IPMAT Rohtak 2020 · Question Paper & Solutions

Taking simple interest (the usual reading when the type is not stated), the interest for one year is the difference of the two amounts:

$$920-800=120\text{ per year}$$

Interest for 2 years $=240$, so the principal is

$$P=800-240=560$$

Check: rate $=\frac{120}{560}\times 100\approx 21.4\%$; $560+3(120)=920$. ✓

Let the amount in A be $x$, so B gets $13900-x$. Two-year interest:

$$0.28x+0.22(13900-x)=3508$$

$$0.06x+3058=3508\Rightarrow x=7500$$

Amount in B $=13900-7500=6400$.

Check: $7500\times 0.28+6400\times 0.22=2100+1408=3508$. ✓

$316^2=99856$, leaving $99999-99856=143$. Using $\sqrt{a^2+b}\approx a+\frac{b}{2a}$:

$$\sqrt{99999}\approx 316+\frac{143}{632}\approx 316.2263$$

A calculator gives $\sqrt{99999}=316.22618\dots$

• Rounded to two decimals: 316.23 (option A) — the correct answer.
• Truncated to two decimals: 316.22 (option B), which is what the official key gives.

Truncation is not rounding: 316.22618 is nearer to 316.23 than to 316.22, so A is right.

$38^3=54872$. Checking nearby values:

• $38.15^3=55524.37$
• $38.155^3=55546.20$
• $38.16^3=55568.04$

Since $55546.20<55555<55568.04$, the cube root lies between 38.155 and 38.16; precisely $\sqrt[3]{55555}=38.15701\dots$

• Rounded to two decimals: 38.16 (option B) — the correct answer.
• Truncated to two decimals: 38.15 (option C), which is what the official key gives.

The key truncates here too, exactly as in Q3.

Non-defective output from each machine, as a share of total production:

$$0.20(0.97)+0.15(0.93)+0.32(0.98)=0.194+0.1395+0.3136=0.6471$$

That is about 64.7%. The closest option is 64% (D); no other option is near.

Note that the three machine shares add up to only $67\%$, so the data is flawed. If the shares were rescaled to 100%, the non-defective share would be $0.6471/0.67\approx 96.6\%$, which is not an option either. The key's 64% only works with the shares taken as printed, and even then it is approximate.

Pandey takes $\frac{1000}{4}=250$ s for the race.

To find Koustab's margin over Pandey, we need Koustab's time or speed. The only information about Koustab is that he loses to Rishi by 50 m, and Rishi's speed or time is never given. So Koustab's time cannot be found, and the question cannot be answered from the data given.

The printed options have no units and are not tied to any stated data. The official key's answer is E, which is not one of the four options. This is best read as "cannot be determined" or a dropped question.

When moving in the same direction, they meet again once the faster walker has gained one full lap on the slower one.

Relative speed $=5-4=1$ km/h.

$$\text{Time}=\frac{115}{1}=115\text{ hours}$$

Check: in 115 h Chela walks 575 km (5 laps) and Guru 460 km (4 laps), so both are back at the start. ✓

Distinct objects into identical non-empty boxes means splitting the 5 racquets into 3 unlabelled groups. The group sizes can be:

• 3, 1, 1: choose the group of 3 in $\left(\genfrac{}{}{0ex}{}{5}{3}\right)=10$ ways; the remaining two are singletons. Total 10.
• 2, 2, 1: choose the singleton in 5 ways, then split the remaining 4 into two unordered pairs in $\frac{\left(\genfrac{}{}{0ex}{}{4}{2}\right)}{2}=3$ ways. Total 15.

$$10+15=25$$

This is the Stirling number $S(5,3)=25$. Cross-check: labelled boxes give $3^5-3\cdot 2^5+3=150$, and $150/3!=25$. ✓

In a signpost, the order of symbols matters, so count arrangements of $r$ symbols for $r=1$ to $6$:

$$\sum _{r=1}^6{}^6{P}_r=6+30+120+360+720+720=1956$$

• Identical copies: choose 0–12 Beatles CDs (13 ways) and 0–7 Pink Floyd CDs (8 ways).
• Different CDs: each is in or out, giving $2^3=8$ ways for Michael Jackson and $2^2=4$ for Madonna.

