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IMAT 2021 · Answers & Worked Solution

IMAT 2021 Answers & Worked Solution

All 60 answers, solved and explained — General Knowledge, Logical Reasoning, Biology, Chemistry, Physics & Mathematics. Verified line by line by the LOCOMOTIVE academic team.

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General Knowledge & Logical Reasoning

Current affairs, history, culture, logical and critical-thinking problems · 22 questions
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Of all the food we buy, bread suffers the worst fate when it comes to waste. 32% of it ends up being thrown away. We value other types of food a lot more, as the average for all food and drink being wasted is 15%. The proportion of meat and fish thrown away is below average (13%) and our most precious item is alcohol - we throw away just 6% of it. Which one of the following is an underlying assumption of the above argument?

  • ABread is a low-quality food.
  • BWe should be more moderate when it comes to buying bread.
  • CThe more expensive a food or drink is, the less likely it is that it will be wasted.
  • DBread goes stale faster so is more likely to be thrown away.
  • EThe main reason why we throw food away is that we do not value it much.
Correct answer: E The main reason why we throw food away is that we do not value it much.

Full explanation

The underlying assumption of the argument is that the value we place on food influences how much of it we waste. The argument compares bread (which is wasted the most) to alcohol (which is wasted the least) and other foods in terms of how much is thrown away.

Option A Explanation:

A) Bread is a low-quality food.

This is not necessarily true, and the argument does not make a claim about the quality of bread. The focus is on how much we value different foods, not their quality.

Option B Explanation:

B) We should be more moderate when it comes to buying bread.

This is a suggestion, not an assumption of the argument.

Option C Explanation:

C) The more expensive a food or drink is, the less likely it is that it will be wasted.

This might be true in some cases, but the argument does not explicitly focus on the cost of food or drink, only the value placed on them.

Option D Explanation:

D) Bread goes stale faster so is more likely to be thrown away.

While this could explain some of the waste, the argument does not mention the freshness or shelf life of bread as the cause for its higher waste rate.

Option E Explanation:

E) The main reason why we throw food away is that we do not value it much.

This is the best assumption. The argument suggests that the more we value something, the less we waste it (alcohol is thrown away the least, while bread, which is seemingly less valued, is wasted the most).

Summary to learn

A critical-reasoning assumption is an unstated premise the argument needs in order for its conclusion to follow — it is not just any true-sounding fact about the topic. When an argument draws a conclusion from a pattern in the evidence (here, that less-valued items get wasted more), the assumption is usually the general causal or explanatory link that would have to hold for that pattern to support the conclusion in the first place. A good way to test a candidate assumption is to imagine it were false: if the argument would then fall apart, it was genuinely required.

It is usual, when seating people round a table at a social function, to alternate males with females, but if there are unequal numbers of each, this is impossible. At one party, 14 women and only 6 men were present. They were seated round a circular table so that as few women as possible had no male sitting directly next to them. How many women had no male sitting directly next to them?

  • A8
  • B7
  • C2
  • D6
  • E4
Correct answer: C 2

Full explanation

First, we can arrange the 6 men in a circle, which creates 6 spaces between each pair of men.

Next, we need to place the 14 women in these 6 spaces. To do so, we must place at least 2 women in each space, using up 12 women in total. This leaves 2 women, who must be seated in spaces that already contain women. As a result, these 2 women will not have any men sitting directly next to them.

Thus, 2 women will have no man sitting directly next to them.

Summary to learn

Circular seating problems with unequal group sizes reduce to a spacing calculation: arranging the smaller group first creates one gap between each adjacent pair, and those gaps are the only places the larger group can sit. Distributing the larger group as evenly as possible across the gaps (at least a minimum number in each) uses up as many of them as possible while leaving both neighbours filled; whatever is left over has to double up in an already-filled gap, and it is exactly those leftover members who end up without the desired neighbour on both sides.

Teams from five US states have reached the final of a competition. The event organisers are trying to design a sign for each state. One idea involves the name, in capital letters, being placed vertically on a sign board which spins when one of the team presses their buzzer to answer a question. They want the sign to read correctly regardless of whether it is read from the front or the back. Unfortunately they realise that most of the states for which this would have worked have not reached the final. Which one of the following is the only state in the final for which this style of sign would work?

  • AMontana
  • BIdaho
  • CAlabama
  • DOklahoma
  • EHawaii
Correct answer: E Hawaii

Full explanation

To solve this, we need to determine which state's name can be read correctly from both the front and the back when placed vertically on a sign board.

Option A Explanation:

A) Montana

The letters "M, O, T and A" are symmetric, but "N" is not, so this would not work.

Option B Explanation:

B) Idaho

The letters "I, A, H and O" are symmetric, but "D," is not. This would not work.

Option C Explanation:

C) Alabama

The letters "A, and M" are symmetric, but "L and B" are not. This would not work.

Option D Explanation:

D) Oklahoma

The letters "O, A, H and M" are symmetric, but "K and L" are not. This would not work.

Option E Explanation:

E) Hawaii

All the letters "H," "A," "W," "I" are symmetric. Thus, this is the only state whose name can be read the same from both front and back

Summary to learn

A word or name has vertical (top-to-bottom) symmetry only if every one of its letters, written in capitals, is itself symmetric about a horizontal axis running through its middle — letters such as B, C, D, E, H, I, K, O and X qualify, while letters like F, G, J, L, N, P, Q, R, S, W, Y and Z do not. A single asymmetric letter anywhere in the word breaks the whole word's symmetry, so checking a candidate word means checking every one of its letters individually, not just its overall shape.

For many years, children and young people have been protected from exploitation by the entertainment industry. In recent years, however, the number of young people suddenly thrust into the limelight has increased, and many of them feel that they must seize any opportunity to achieve recognition before this window passes them by. Dealing with fame, performing in front of large audiences, the rigours of rehearsal and the general stresses of what is a difficult occupation take maturity and can rob children of their childhood. Rejection, disappointment and failure are felt more keenly by young people because they lack wider experience and this can make for a very unhappy childhood. These factors would indicate that young performers need further protection by law.

Which one of the following best expresses the main conclusion of the above argument?

  • AYoung people feel rejection, disappointment and failure more because they lack wider experience.
  • BYoung performers are robbed of their childhood by the demands of performing.
  • CYoung people can be suddenly thrust into the limelight.
  • DYoung people have been protected from exploitation by the entertainment industry for many years.
  • EYoung performers need further protection by law.
Correct answer: E Young performers need further protection by law.

Full explanation

The argument explicitly presents its main conclusion at the end of the paragraph, following a discussion of supporting reasons: "These factors would indicate that young performers need further protection by law."

Challenges such as stress, rejection, and the loss of childhood in the entertainment industry highlight the need for stronger legal protections for young performers.

Option A Explanation:

A) Young people feel rejection, disappointment and failure more because they lack wider experience.

