daughter and T (S's brother) is R's son.

So R's children S and T are Q's niece and nephew. Strictly, only S is a niece and T is a nephew, but the question uses "niece" loosely for both.

The other options fail. P is Q's sister, and R is Q's sibling. Q cannot be his own niece.

The only option naming R's children is S and T.

'Flowers' appears in 'sik hee' and 'pee mit hee'. The common code word is hee, so hee = flowers.

In 'sik hee' = 'red flowers', the other word gives sik = red.

(Also, 'pee' = 'are' from the first and third codes.)

Track her facing direction:

• Walks south 10 m.
• Turns left: facing east, walks 20 m.
• Turns right: facing south, walks 20 m.
• Turns right: facing west, walks 20 m.
• Turns right: facing north, walks 10 m.

She is moving North.

Some tall men are Indian and some are not. Some Indians are black-haired and some are not. Some tall men are black-haired and some are not. A person can also be all three.

So each pair overlaps partially, with a common region for all three. Three mutually intersecting circles show this, which is figure D.

• A (nested circles) wrongly makes one class a subset of another.
• B wrongly makes one class disjoint from the others.
• C wrongly puts two classes inside the third.

Chandrika's rank from the top $=26-8=18$.

Rank from the bottom $=42-18+1=25$th.

Count days from 6 March to 15 August 2014:

March (after the 6th) 25 + April 30 + May 31 + June 30 + July 31 + August 15 $=162$ days.

$162=7\times 23+1$, so 15 August is 1 day of the week after 6 March.

6 March $=$ Friday $-1$ day $=$ Thursday. (The calendar confirms 6 March 2014 was a Thursday.)

Positions: C1 R2 E3 A4 T5 I6 V7 E8. A pair qualifies when the gap in positions equals the gap in the alphabet.

• C–E (positions 1, 3): gap 2; C→E is 2 ✓
• T–V (positions 5, 7): gap 2; T→V is 2 ✓
• A–E (positions 4, 8): gap 4; A→E is 4 ✓

Checking every other pair (in both directions) gives no more matches. Total: Three.

Check each digit's neighbours:

• 7: B 7 C, letter on both sides ✓
• 9: D 9 Z, letter on both sides ✓
• 3: S 3 ↑, followed by a symbol ✗
• 5: ↑ 5 N, preceded by a symbol ✗

Count: Two.

A meeting or seminar unfolds as follows:

1. Arrival (C)
2. Introduction (E)
3. Presentation (A)
4. Discussion (D)
5. Recommendation (B)

The sequence is C, E, A, D, B. Option B puts recommendation before presentation, and option D has introductions before arrival. Both are illogical.

• I: $a\in \{9,10\}$, and b is unknown, so not sufficient.
• II: $b\in \{8,9\}$, and a is unknown, so not sufficient.
• Together: $a+b\in \{17,18,19\}$. For example, $9+8=17$ is odd, but $9+9=18$ is even.

Even both statements together are not sufficient.

From the pie chart, D (labour) $=100-(49+39.5+11)=0.5\%$.

Current labour cost $=0.5\%\times 120=0.6$ lakh.

Increase $=2.4-0.6=1.8$ lakh, so

$$\frac{1.8}{0.6}\times 100=300\%$$

(400% is the tempting trap. It is the new cost as a percentage of the old, not the increase.)

The statements only say that the women politicians cannot vote. Nothing is said about men or about politicians who are not women.

• I ("male politicians can vote") is not implied. It adds new information.
• II ("some politicians can vote") is not implied either. What does follow is "some politicians cannot vote".

Neither conclusion follows.

Positions: S1 O2 L3 U4 T5 I6 O7 N8. Pairs whose position gap equals their alphabet gap:

• U–T (positions 4, 5): adjacent in both ✓
• O–N (positions 7, 8): adjacent in both ✓
• L–I (positions 3, 6): gap 3; I→L is 3 ✓

No other pair matches. Total: Three.

• A is true: a breaking bulb pops audibly.
• R is false: a bulb holds a vacuum or low-pressure inert gas. When it breaks, outside air rushes in to fill the low-pressure space, and that inrush makes the bang. Air does not rush out.

Answer: A is true but R is false.

Let there be $s$ sons and $d$ daughters.

• A daughter has $s$ brothers and $d-1$ sisters: $s=d-1$.
• A son has $d$ sisters and $s-1$ brothers: $d=2(s-1)$.

Substitute: $s+1=2s-2\Rightarrow s=3$, $d=4$.

Check: a daughter has 3 brothers and 3 sisters; a son has 4 sisters and 2 brothers ✓.

Read each number's region from the figure. History is the top-centre circle and Science the bottom circle; Mathematics and Geography overlap in a narrow central lens.

• History: $16+14+13+12+20+18+18+13=124$
• Science: $19+15+13+16+20+18+18=119$
• Mathematics: $9+14+13+20+18+15=89$
• Geography: $9+12+13+20+18+16=88$

Here the upper 13 is Maths ∩ History ∩ Geography, the lower 13 is History ∩ Science, and 20 lies in all four circles.

History has the most students (124).