$$13\times 8\times 8\times 4=3328$$

Subtract the one empty selection: $3328-1=3327$.

$$\left(\genfrac{}{}{0ex}{}{20}{16}\right)=\left(\genfrac{}{}{0ex}{}{20}{4}\right)=\frac{20\cdot 19\cdot 18\cdot 17}{24}=\frac{116280}{24}=4845$$

Total ways to draw 3 from 9: $\left(\genfrac{}{}{0ex}{}{9}{3}\right)=84$. Draws with no black shirt (from the 6 non-black): $\left(\genfrac{}{}{0ex}{}{6}{3}\right)=20$.

$$84-20=64$$

Direct check: exactly 1 black $=3\cdot 15=45$; exactly 2 $=3\cdot 6=18$; exactly 3 $=1$. Total $45+18+1=64$. ✓

Circular arrangements of $n$ distinct people: $(n-1)!$.

$$(7-1)!=6!=720$$

Let the original average be $a$. With $459+36=495$ managers the average is $a-1$:

$$495(a-1)-459a=81$$

$$36a-495=81\Rightarrow a=16$$

Original spending $=459\times 16=7344$.

Check: new spending $=495\times 15=7425$, and $7425-7344=81$. ✓

Present total age $=9\times 22=198$. Without LAVGIR, the other 8 total $198-6=192$.

Six years ago (just before his birth), each of those 8 was 6 years younger:

$$192-8\times 6=144$$

Average $=144/8=18$.

In an AP, the average equals the mean of the first and last terms:

$$\frac{\text{shortest}+37}{2}=19\Rightarrow \text{shortest}=1$$

(The question says "weight", but it clearly means height.)

Adding the same amount to every value raises the average by that amount:

$$20000+2000=22000$$

• Mon + Tue + Wed $=3\times 32=96$
• Wed + Thu + Fri + Sat $=4\times 30=120$
• All six days $=6\times 26=156$

Wednesday appears in both groups, so it is counted twice:

$$\text{Wed}=96+120-156=60$$

Mon–Sat total $=6\times 4200=25200$.

Tue–Sun total $=25200-1200+1500=25500$.

$$\text{Average}=\frac{25500}{6}=4250$$

Put the 2 fixed players in the team; the other 3 places are filled from the remaining 8 players:

$$\left(\genfrac{}{}{0ex}{}{8}{3}\right)=56$$

Number the positions 1–8 from left to right. Facing north, "right" means a higher number.

• Yellow is fourth to the right of M, and neither is at an end. So M is at 2 or 3 and yellow at 6 or 7.
• S is two places from yellow and not at an end.
• N is 3 places left of R (violet); T is immediately left of black; O likes brown.

Case M = 3, yellow = 7: this gives the arrangement

$$N(\text{Red}),P(\text{Blue}),M(\text{White}),R(\text{Violet}),S(\text{Pink}),O(\text{Brown}),T(\text{Yellow}),Q(\text{Black})$$

Checks:

• T(7) and violet R(4) have 2 girls between; S(5) and blue P(2) also have 2.
• Red(1)–White(3) and White(3)–Pink(5) each have 1 girl between.
• P(2) is not next to T(7), and S is pink (not red).

Here one girl (P) sits between N and M, which is the official answer.

Caveat: read literally, the clues also allow $O,M,P,S,N,T,Q,R$ (M = 2, yellow = 6). In that line, red, white and pink sit side by side at 3, 4, 5, so the "equal number between" is zero on both sides. That arrangement puts two girls between M and N. The official answer assumes each "number of girls between" is at least one.

In the arrangement from Q21, $N,P,M,R,S,O,T,Q$, T is at position 7. That is fourth to the right of M (position 3), which is exactly where yellow sits, and black Q is immediately to T's right.

The other arrangement that fits a literal reading, $O,M,P,S,N,T,Q,R$, also has T at the yellow seat (position 6, fourth right of M at 2). So T likes yellow either way, and the answer is certain.