This is a supporting premise, not the conclusion. It explains why rejection is harder for young people.

Option B Explanation:

B) Young performers are robbed of their childhood by the demands of performing.

This is also a supporting point---it describes the negative impact of performing, but it doesn't state what should be done about it.

Option C Explanation:

C) Young people can be suddenly thrust into the limelight.

This is a background fact rather than the conclusion.

Option D Explanation:

D) Young people have been protected from exploitation by the entertainment industry for many years.

This is an introductory statement setting the context, not the main claim being argued.

Option E Explanation:

E) Young performers need further protection by law.

This best expresses the main conclusion of the above argument.

Summary to learn

An argument's main conclusion is the single overall claim that everything else in the passage exists to support — not necessarily the last sentence, and not any statement that merely restates a supporting reason, describes a negative consequence, or sets up background context. Distinguishing a conclusion from a premise means asking which statement the others are being used as evidence for, rather than looking for surface cues like sentence position or a conclusion word such as "therefore".

In a survey of cats' eating habits, 10% of the cats tested showed a clear preference for Moggiemeat, 20% preferred Fuss-a-Puss and 40% preferred Yummy Paws. An additional 6 cats did not seem to care at all which of the three foods they ate, while the remaining 27 cats in the survey would not touch any of these foods. How many cats were in the survey?

  • A90
  • B103
  • C110
  • D63
  • E33
Correct answer: C 110

Full explanation

According to the survey,

- 10% of the cats preferred Moggiemeat.

- 20% of the cats preferred Fuss-a-Puss.

- 40% of the cats preferred Yummy Paws.

- 6 cats did not care which food they ate.

- 27 cats would not touch any of these foods.

The sum of cats with clear preference is 10% + 20% + 40% = 70%

The remaining 30% is made up of 6 indifferent cats, and the 27 cats that refused to eat any (total 33)

Since 30% corresponds to 33 cats,

total number of cats x 3/10 =33

total number of cats = 33 x 10/3 =110 cats

Summary to learn

When a total is split into stated percentages of clearly separate subgroups plus some subgroups given as raw counts, the whole can be reconstructed by first adding up the percentages that are known, subtracting from 100% to find what percentage the raw-count groups together represent, and then using that percentage-to-count correspondence to solve for the overall total via simple proportion.

From ever younger ages, people are reporting symptoms of anxiety due to the pressure to be 'perfect' in all areas of life. It seems that, in many cultures, there is an increasing sense or competition in everything from school results to the job market to personal appearance and even how one's social life looks on social media. As a result, many people experience problems associated with low self-confidence. But rather than reach for a pill or a self-help book to tackle their problems, more of these individuals should just go outside for a run or a walk. While it sounds simplistic, this recommendation is supported by the research finding that people who do a lot of outdoor activities tend to have high self-esteem. Which one of the following is the best statement of the flaw in the above argument?

  • AIt assumes that high levels of self-confidence or self-esteem are all that are needed for a person to enjoy good mental health.
  • BIt ignores the likelihood that many people with varying levels of self-confidence would benefit from the advice of a mental health professional.
  • CIt ignores the fact that not everyone with low self-esteem has the desire to go for a run or a walk outside.
  • DIt assumes that people who manage to appear 'perfect' in the different parts of their lives will not suffer from problems with self-confidence.
  • EIt ignores the possibility that people with higher self-esteem might be more inclined to take part in outdoor activities.
Correct answer: E It ignores the possibility that people with higher self-esteem might be more inclined to take part in outdoor activities.

Full explanation

The argument assumes a causal relationship between outdoor activities and high self-esteem: it suggests that engaging in outdoor activities leads to higher self-esteem. However, it fails to consider the reverse possibility---that people who already have high self-esteem are more likely to engage in outdoor activities in the first place.

This is a correlation vs. causation fallacy, where the argument assumes that because two things are related, one must be causing the other.

Option A Explanation:

A) It assumes that high levels of self-confidence or self-esteem are all that are needed for a person to enjoy good mental health.

The argument does not assume that self-confidence is the only factor for mental well-being---it simply promotes outdoor activities as a solution.

Option B Explanation:

B) It ignores the likelihood that many people with varying levels of self-confidence would benefit from the advice of a mental health professional.

While professional mental health support is important, the argument's flaw is not about disregarding therapy but rather about making a faulty causal assumption.

Option C Explanation:

C) It ignores the fact that not everyone with low self-esteem has the desire to go for a run or a walk outside.

The argument's flaw is not about individual preferences but about the incorrect assumption regarding causality.

Option D Explanation:

D) It assumes that people who manage to appear 'perfect' in the different parts of their lives will not suffer from problems with self-confidence.

The argument does not claim that appearing "perfect" eliminates self-confidence issues.

Option E Explanation:

E) It ignores the possibility that people with higher self-esteem might be more inclined to take part in outdoor activities.

This correctly describes the flaw in the argument.

Summary to learn

An argument that concludes "A causes B" purely from an observed correlation between A and B commits the correlation-causation fallacy unless it also rules out reverse causation (B causing A) and other third factors that might produce both. The strongest logical flaw to identify in such an argument is usually the specific alternative explanation the argument overlooked, rather than an unrelated criticism of the advice being given.

Simon plans to send Christmas cards to 35 friends. He is going to choose a single design to send to them all and knows that some of the recipients really do not like glitter cards so he will not buy this type. He wants 2-fold cards so that he can write a letter on the inside for 5 of them. The following table shows the possibilities that he is considering.

card typeno. in packglitter1-fold2-foldpack price
religious5no–yes£1.80
robins8noyes–£1.95
village scene20yes–yes£2.50
cartoon12noyes–£2.20
father xmas10no–yes£3.10

What is the lowest amount of money that Simon could spend on his cards?

  • A£9.75
  • B£6.00
  • C£12.40
  • D£12.60
  • E£5.00
Correct answer: C £12.40

Full explanation

We have to find proper card type first that fits all the needs.

Simon wants 2-fold, no glitter cards. Thus, we can exclude the Robins, Village scene and Cartoon designs.

Between religious and father xmas card types, the former card type will cost 12.6 in total for 35 cards and the latter will cost 12.4 in total.

Thus, the lowest amount of money that Simon could spend on these cards is C) £12.40

Summary to learn

A multi-constraint "cheapest option" problem is solved in two stages: first eliminate every option that fails any hard requirement (here, no glitter and must be 2-fold), and only then compare cost among whatever survives. Once the field is narrowed, the true cost of an item that comes in fixed-size packs is however many whole packs are needed to cover the required quantity — rounding the pack count up, never down, since a partial pack still has to be bought in full.

Our three local universities have agreed that they will offer a place to everyone from our school who applies to them. Because you attend a different school, you are not guaranteed an offer from these universities. Which one of the following most closely parallels the reasoning used in the above argument?