Place A at $(0,0)$ with east as $+x$ and north as $+y$.

• F is 2 km north of A: $(0,2)$
• C is 1 km west of A: $(-1,0)$
• G is 2 km east of C: $(1,0)$
• D is 2 km south of G: $(1,-2)$
• E is 2 km west of B, with D their midpoint: $B=(2,-2)$, $E=(0,-2)$ (consistent)

$$DF=\sqrt{(1-0{)}^2+(-2-2{)}^2}=\sqrt{1+16}=\sqrt{17}\text{ km}$$

$(63,49,35)=(7\times 9,7\times 7,7\times 5)$: a common factor times 9, 7, 5.

$(81,63,45)=(9\times 9,9\times 7,9\times 5)$ has the same structure.

• $(72,48,24)=24\times (3,2,1)$ does not.
• $(72,40,24)$ and $(64,40,28)$ have no such common pattern.

Pink is obtained by mixing red and white, so the first colour is the mix of the other two.

Green is obtained by mixing blue and yellow, which is the same relationship.

• Brown is not made from black and blue.
• Orange comes from red and yellow, not yellow and black.
• Yellow is not made from red and green in paint mixing.

A gale is a very strong, intense wind, so the second word is a higher degree of the first.

Passion is intense love, which is the same "mild → intense" relationship.

• Disaster : Calamity are near-synonyms of similar intensity.
• Disgust : Infatuation are unrelated or opposite feelings.
• Storm : Sea is a thing and its location.

Digit sums:

• $5+6+9+8=28$
• $7+8+9+4=28$
• $8+7+9+3=27$
• $9+8+6+5=28$

Only 8793 has a digit sum different from 28.

Letter positions and steps:

• BdEg: 2, 4, 5, 7, so steps +2, +1, +2
• KmNp: 11, 13, 14, 16, so steps +2, +1, +2
• PrSu: 16, 18, 19, 21, so steps +2, +1, +2
• TwXz: 20, 23, 24, 26, so steps +3, +1, +2

TwXz breaks the pattern.

The passage blames fossil-fuel depletion, air and water pollution, and deforestation directly on unplanned use of resources. The situation in which they would not occur is therefore the opposite: planned use.

• Improper, over-use and unplanned use are all versions of the cause the passage names, so they cannot be where the problems "never occur".

*Venerate* means to regard with great respect or reverence, so Respect is the synonym.

Abuse, accuse and defame all imply disrespect, the opposite sense.

*Audacious* means bold, daring or fearless. Its opposite is Cowardly.

• *Manifest* and *obvious* mean clear or evident, which is unrelated.
• *Venture* (to dare) is closer to a synonym.

The standard idiom is "What is the time by your watch?", where *by* means "according to".

"On/in/with your watch" are not idiomatic in this sense. (Informally people may say "on your watch", but the grammar-book answer is *by*.)

Fit works in both:

• "not fit for his position" (suitable)
• "in a fit of anger" (a sudden outburst)

*Capable* and *qualified* can fill sentence A but not B, and *true* fits neither.

A cosmopolitan is a citizen of the world, at ease in any country.

• A *citizen* belongs to one state.
• A *denizen* is an inhabitant of a particular place.
• *Metropolitan* relates to a big city.

To be under a cloud is to be under suspicion or in disgrace, which fits "alleged involvement in espionage".

• *Under observation* is close but weaker: the idiom implies suspicion or discredit, not merely being watched.
• *Cloudy weather* is the literal trap.
• *Favourable luck* is the opposite.

A trifle is a thing of little value or importance.

• *Useless* is an adjective meaning of no use, not a noun for an unimportant thing.
• *Twinkling* means an instant.
• *Vague* means unclear.

The correct spelling is VIOLENCE (viol-ence, from *violent*).

VIOLANCE, VOILANCE and VAILANCE all misspell it.

*Drank* is simple past, so the passive is was + past participle. The past participle of *drink* is *drunk*.

"All the milk was drunk by the cat."

• *Had been drunk* is past perfect and *has been drunk* is present perfect, so both change the tense.
• *Was drank* wrongly uses the past-tense form.

In reported speech after a past reporting verb, *must* (obligation) becomes had to, and *I* becomes *he*:

"He said that he had to go at once."

• "had gone" wrongly changes the meaning to a completed action.
• "asked to go" changes the verb.
• "told if" is ungrammatical.

"Welcome to the ceremony" is a present-time greeting (short for "You are welcome" or "We welcome you"). It uses the simple base form, so it is present indefinite (simple present).

There is no *had*, *has/have* or past form, which rules out past indefinite, past perfect and present perfect.

V, I, III, VI, IV, II gives "Is it not what you wanted?", a natural, grammatical question.

• Option C ("What is wanted it not you") and option D ("What is not you it wanted") are meaningless.
• Option B ("What you wanted is it not") is awkward and not standard English.

A man is a single unit, and humanity is the whole made up of such units (individual : collective).

A drop is a single unit of the ocean in the same way.

• Flower : Fragrance is a thing and what it gives off.
• Frame : Picture is a holder and what it holds.
• Scholar : Books is a user and the things used.