• B is the father of Q and R (his only two children), and R is P's daughter, so P is their mother.
• A is P's granddaughter, so A is a child of Q or R.
• S is A's father and is a different person from Q, so A must be R's child and S is R's husband.

The husband of Q's sister is Q's brother-in-law.

Only the front and right faces are visible. Each visible face also rules out its opposite face ($7-x$), which leaves two possible values for the top.

• Die I: front 3, right 6. This rules out 3, 4, 6 and 1, so the top is 2 or 5. Even, so 2.
• Die III: front 6, right 3. This rules out the same numbers, so the top is 2 or 5. Even, so 2.
• Die V: front 1, right 5. This rules out 1, 6, 5 and 2, so the top is 3 or 4. Even, so 4.

$$2+2+4=8$$

Each digit maps to a fixed letter:

• From 15789 → XTZAL: 1→X, 5→T, 7→Z, 8→A, 9→L.
• From 2346 → NPSU: 2→N, 3→P, 4→S, 6→U.

So 2, 3, 5, 4, 9 → N, P, T, S, L = NPTSL.

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

1. 80 m south → $(0,-80)$.
2. Facing south, a right turn faces west; 80 m → $(-80,-80)$.
3. Facing west, a left turn faces south; 60 m → $(-80,-140)$.
4. Facing south, a left turn faces east; 80 m → $(0,-140)$.

He ends directly south of the start, 140 m away.

• II must be true: cats that swim are still cats, and all cats like to run.
• I need not be true: nothing links the swimmers to the cats that look like their masters.
• III is false: every cat runs, and some cats look like their masters, so some runners do look like their masters.

So II only.

• Calvin's 8 is less than Kemp, so Kemp $>8$. (Kemp $>5$ is then automatic.)
• Miller's 15 exceeds Kemp + Rogers, so Kemp $+5<15$ and Kemp $<10$.

The only whole number with $8<\text{Kemp}<10$ is 9.

• P is last, and Q is just before P: positions 3 and 4 are Q and P.
• R is ahead of Q but scored below T, so T is 1st and R is 2nd.

Ranking: T, R, Q, P. The second highest is R.

The terms are products of consecutive integers: $7\cdot 8,8\cdot 9,9\cdot 10,10\cdot 11,11\cdot 12$. The next should be $12\cdot 13=156$.

The gaps confirm it: they are 16, 18, 20, 22, so the next gap should be 24 ($132+24=156$). The 139 is wrong.

Turn each clue into left-to-right order:

• Gourav < Jayant < Bipin
• Bipin < Kavikant < Anurag
• Anurag < Komal < Ramu

These chain into one line:

Gourav, Jayant, Bipin, Kavikant, Anurag, Komal, Ramu

The 4th (middle) boy is Kavikant.

Salman Khan's position from the left is $78-20+1=59$.

Between positions 25 and 59:

$$59-25-1=33$$

Each term is 3 times the previous plus 2:

$12\times 3+2=38$, $38\times 3+2=116$, $116\times 3+2=350$, $350\times 3+2=1052$.

Next: $1052\times 3+2=3158$.

D: $M\times N$ means M is N's father. $N-C$ means N is C's sister, so C is also M's child. $C+F$ means C is F's brother, so C is male. So C is M's son. ✓

Why the others fail:

• A $M-N\times C+F$: M is the sister of N, and N is C's father, so M is C's aunt.
• B $F-C+N\times M$: C is the brother of N, and N is M's father, so C is M's uncle.
• C $N+M-F\times C$: M is the sister of F, and F is C's father, so M is C's aunt.

A person who committed a theft confesses to it. In the same way, a person admits a fault. In both pairs the wrongdoer owns up to a wrong.

• *Murder : Commit* is the act of doing the wrong, not owning up to it.
• *Fight : Dare* and *Mistake : Agree* have no admission relationship.

• II follows: all boats are submarines, and boats exist, so some submarines are boats.
• III follows: the ships that are boats are also submarines, so some submarines are ships.
• I does not follow: the submarines that are yachts need not include any boats.
• IV does not follow: likewise, those yachts need not be ships.