  • AIn our country, everyone who becomes a teacher must have a university degree. Since you do not have a degree, you are not qualified to become a teacher.
  • BEveryone who has a free bus pass is entitled to travel on buses after 9:30 am without payment. Since it is after 9:30 am and you have a free bus pass, you do not have to pay for this bus journey.
  • CThe only way to stand for election to Parliament is to be nominated by voters in a geographical constituency. Since you have not been nominated, you cannot stand for election.
  • DEveryone who becomes a student at our college has achieved a high score in their high school examinations. You have a high score, and therefore you are sure to be accepted as a student at our college.
  • EEveryone over the age of 60 is entitled to a bus pass, which gives them free travel on buses after 9:30 am. Since you are younger than 60, you are not entitled to free bus travel.
Correct answer: E Everyone over the age of 60 is entitled to a bus pass, which gives them free travel on buses after 9:30 am. Since you are younger than 60, you are not entitled to free bus travel.

Full explanation

- X = Attending a particular school.

- Y = Being offered a place at the local universities.

The argument states that if you attend a specific school (X), you are guaranteed an offer from the local universities (Y). If you don't attend that school (you don't have X), you are not guaranteed an offer (you don't get Y).

This reasoning can be restated as:

- If X, then Y.

- Since you do not have X, you are not guaranteed Y.

Option A Explanation:

A) In our country, everyone who becomes a teacher must have a university degree. Since you do not have a degree, you are not qualified to become a teacher.

If you think of having a university degree as X, becoming a teacher is Y. In this case, X cannot guaranteed Y. It is stated as just one of the necessary qualification. Thus, this statement does not parallel the stated reasoning.

Option B Explanation:

B) Everyone who has a free bus pass is entitled to travel on buses after 9:30 am without payment. Since it is after 9:30 am and you have a free bus pass, you do not have to pay for this bus journey.

If you have a free bus pass (X), then you can travel without payment (Y).

Since you have a bus pass (X), you do not have to pay (Y).

This doesn't fit the original statement reasoning.

Option C Explanation:

C) The only way to stand for election to Parliament is to be nominated by voters in a geographical constituency. Since you have not been nominated, you cannot stand for election.

If being nominated is X, then standing an election is Y.

The second statement says that since no X, there is no Y.

This reasoning is similar, but the focus is on exclusion based on a necessary condition, not on a guarantee like option A.

Option D Explanation:

D) Everyone who becomes a student at our college has achieved a high score in their high school examinations. You have a high score, and therefore you are sure to be accepted as a student at our college.

If you have a high score (X), you are accepted as a student (Y).

Since you have a high score (X), you are accepted (Y).

This doesn't fit the original statement reasoning.

Option E Explanation:

E) Everyone over the age of 60 is entitled to a bus pass, which gives them free travel on buses after 9:30 am. Since you are younger than 60, you are not entitled to free bus travel.

If you are over 60 (X), you are entitled to a bus pass (Y).

Since you are not over 60 (not X), you are not entitled to a bus pass (not Y).

This reasoning is the same structure as the original argument: a specific condition (X) leads to a guarantee (Y), and lacking the condition (not X) leads to being excluded from the guarantee (not Y).

Summary to learn

Two arguments share the same logical structure only when they match role-for-role: what plays the role of the condition (X), what plays the role of the guaranteed outcome (Y), and how the "if X then Y" relationship is used in the conclusion (in this case, arguing from "not X" to "not Y"). An option that discusses a similar-sounding topic but changes the shape of that relationship — for example turning a guarantee into a bare necessary condition, or arguing from X to Y instead of from not-X to not-Y — is not a genuine structural match, however similar its subject matter looks.

A young woman (A), knowing that she was dying, requested that her mother (B), who was awaiting a kidney transplant, should be allowed to receive her kidneys after her death. The request was not allowed, and A's kidneys were received by another patient (C), who was higher up the waiting list than B because his medical need for a transplant was more urgent. The committee overseeing transplant decisions argued that the system it used had to be administered solely in accordance with the rationale behind its waiting list. Their decision seemed to others unduly bureaucratic, especially as B will be left to care for A's young child. Which one of the following best illustrates the principle behind the committee's decision?

  • ADecisions on transplants cannot be influenced by emotions.
  • BDecisions on transplants should include social considerations.
  • CDonations between family members are not allowed.
  • DThe donor's wishes should not be considered.
  • EDecisions on transplants should focus on the medical need of the potential recipient.
Correct answer: E Decisions on transplants should focus on the medical need of the potential recipient.

Full explanation

The principle behind the committee's decision can be identified from the following sentence mentioned in the paragraph "The committee overseeing transplant decisions argued that the system it used had to be administered solely in accordance with the rationale behind its waiting writ list." In other words, it says that the committee decision is based on the waiting list which is organized according to the order of urgency.

Option A Explanation:

A) Decisions on transplants cannot be influenced by emotions.

The committee does not say anything about emotions. It only states about the waiting list and the order of Urgency. Thus, this statement is false.

Option B Explanation:

B) Decisions on transplants should include social considerations.

The committee does not say anything about social considerations. It only states about the waiting list and the order of Urgency. Thus, this statement is false.

Option C Explanation:

C) Donations between family members are not allowed.

The committee does not say anything about the donations between family members. It only states about the waiting list and the order of Urgency. Thus, this statement is false.

Option D Explanation:

D) The donor's wishes should not be considered.

The committee does not say anything about the donor's wishes. It only states about the waiting list and the order of Urgency. Thus, this statement is false.

Option E Explanation:

E) Decisions on transplants should focus on the medical need of the potential recipient.

This option correctly states the principle behind the committee's decision.

Summary to learn

The "principle" behind a decision in a critical-reasoning passage is the general rule the decision-maker is applying, which can usually be read directly off their own stated justification rather than inferred from the surrounding emotional or social details of the scenario. Distractor options often describe the emotional weight of the situation (family ties, the donor's wishes) rather than the actual rule the decision-maker cited for making the call the way they did.

When I first woke up early this morning the display of my bedside digital clock showed:

IMAT 2021 question 10 clock showing 20:50, the first time seen

I presumed that it was faulty, but, after drifting off to sleep again, when I next awoke and saw the clock I realised that someone must have turned the clock upside down and that it was exactly an hour and a half since I had looked at it before.

What did I see when I woke up the second time?

  • A
    IMAT 2021 question 10 clock display option A
  • B
    IMAT 2021 question 10 clock display option B (correct)
  • C
    IMAT 2021 question 10 clock display option C
  • D
    IMAT 2021 question 10 clock display option D (identical to option C in the source)
  • E
    IMAT 2021 question 10 clock display option E
Correct answer: B Option B

Full explanation

Reading a digital display upside down is a two-step flip, and it helps to know the rule before touching the numbers: reverse the order the digits appear in, and rotate each digit on its own axis. Most digits survive that rotation looking like themselves — 0, 1, 2, 5 and 8 all come back unchanged — but 6 and 9 swap places with each other, and 3, 4 and 7 don't turn into any digit at all. A rotated 3, in particular, comes out looking like the letter E on a seven-segment display, and that detail is what this whole question hinges on.