• R ("and this for the simple reason") opens and needs a clause to follow.
• Q ("that in a democratic set-up like India,") supplies the *that* clause giving the reason.
• S ("majority communalism can acquire power") gives that clause its subject and verb.
• P ("far beyond that any minority communalism can") completes the comparison begun by "acquire power".

R-Q-S-P reads: "and this for the simple reason that in a democratic set-up like India, majority communalism can acquire power far beyond that any minority communalism can."

Option A (QRSP) leaves "and this for the simple reason" dangling in the middle.

The relative pronoun *who* refers to its antecedent those, which is plural, so the verb must be plural: "one of those who are so foolish".

The error is in "who is". "She is not", "one of" and "so foolish" are correct.

• "agreed in principle" means agreed in general terms.
• "the principle of Archimedes" is a scientific law.

*Basis* fits only II ("on the basis of"), and "in basis" is not idiomatic. *General* and *view* fail II.

The passage opens by saying each protein type is specific to its function. It then groups proteins by what they do: strength and elasticity, oxygen binding, setting and foaming, and directing reactions as enzymes.

• It never counts molecules.
• Body location is mentioned only incidentally.
• Names are merely examples.

So proteins are classified according to their functions.

• Danger : Peril are synonyms ✓
• Infringe : Break are synonyms (e.g. break or infringe a rule) ✓
• Luxury : Pleasure are closely related (indulgent comfort) ✓
• Indulge : Deny are opposites (to allow yourself something vs to refuse it) ✗

So Indulge : Deny is the wrong pair.

• Excitable : Calm are opposites ✓
• Numb : Active are opposites (deadened, inert vs lively) ✓
• Obnoxious : Free are opposites in the older sense of *obnoxious*, "liable or exposed to" (as in "obnoxious to punishment"), whose opposite is *free (from)* or exempt ✓
• Exquisite : Delicate are similar in meaning (finely made, beautiful), not opposite ✗

The pair that is not antonymous is Exquisite : Delicate.

Use for with a *period* of time ("for a long time", "for three days"). Use since with a *point* in time ("since Monday").

"A long time" is a duration, so for is correct. *By* and *from* do not fit.

*Frightened* takes the preposition of before a gerund: "frightened of being killed".

• "Frightened to be killed" is unidiomatic.
• "for/from being killed" are wrong prepositions.

Amnesty is an official general pardon, typically for political offences.

• *Pardon* is too general: it can be individual and for any crime.
• *Excuse* and *honesty* are unrelated.

To be all at sea is to be confused or bewildered, not knowing what to do. That is puzzled.

Happy, sad and triumphant describe emotions, not confusion.

By fits and starts means in short, irregular bursts rather than steadily, i.e. irregularly.

• *Regularly* is the opposite.
• *Rarely* is about frequency, not unevenness.
• *Disinterestedly* means impartially.

The correct spelling is CURRICULAR (from *curriculum*), so CURRICULER is misspelt.

DIAGNOSIS, DIFFICULTIES and ESSENTIALLY are all spelt correctly.

*Who* (subject) becomes by whom in the passive, the object *it* becomes the subject, and the simple past *wrote* becomes was written:

"By whom was it written?"

• Options A and B use *who* instead of the object form *whom*, and they change the tense.
• Option C adds a modal (*might*) that changes the meaning.

The reporting verb *says* is in the present, so the tense inside stays the same, *is* → *am*. The pronoun *he* returns to *I*.

"He says, 'I am very sorry'."

• Options A and B change *says* to *said*.
• Option D alters both the verb and the tense.

The structure *shall/will + be + verb-ing* ("shall be reaching") is the future continuous tense.

• Future indefinite would be "shall reach".
• Future perfect continuous would be "shall have been reaching".
• Present continuous would be "is reaching".

IV, II, VI, III, V, I gives "There are three routes of development.", a grammatical sentence.

• Option A ("routes of development are there three") and option B are scrambled.
• Option D ("three are there routes of development") is ungrammatical.

*Liquefy* means to turn into liquid. *Petrify* means to turn into stone, i.e. make solid. The pair shows opposite changes of state.

Melt : Freeze matches: solid → liquid vs liquid → solid.

• *Soften : Frighten* is a trap built on petrify's figurative sense, "terrify".
• *Blend : Separate* are opposites but not changes of physical state.
• *Cash : Invest* is unrelated.

• S ("the only hopeful sign in such a situation") is the subject.
• Q ("is that there is an increasing tendency") gives the verb and the *that* clause.
• P ("among ordinary people to see health as a") continues "tendency".
• R ("right and responsibility") completes "see health as a …".

S-Q-P-R reads as one sentence. Option D (S, Q, R, P) puts "right and responsibility" before the phrase it completes.

The subject is Mr. Gupta (singular). A phrase like "accompanied by his secretary" does not make the subject plural, so the verb should be has arrived.

The error is "have". "Accompanied", "his secretary" and "at the office" are correct.

Still fits both:

• "sat still" means without moving.
• "We have still to receive the documents" means we have yet to receive them.

*Quiet* or *quietly* can fit sentence I but make no sense in II. *Out* makes no sense in II ("We have out to receive").