So only II and III follow.

• I follows: nothing rules out a link between WhatsApp and Google. The Google items that are not Twitter could be Facebook, and hence WhatsApp. So the possibility holds.
• II follows: no Twitter is Facebook, and Twitter exists (some Google is Twitter). So those Twitter items can never be Facebook.

So both follow.

Number the positions 1–7 from left to right.

1. Fiat is at one end, and Fargo is fourth to its right, so Fiat must be at the left end: Fiat = 1, Fargo = 5.
2. Cadillac is next to the right of Fargo: Cadillac = 6.
3. Ambassador is third to the right of Fiat: Ambassador = 4.
4. Maruti is between Ambassador and Bedford. Position 5 is taken, so Maruti = 3 and Bedford = 2.
5. The last place goes to Mercedes = 7.

Order: Fiat, Bedford, Maruti, Ambassador, Fargo, Cadillac, Mercedes.

Cadillac (6) is between Fargo and Mercedes.

The order is Fiat, Bedford, Maruti, Ambassador, Fargo, Cadillac, Mercedes (see Q38).

• A is true: Maruti (3) is immediately left of Ambassador (4).
• B is false: Bedford is to the right of Fiat.
• C is false: the ends are Fiat and Mercedes.
• D is false: Fiat is to the left of Maruti.

Replace the letters with operators:

$$(10\times 4)+(4\times 4)-6=40+16-6=50$$

A sedative is taken to bring about or aid sleep. In the same way, a mnemonic is a device that aids memory.

• *Challenging : knowledge*: something challenging does not produce knowledge.
• *Vocal : eloquence*: being vocal (outspoken) does not create eloquence.
• *Dramatic : story*: an adjective describing a story, not something that brings one about.

(In the PDF the options for B and C run into each other: "mnemoni / memory / c: vocal : eloquence". They read as B = mnemonic : memory and C = vocal : eloquence.)

*Jeopardy* and *peril* are synonyms (danger). *Jealousy* and *envy* are the only synonym pair.

• *Lust* and *romance* are related feelings but not synonyms of jealousy.
• *Secure* is closer to an opposite state.

*Agog* means eager or excited, and it is often used as "all agog".

• A "all agog to see" (eager to do something) is correct.
• B "all agog at" the announcement (excited about it) is correct.
• C "set … agog with excitement" is a standard pattern.

All three are correct, so D.

*Tantamount* is an adjective meaning "equivalent in effect". It is used as *be tantamount to*.

• A "is tantamount to cruelty" is correct.
• C "was tantamount to an admission of guilt" is correct.
• B "Overlooking state norms tantamounts to a crime" treats the adjective as a verb. *Tantamount* has no verb form, so the sentence should read "is tantamount to a crime".

B is the incorrect usage, so the answer should be B. The official key's "All are correct" (D) cannot be defended.

The joined sentence is: "Some of the important themes are to ensure that students have ready access to the right learning material, especially in their own languages, because it ensures a better understanding of subjects."

• The verb are needs a plural subject, and *some of the themes* is plural.
• *One of the themes* and *each of the themes* take the singular *is*.
• *Someone* refers to a person, not a theme.

The second sentence adds a reservation to the good news in the first, so the connector must show concession or contrast.

"The unemployment rate has dropped sharply this quarter, though it may only be temporary." *Though* makes one complex sentence that grants the drop and adds the caveat.

• *Likewise* signals similarity, which is wrong here.
• *Still* ("yet, nevertheless") would put the emphasis back on the drop, the reverse of the intended caveat.
• *But* also joins the two correctly: "…this quarter, but it may only be temporary." So the question does not have a single right answer. The key picks *though*.

A "but" link needs two ideas where the second pushes against the first.

III – IV: III admits a limit: with over a billion people and many languages, no one can address them all at once. IV says that, even so, Doordarshan's promotions must go beyond reporting facts and tell the story between the lines. The pair reads as a limitation followed by what must still be done: "…one cannot address all of them together all the time, but Doordarshan's promotions must go beyond…"

• I – II: commerce (goods being sold) and news focus are unrelated, so there is no contrast.
• II – IV: II already contains its own *but*, and IV does not oppose it.
• I – III: I is about the global market, while III is about India's diverse audience. "But" does not join them meaningfully.