The narrator's clock has been turned upside down without them realising, so what they're reading is not the true time — it's the true time seen through that flip. To undo it, reverse the four digits and rotate each one: 20:50 reversed is 0, 5, 0, 2, and every one of those digits rotates to itself, so the true reading is 05:02. The clock was never faulty; it was quietly keeping perfect time from an upside-down position.

Ninety minutes is real, physical time, so the true time by the second waking is 05:02 + 1:30 = 06:32. The clock is still upside down, so to find out what the narrator actually sees now, apply the same flip again: reverse 0, 6, 3, 2 to get 2, 3, 6, 0, then rotate each one — 2 stays 2, 3 becomes that tell-tale E shape, 6 becomes 9, and 0 stays 0. That gives 2E:90, which is exactly option B.

Option A is just the original 20:50 with nothing done to it — a trap for anyone who checks that a flip happened at all but not what it actually produces. Options C, D and E each swap in a stray letter where option B's leading '2' should sit, which is what happens if the reversing and the rotating aren't both carried through consistently on every digit. A good way to sanity-check an answer like this is to flip it a second time — flip 2E:90 again and you should land right back on 20:50.

Summary to learn

Reading a digital display upside down is a two-step flip, and it helps to know the rule before touching the numbers: reverse the order the digits appear in, and rotate each digit on its own axis. Most digits survive that rotation looking like themselves — 0, 1, 2, 5 and 8 all come back unchanged — but 6 and 9 swap places with each other, and 3, 4 and 7 don't turn into any digit at all (a rotated 3, on a seven-segment display, comes out looking like the letter E).

Which of the following pairs of theatre/city is the only correct one?

  • AThe Bolshoi Theatre - Saint Petersburg
  • BThe Palais Garnier Opera House - Brussels
  • CSan Carlo - Venice
  • DMetropolitan Opera House - New York
  • ELa Fenice - Florence
Correct answer: D Metropolitan Opera House - New York

Full explanation

Option A Explanation:

A) The Bolshoi Theatre - Saint Petersburg

The Bolshoi Theatre is in Moscow, not Saint Petersburg.

Option B Explanation:

B) The Palais Garnier Opera House - Brussels

The Palais Garnier is in Paris, not Brussels.

Option C Explanation:

C) San Carlo - Venice

San Carlo (Teatro di San Carlo) is in Naples, not Venice.

Option D Explanation:

D) Metropolitan Opera House - New York

Correct. The Metropolitan Opera House (commonly called the Met) is located in New York City and is one of the world's most famous opera houses.

Option E Explanation:

E) La Fenice - Florence

La Fenice is in Venice, not Florence.

Summary to learn

The Bolshoi Theatre is in Moscow (not Saint Petersburg), the Palais Garnier opera house is in Paris (not Brussels), Teatro di San Carlo is in Naples (not Venice), and La Fenice is in Venice (not Florence). New York's Metropolitan Opera House is the one correct theatre/city pairing among these five world-famous opera and ballet venues.

Which one of the following directors directed the films that make up The Godfather trilogy?

  • ABrian De Palma
  • BSergio Leone
  • CMartin Scorsese
  • DFrancis Ford Coppola
  • EMatteo Garrone
Correct answer: D Francis Ford Coppola

Full explanation

Francis Ford Coppola wrote and directed all three Godfather films — The Godfather (1972), The Godfather Part II (1974) and The Godfather Part III (1990) — adapting Mario Puzo's novel into what's still regarded as one of the high points of American cinema, especially the first two instalments.

The other names are tempting precisely because they all made their names in the same era and often the same genre. Brian De Palma directed Scarface, another landmark gangster film, but not this trilogy. Sergio Leone built his reputation on operatic crime epics like Once Upon a Time in America. Martin Scorsese has returned to organised crime again and again, in Goodfellas and Casino among others. Matteo Garrone directed the acclaimed Italian mafia drama Gomorrah. All five belong to the same neighbourhood of cinema — only Coppola belongs to the Godfather trilogy itself.

Summary to learn

Francis Ford Coppola wrote and directed all three Godfather films — The Godfather (1972), The Godfather Part II (1974) and The Godfather Part III (1990) — adapting Mario Puzo's novel into what's still regarded as one of the high points of American cinema. The other four directors are tempting precisely because they made their names in the same era and genre: Brian De Palma directed Scarface, Sergio Leone built his reputation on operatic crime epics like Once Upon a Time in America, Martin Scorsese returned to organised crime repeatedly in Goodfellas and Casino, and Matteo Garrone directed the acclaimed Italian mafia drama Gomorrah.

Which one of the following treaties established the European Coal and Steel Community (ECSC)?

  • AAmsterdam
  • BNice
  • CParis
  • DRome
  • ELisbon
Correct answer: C Paris

Full explanation

The Treaty of Paris, signed in 1951 and in force from 1952, established the European Coal and Steel Community — the first of the communities that eventually grew into today's European Union. Six countries joined at the outset: Belgium, France, Italy, Luxembourg, the Netherlands and West Germany. Pooling coal and steel production, the industries most needed to wage war, was a deliberate way of making conflict between France and Germany not just undesirable but practically difficult.

The other treaties on this list are all genuine EU milestones, just not this one. The Treaty of Rome (1957) came next and created the European Economic Community and Euratom. The Treaty of Amsterdam (1997) and the Treaty of Nice (2001) both amended the EU's founding treaties to prepare its institutions for a larger membership. The Treaty of Lisbon (2007) is the most recent major overhaul, reshaping how the EU's institutions work today. Keeping the order straight — Paris, then Rome, then the later amending treaties — is the quickest way to place any one of them correctly.

Summary to learn

The Treaty of Paris (1951, in force 1952) established the European Coal and Steel Community, the first of the communities that grew into today's EU, among six founding states: Belgium, France, Italy, Luxembourg, the Netherlands and West Germany. The later EU treaty timeline runs Rome (1957, created the EEC and Euratom), then Amsterdam (1997) and Nice (2001), which amended the founding treaties ahead of enlargement, then Lisbon (2007), the most recent major institutional overhaul.

Which one of the following pairs of scholar/field of study is NOT correct?

  • AMaria Montessori - pedagogy
  • BHans Jonas - medicine
  • CJohn Maynard Keynes - economics
  • DMax Planck - physics
  • EB. F. Skinner - psychology
Correct answer: B Hans Jonas - medicine

Full explanation

Option A Explanation:

A) Maria Montessori - pedagogy

Developed the Montessori method of education.

Option B Explanation:

B) Hans Jonas - medicine

Hans Jonas was a philosopher, not a medical scholar. He is best known for his work in ethics, philosophy of biology, and technology.

Option C Explanation:

C) John Maynard Keynes - economics

Developed Keynesian economics.

Option D Explanation:

D) Max Planck - physics

Founder of quantum theory.

Option E Explanation:

E) B. F. Skinner - psychology

Known for behaviorism and operant conditioning.

Summary to learn

Maria Montessori is known for pedagogy (the Montessori method of education), John Maynard Keynes for economics (Keynesian economics), Max Planck for physics (founder of quantum theory), and B. F. Skinner for psychology (behaviourism and operant conditioning) — all correctly paired. Hans Jonas, despite the surface plausibility, was a philosopher known for ethics and the philosophy of technology and biology, not a medical scholar.

The Rosetta Stone provided the key to decipher

  • Acharacters of the Ancient Greek alphabet
  • BEgyptian hieroglyphs
  • Ccharacters of the Phoenician alphabet
  • Dthe Code of Hammurabi
  • Ethe Sumerian language
Correct answer: B Egyptian hieroglyphs

Full explanation

The correct answer is:

B) Egyptian hieroglyphs

The Rosetta Stone was the key to deciphering Egyptian hieroglyphs. It was discovered in 1799 and contained the same text written in three scripts:

1. Ancient Greek

2. Demotic script (a later Egyptian script)

3. Egyptian hieroglyphs

Since scholars already understood Ancient Greek, Jean-François Champollion was able to use it to decipher the hieroglyphs in 1822, unlocking the ability to read ancient Egyptian texts.

The other options are all genuine ancient scripts or legal texts, which is exactly what makes them tempting: the Phoenician alphabet, the Sumerian language (written in cuneiform) and the Code of Hammurabi were each studied and deciphered using entirely different evidence. Ancient Greek, meanwhile, wasn't the mystery at all on the Rosetta Stone — it was the half scholars could already read, and that's precisely what made cracking the other two scripts possible.

Summary to learn

The Rosetta Stone carries the same decree written in three scripts — Ancient Greek, Egyptian Demotic, and Egyptian hieroglyphs. Because scholars already understood Ancient Greek, that known script served as the key: comparing it against the other two let Jean-François Champollion decipher Egyptian hieroglyphs in 1822, unlocking the ability to read ancient Egyptian texts more broadly. Ancient Greek itself was never the mystery the stone solved — it was the tool used to solve it.

The expression 'perfect bicameral system' refers to

  • Athe form of government that assigns identical power to two institutional figures.
  • Bthe kind of parliamentary monarchy where monarch and parliament have the same powers.
  • Cthe judicial system whereby the first sentence must be confirmed by the first round of appeal.
  • Dthe perfect separation of the magistrate judge and public prosecutor.
  • Ethe legislative procedure that assigns identical powers to the two chambers of a parliament.
Correct answer: E the legislative procedure that assigns identical powers to the two chambers of a parliament.

Full explanation

A bicameral system refers to a legislature with two chambers (e.g., a Senate and a House of Representatives). A perfect bicameral system means that both chambers have equal powers in the legislative process.

Option A Explanation:

A) the form of government that assigns identical power to two institutional figures.

Incorrect. Bicameralism refers to legislatures, not institutional figures.

Option B Explanation:

B) the kind of parliamentary monarchy where monarch and parliament have the same powers.

Incorrect. This describes a government system, not bicameralism.

Option C Explanation:

C) the judicial system whereby the first sentence must be confirmed by the first round of appeal.

Incorrect. Bicameralism is about legislatures, not courts.

Option D Explanation:

D) the perfect separation of the magistrate judge and public prosecutor.

Incorrect. This relates to judicial independence, not bicameralism.

Option E Explanation:

E) the legislative procedure that assigns identical powers to the two chambers of a parliament.

Correct. This matches the definition of a perfect bicameral system.

Summary to learn

A bicameral legislature has two chambers (such as a senate and a lower house); it is a "perfect" bicameral system specifically when both chambers hold equal legislative powers, so that neither can pass or block laws without the other's agreement. This is a property of how a legislature's two chambers relate to each other, not a description of any judicial system, monarchy, or separation of prosecutorial roles.

Which one of the following pairs of Russian writers/works is NOT correct?

  • AVladimir Nabokov - Lolita
  • BMikhail Bulgakov - Uncle Vanya
  • CLeo Tolstoy - Anna Karenina
  • DBoris Pasternak - Doctor Zhivago
  • EFyodor Dostoyevsky - The Brothers Karamazov
Correct answer: B Mikhail Bulgakov - Uncle Vanya

Full explanation

Option A Explanation:

A) Vladimir Nabokov - Lolita

Lolita (1955) is Nabokov's most famous novel.

Option B Explanation:

B) Mikhail Bulgakov - Uncle Vanya

Uncle Vanya (1899) was written by Anton Chekhov, not Bulgakov.

Bulgakov is best known for The Master and Margarita (published posthumously in 1966).

Option C Explanation:

C) Leo Tolstoy - Anna Karenina

Anna Karenina (1877) is one of Tolstoy's masterpieces.

Option D Explanation:

D) Boris Pasternak - Doctor Zhivago

Doctor Zhivago (1957) is Pasternak's famous novel, for which he won the Nobel Prize.

Option E Explanation:

E) Fyodor Dostoyevsky - The Brothers Karamazov

The Brothers Karamazov (1880) is one of Dostoyevsky's most significant works.

Summary to learn

Vladimir Nabokov wrote Lolita (1955), Leo Tolstoy wrote Anna Karenina (1877), Boris Pasternak wrote Doctor Zhivago (1957, Nobel Prize), and Fyodor Dostoyevsky wrote The Brothers Karamazov (1880) — all correctly paired. Uncle Vanya (1899), however, was written by Anton Chekhov, not by Mikhail Bulgakov, who is instead best known for The Master and Margarita.

What does the letter A stand for in the international organisation FAO?

  • AAutomotive
  • BAgriculture
  • CAerospace
  • DAesthetics
  • EArchitecture
Correct answer: B Agriculture

Full explanation

The correct answer is:

B) Agriculture

FAO stands for Food and Agriculture Organization.

It is a specialized agency of the United Nations (UN) that leads international efforts to combat hunger and improve agriculture, forestry, and fisheries worldwide. It was founded in 1945 and is headquartered in Rome, Italy.

The other options aren't real expansions of the acronym at all — Automotive, Aerospace, Aesthetics and Architecture are simply plausible-sounding A-words with no connection to this organisation. The safest way past this kind of distractor is to recall the organisation's full name first, rather than trying to guess which word fits the letter.