*Because* needs an effect followed by its cause.

I – IV (key): "It is ironic that minorities have come to be identified with religion rather than community or profession, because secularism today has come to mean preserving religious minorities in their traditional modes." IV gives a cause for I: if secularism is read as protecting minorities *as religious groups*, minorities come to be defined by religion. To join them, the "This is the reason that" opening of IV has to be dropped.

• III – IV: IV already opens with "This is the reason", so adding *because* is redundant. III does not directly cause IV either.
• I – II: unrelated. II's "such organizations" has nothing in I to refer back to.
• II – III: this also forms a sound cause and effect: "…testimony to the growing antagonism to secularism, because secularism is being taken as a threat to religious identities." So the question has two defensible pairs.

"The milkman in my neighbourhood likes to talk to his customers while he provides them milk every morning." *While* (at the same time as) connects the two actions naturally.

• *Even if* adds a condition that makes no sense here.
• *In addition* is an adverbial phrase, not a conjunction, so it cannot join the clauses.
• *Rightly* is an adverb of judgement.

"So lazy that…" needs a result that laziness would cause. Rarely finishing work on time is that result.

• A (cannot depend on others) and B (cannot delay the schedule) do not follow from laziness.
• D (dislikes postponing work) describes the opposite of a lazy person, and "dislike" is also a grammar error.

The sentence says the listener's high opinion of Prashant is not justified. Option A says exactly that.

• B and D claim he is better than, or as good as, the listener thinks. That contradicts "he is not so".
• C ("philosophical, keep it up") has nothing to do with the original.

Names of epics and sacred books take the definite article: *the Ramayana*, *the Mahabharata*, *the Bible*. Part (a) should read "The war of the Mahabharata" (or "The Mahabharata war").

Parts (b) and (c) are acceptable as written, so the error is in (a).

*Little* without *a* means "hardly any", which is a negative sense. *A little* means "some".

The instruction is to add some sugar, so part (b) should be "drop a little sugar".

The subject is ancestors living in a place, which happens over generations.

• *Days* and *seasons* are far too short for ancestral residence.
• *Infinity* is illogical: no one has lived anywhere forever.

*Shiftless* means lacking ambition or energy, i.e. lazy. It pairs naturally with *idle* in the passage.

• *Carefree* is tempting, but it only means untroubled; it does not imply a lack of effort.
• *Amiable* (friendly) and *ruthless* (cruel) are unrelated.

The passage contrasts Gandhi's simple, self-sufficient village life with the tempting "glittering prizes" of the modern age. Those prizes are the consumer goods and material comforts of an industrial, commercial culture, so A.

• B (rural replaced by urban interests) is narrower than the phrase.
• C (removal of poverty) and D (absence of violence and corruption) are goals, not temptations Gandhi asked villagers to reject.

The "idyllic and rural paradise" refers back to Gandhi's vision: villagers self-sufficient in food, weaving their own cloth, and turning down modern temptations. That is self-sufficiency and simple living, option B.

• A and C are what Gandhi rejected.
• D is the opposite of the passage's point: those in power did not share the vision.

*Audacious* is defined as showing a willingness to take bold risks, or to shock or offend. It covers both parts of the description.

• *Bold* and *risk-taker* capture only the risk-taking, not the shocking behaviour.
• *Bodacious* is informal slang for "excellent" or "remarkable".

*Fumigate* means to disinfect or purify an area with chemical fumes or smoke, specifically to kill pests or germs.

• *Spray* is any liquid application and does not imply smoke or gas.
• *Decontaminate* is the general removal of dangerous substances, not specifically pests by fumes.

So "All of the above" fails.

The definition describes a state (a condition), so the noun hypochondria fits.

• *Hypochondriac* is the person who has this condition, which is the tempting trap.
• *Hypoallergenic* means unlikely to cause allergies.