Summary to learn

FAO stands for the Food and Agriculture Organization, a United Nations agency founded in 1945 and headquartered in Rome that leads international efforts against hunger and works to improve agriculture, forestry and fisheries worldwide. The safest way past an acronym-expansion distractor question like this is to recall the organisation's full name directly, rather than guessing which plausible-sounding word fits the missing letter.

Which one of the following pairs of scholar/scientific discovery is NOT correct?

  • AHans Wilhelm Geiger - particle detector
  • BWilhelm Conrad Röntgen - x-ray
  • CDmitri Mendeleev - periodic table of elements
  • DEvangelista Torricelli - mercury barometer
  • ENiels Bohr - electron microscope
Correct answer: E Niels Bohr - electron microscope

Full explanation

Option A Explanation:

A) Hans Wilhelm Geiger - particle detector

Hans Wilhelm Geiger developed the Geiger counter, a particle detector used to measure ionizing radiation.

Option B Explanation:

B) Wilhelm Conrad Röntgen - x-ray

Wilhelm Conrad Röntgen discovered X-rays in 1895.

Option C Explanation:

C) Dmitri Mendeleev - periodic table of elements

Dmitri Mendeleev formulated the periodic table of elements in 1869.

Option D Explanation:

D) Evangelista Torricelli - mercury barometer

Evangelista Torricelli invented the mercury barometer in 1643.

Option E Explanation:

E) Niels Bohr - electron microscope

Niels Bohr was a physicist known for his contributions to quantum mechanics and the Bohr model of the atom, but he did not invent the electron microscope. The electron microscope was developed by Ernst Ruska and Max Knoll in the 1930s.

Summary to learn

Hans Geiger is credited with the Geiger counter (particle detector), Wilhelm Conrad Röntgen with discovering X-rays (1895), Dmitri Mendeleev with formulating the periodic table (1869), and Evangelista Torricelli with inventing the mercury barometer (1643) — all correctly matched. Niels Bohr, despite major contributions to quantum mechanics and atomic theory, did not invent the electron microscope — that was Ernst Ruska and Max Knoll, in the 1930s.

Which one of the following writers is the author of the best-selling novel My Brilliant Friend?

  • AElena Ferrante
  • BKazuo Ishiguro
  • CPaulo Coelho
  • DKhaled Hosseini
  • EIan McEwan
Correct answer: A Elena Ferrante

Full explanation

The correct answer is:

A) Elena Ferrante

Elena Ferrante is the author of My Brilliant Friend (L'amica geniale in Italian), the first book in the Neapolitan Novels series.

Ferrante is a pseudonymous Italian writer, and her true identity remains unknown. The novel, published in 2011, follows the lifelong friendship between two women, Elena Greco and Lila Cerullo, set in post-war Naples.

The other four are all major contemporary novelists, just known for different acclaimed books: Kazuo Ishiguro for The Remains of the Day, Paulo Coelho for The Alchemist, Khaled Hosseini for The Kite Runner, and Ian McEwan for Atonement. None of them wrote the Neapolitan Novels.

Summary to learn

Elena Ferrante is the pseudonymous author of My Brilliant Friend (2011), the first book in her Neapolitan Novels series, following the lifelong friendship of two women, Elena Greco and Lila Cerullo, in post-war Naples. The other four are all major contemporary novelists known for different acclaimed books: Kazuo Ishiguro for The Remains of the Day, Paulo Coelho for The Alchemist, Khaled Hosseini for The Kite Runner, and Ian McEwan for Atonement.

Which one of the following institutions of the European Union is elected by direct universal suffrage?

  • AEuropean Commission
  • BEuropean Parliament
  • CCouncil of the European Union
  • DCourt of Justice of the European Union
  • EEuropean Economic and Social Committee
Correct answer: B European Parliament

Full explanation

Option A Explanation:

A) European Commission

Incorrect. Members are appointed by national governments.

Option B Explanation:

B) European Parliament

Correct. The European Parliament is the only institution of the European Union that is elected by direct universal suffrage. Members of the European Parliament (MEPs) are elected by citizens of EU member states every five years.

Option C Explanation:

C) Council of the European Union

Incorrect. Composed of government ministers from member states.

Option D Explanation:

D) Court of Justice of the European Union

Incorrect. Judges are appointed by member states.

Option E Explanation:

E) European Economic and Social Committee

Incorrect. Members are appointed to represent various economic and social groups.

Summary to learn

Among the European Union's institutions, only the European Parliament is elected directly by citizens of member states (its MEPs, every five years); the European Commission's members are appointed by national governments, the Council of the EU is composed of government ministers, the Court of Justice's judges are appointed by member states, and the European Economic and Social Committee's members are appointed to represent economic and social interest groups.

Which one of the following global organisations sets and enforces rules of trade between nations?

  • AWTO
  • BWorld Bank
  • CWorld Economic Forum
  • DOECD
  • EIMF
Correct answer: A WTO

Full explanation

Option A Explanation:

A) WTO

Correct. The World Trade Organization (WTO) is responsible for setting and enforcing trade rules between nations. It oversees international trade agreements, resolves disputes, and promotes free trade while ensuring fair competition.

Option B Explanation:

B) World Bank

Incorrect. Provides financial and technical assistance for development projects.

Option C Explanation:

C) World Economic Forum

Incorrect. A non-governmental organization that hosts discussions on global economic policies but doesn't enforce trade rules.

Option D Explanation:

D) OECD

Incorrect. It represents Organisation for Economic Co-operation and Development. It focuses on economic policy coordination among member countries, not trade enforcement.

Option E Explanation:

E) IMF

Incorrect. IMF represents International Monetary Fund.

Focuses on financial stability and monetary cooperation, not trade regulations.

Summary to learn

The World Trade Organization (WTO) is the global body that sets and enforces the rules of trade between nations, overseeing trade agreements, resolving disputes, and promoting fair competition. It is distinct from other well-known international economic bodies with different mandates: the World Bank provides financial and technical assistance for development projects, the World Economic Forum is a non-governmental discussion forum with no enforcement power, the OECD focuses on economic policy coordination among member countries rather than trade enforcement, and the IMF focuses on financial stability and monetary cooperation.

Biology

Cell biology, genetics, molecular biology & human physiology · 18 questions
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Which of the following reactions or biological processes involves a redox reaction?

  • Aa cytosine and guanine pairing
  • Bdepolarisation of a neuron
  • Cglucose + glucose ⇋ maltose + water
  • Dpolymerisation of amino acid
  • ENAD⁺+ H₂ ⇋ NADH + H⁺
Correct answer: E NAD⁺+ H₂ ⇋ NADH + H⁺

Full explanation

In many chemical reactions, there is a transfer of one or more electrons (e-) from one reactant to another. These electron transfers are called oxidation-reduction reactions, or redox reactions for short.

Option A Explanation:

A) a cytosine and guanine pairing

Cytosine and guanine pairing involves hydrogen bonding and electron transfer is not involved in this bonding process. Thus, this is not a redox reaction. This option is false.

Option B Explanation:

B) depolarisation of a neuron

Depolarisation of a neuron is a result of ion concentration changes. This is not a redox reaction. Thus, this option is false.

Option C Explanation:

C) glucose + glucose ⇋ maltose + water

This is a condensation reaction which does not contain electron transfer. Thus, this is not a redox reaction. This option is false.

Option D Explanation:

D) polymerisation of amino acid

Polymerisation reactions do not contain electron transfer. Thus, this is not a redox reaction. This option is false.

Option E Explanation:

E) NAD⁺+ H₂ ⇋ NADH + H⁺

In this reaction, electron is transferred from H₂ to NAD⁺, resulting in NADH and H⁺. Thus, this reaction is a redox reaction and it occurs commonly in the cellular respiration process, NAD⁺ serving as electron carrier throughout the pathway.

This option is true.

Summary to learn

A redox (oxidation-reduction) reaction is specifically one involving the transfer of electrons between reactants — not every chemical or biological change qualifies. Hydrogen bonding (as in base pairing), ion-driven changes in membrane potential (as in neuron depolarisation), condensation reactions that release water (as in forming maltose), and polymerisation reactions (as in linking amino acids) all involve no electron transfer and so are not redox reactions; NAD⁺ accepting electrons (and a proton-bearing hydrogen) to become NADH, as happens throughout cellular respiration, is a genuine redox reaction.

In which of the following places are proton pumps found?

1. The chloroplast stroma

2. The gap between the thylakoid membranes

3. The membrane of the granum

  • A1 and 3 only
  • B1 only
  • C2 only
  • D1 and 2 only
  • E3 only
Correct answer: E 3 only

Full explanation

Proton pumps are located in the thylakoid membrane, which forms the structure of the grana in chloroplasts. These pumps play a crucial role in the light-dependent reactions of photosynthesis, where they actively transport protons (H⁺ ions) from the stroma into the thylakoid lumen, creating a proton gradient necessary for ATP synthesis. Proton pumps are not found in the stroma, which is where the Calvin cycle (light-independent reactions) occurs, nor are they found in the gap between thylakoid membranes --- this space is where H⁺ ions accumulate but not where the pumping occurs. Therefore, the correct answer is option E) 3 only, indicating the thylakoid membrane as the site of proton pumps.

Summary to learn

Chloroplasts have three distinct compartments relevant to photosynthesis: the stroma (site of the Calvin cycle), the thylakoid lumen (the space inside the thylakoid membranes, where H⁺ ions accumulate), and the thylakoid membrane itself, organised into stacks called grana. Proton pumps sit specifically in the thylakoid membrane, where they actively transport H⁺ ions from the stroma into the thylakoid lumen during the light-dependent reactions, building the proton gradient that drives ATP synthesis.

Which of the following is correct for cholesterol in humans?

  • AIt maintains the fluidity of the cell membrane.
  • BIt is used to make all hormones.
  • CIt forms hydrogen bonds with water which stabilises the cell membrane.
  • DIt is a good source of energy because of the number of hydrogen atoms.
  • EIt transports fatty acids around the body.
Correct answer: A It maintains the fluidity of the cell membrane.

Full explanation

Cholesterol, a type of steroid, is a crucial molecule in animals. It is a common component of animal cell membranes and is also the precursor from which other steroids, such as the vertebrate sex hormones, are synthesized.

Option A Explanation:

A) It maintains the fluidity of the cell membrane.

Cholesterol is a component of animal cell membrane. It helps maintain the fluidity of the membrane by acting as a buffer against temperature change: at higher temperatures it restrains phospholipid movement, preventing the membrane from becoming too fluid, while at lower temperatures it disrupts the regular packing of phospholipids, preventing the membrane from becoming too rigid or solidifying. Thus, this statement is correct.

Option B Explanation:

B) It is used to make all hormones.

Cholesterol is used to make only the vertebrate sex hormones. Other hormones are made mostly from polypeptides. Thus, this statement is false.

Option C Explanation:

C) It forms hydrogen bonds with water which stabilises the cell membrane.

Cholesterol is largely hydrophobic because it consists mainly of a nonpolar hydrocarbon structure with only a small polar hydroxyl group (-OH). While the hydroxyl group can form limited hydrogen bonds, the large nonpolar steroid ring system and hydrocarbon tail dominate its properties, making cholesterol overall hydrophobic. As a result, cholesterol cannot effectively form hydrogen bonds with water and has very low solubility in aqueous environments.

Option D Explanation:

D) It is a good source of energy because of the number of hydrogen atoms.

Cholesterol serves as a component of cell membranes and precursor of steroid hormones. It does not have a role as energy storage molecules. Thus, this option is false.

Option E Explanation:

E) It transports fatty acids around the body.

Cholesterol does not have a role as fatty acid transporter. It is lipoprotein group that transport fatty acids around the body. Thus, this option is false.

Summary to learn

Cholesterol is a steroid lipid that sits within animal cell membranes and also serves as the precursor for vertebrate sex hormones (not all hormones — most others are peptide-based). Its key membrane role is to act as a fluidity buffer: at higher temperatures it restrains phospholipid movement, keeping the membrane from becoming too fluid, while at lower temperatures it disrupts the tight, regular packing of phospholipids, keeping the membrane from becoming too rigid or solidifying. Because cholesterol is overall hydrophobic (a large nonpolar steroid ring system with only a small polar hydroxyl group), it does not meaningfully hydrogen-bond with water, and it plays no role in transporting fatty acids, which is instead the job of lipoproteins.

Polydactyly is a condition caused by a gene mutation. Animals affected by polydactyly have extra digits on one or more limbs. Five inheritance patterns of polydactyly in a species are shown in the diagrams.

IMAT 2021 question 26 figure
IMAT 2021 question 26 figure

Which inheritance pattern can ONLY occur when polydactyly is caused by an autosomal dominant allele and NOT when it is caused by an autosomal recessive allele? [Assume normal cell divisions in all individuals.]

  • A1
  • B4
  • C5
  • D3
  • E2
Correct answer: E 2

Full explanation

No. 1 pattern can occur in both autosomal dominant (homozygous) and recessive (homozygous) cases.

No. 2 pattern represents autosomal dominant disorder. This can be identified in F2 generation in which normal offspring is born from 2 polydactyly parents (heterozygous). All F2 offspring must have the disorder if this pattern is due to autosomal recessive allele.

No. 3 pattern can occur in both autosomal dominant (heterozygous) and recessive (homozygous) cases.

No. 4 pattern can occur in both autosomal dominant (homozygous) and recessive (homozygous) cases.

No. 5 pattern can occur in both autosomal dominant (heterozygous) and recessive (homozygous) cases.

Summary to learn

In an inheritance pedigree, an offspring pattern can only be pinned to one specific mode of inheritance (rather than being consistent with several) when it produces a combination that is impossible under the alternative. Two affected (heterozygous) parents producing an unaffected child is a pattern that autosomal dominant inheritance predicts (since not every offspring need inherit the dominant allele), but autosomal recessive inheritance rules out, because two affected recessive-homozygous parents can only pass on the recessive allele and so could never produce an unaffected offspring — making that specific pattern diagnostic for dominant inheritance alone.

Which one of the following types of nuclei acid is/are found in viruses

1. Single-stranded DNA

2. Double-stranded DNA

3. RNA

  • A1, 2 and 3
  • B2 and 3 only
  • C1 and 3 only
  • D2 only
  • E1 and 2 only
Correct answer: A 1, 2 and 3

Full explanation

Viruses' genomes may consist of double-stranded DNA, single-stranded DNA, double-stranded RNA, or single-stranded RNA, depending on the type of virus. A virus is called a DNA virus or an RNA virus based on the kind of nucleic acid that makes up its genome.

Thus, the correct option is option A) 1,2 and 3

Summary to learn

Unlike cellular life, which always uses double-stranded DNA as its genome, viruses are diverse in their genetic material: depending on the type of virus, a viral genome can be single-stranded DNA, double-stranded DNA, single-stranded RNA, or double-stranded RNA. A virus is classified as a "DNA virus" or an "RNA virus" precisely according to which of these nucleic acid types makes up its own genome.

Which one of the diagrams (not drawn to scale) represents a structure that is formed by mitosis?

  • A
    IMAT 2021 question 28 option A neutrophil (correct)
  • B
    IMAT 2021 question 28 option B bacteria
  • C
    IMAT 2021 question 28 option C chloroplast
  • D
    IMAT 2021 question 28 option D virus
  • E
    IMAT 2021 question 28 option E mitochondria
Correct answer: A Option A (neutrophil — myeloid precursor cells undergo mitotic division to produce neutrophils)

Full explanation

Option A Explanation:

Option A shows the image of a neutrophil. Myeloid precursor cells undergo mitotic divisions and differentiate into myeloblasts, which are committed to becoming neutrophils. Thus, this option is correct.

Option B Explanation:

Option B shows the image of bacteria. Bacteria divide through the process called binary fission, not mitosis. Thus, this option is false. Binary fission is a simple and rapid method of asexual reproduction used primarily by prokaryotic organisms, such as bacteria. In binary fission, a single parent cell replicates its DNA and then divides into two genetically identical daughter cells. The process involves the following basic steps: the DNA is copied, the cell grows larger, and the plasma membrane pinches inward, eventually splitting the cytoplasm. Unlike mitosis in eukaryotes, binary fission does not involve spindle fibers or complex mitotic stages. It is an efficient way for bacteria to reproduce and rapidly increase their population.

Option C Explanation:

Option C shows the image of chloroplast. Chloroplasts arose from a cyanobacterial endosymbiont and multiply by binary division, reminiscent of their free-living ancestor. Thus, chloroplast is not formed by mitosis. This option is false.

Option D Explanation:

Option D shows the image of a virus. Viruses lack metabolic enzymes and equipment for making proteins, such as ribosomes. They are obligate intracellular parasites; in other words, they can replicate only within a host cell by using the host sources. Thus, viruses are formed through replicative cycles in the host cell, not through mitosis. This option is false.

Option E Explanation:

Option E shows the image of mitochondria. Mitochondria divide into two separate mitochondrial organelles through the process called mitochondrial fission, not mitosis. Thus, mitochondria is not formed by mitosis and this option is false.

Summary to learn

Mitosis is the process by which a single eukaryotic cell divides to produce two genetically identical daughter cells, and it is specifically how myeloid precursor cells in bone marrow divide and differentiate into neutrophils. It is not, however, how every kind of biological structure is produced: bacteria reproduce by binary fission (DNA replication followed by the cell splitting in two, with no spindle fibres or mitotic stages at all), mitochondria and chloroplasts divide by their own fission processes inherited from their free-living bacterial ancestors, and viruses are not "produced" by any division at all — as obligate intracellular parasites lacking their own ribosomes and metabolic machinery, they can only be assembled through replicative cycles inside a host cell.

The graph below shows the change in blood cell count of a human over time.

IMAT 2021 question 29 figure

Which of the following could explain the shape of the above graph?

1. A reduction in the concentration of oxygen in the atmosphere

2. A response to a bacterial infection

3. Increased differentiation of bone marrow stem cells

  • A2 and 3 only
  • B1 and 2 only
  • C1 only
  • D1, 2 and 3
  • E2 only
Correct answer: D 1, 2 and 3

Full explanation

From the given graph, it can be concluded that there is a sudden rise in the blood cell count in a specific time period. Blood cells can be RBCs or WBCs. It can be due to several reasons. 3 explanations are given.

1. A reduction in the concentration of oxygen in the atmosphere This is a correct explanation because the body adjust the reduction in environmental oxygen concentration (Hypoxia) by stimulating RBC production, thereby increasing the blood cell count in the blood.

2. A response to a bacterial infection This is another correct explanation because infections, especially bacterial ones, trigger an immune response, leading to an increase in white blood cell (WBC) count (leukocytosis) to fight the infection.

3. Increased differentiation of bone marrow stem cells This is also a correct explanation because if bone marrow stem cells are stimulated, the production of blood cells increases, leading to a rise in blood count.

Thus, the correct option is option D) 1, 2 and 3

Summary to learn

A sudden rise in blood cell count can have several independent, non-exclusive causes acting on either red or white blood cells: falling atmospheric oxygen (hypoxia) stimulates extra red blood cell production to compensate; a bacterial infection triggers an immune response that raises white blood cell count (leukocytosis) to fight it off; and any direct stimulation of bone marrow stem cells increases blood cell output generally, regardless of the specific trigger behind that stimulation.

Three fatty acids with the formula C₈H₁₆O₂ react with glycerol (C₃H₈O₃) to form a triglyceride. Which of the following is the correct formula for the triglyceride?

  • AC₂₇H₅₆O₉
  • BC₂₇H₄₈O₆
  • CC₂₇H₅₂O₇
  • DC₂₇H₅₀O₆
  • EC₂₇H₈₄O₉
Correct answer: D C₂₇H₅₀O₆

Full explanation

To form a triglyceride, three fatty acids with the molecular formula C₈H₁₆O₂ undergo three-step esterification reaction with glycerol (C₃H₈O₃). In this process, each fatty acid forms an ester bond with one of the three hydroxyl groups on the glycerol molecule. For every ester bond formed, one molecule of water (H₂O) is released, resulting in the removal of three water molecules overall. This leads to the formation of a triglyceride composed of the glycerol backbone linked to three fatty acid chains via ester linkages.

The correct formula would be D) C₂₇H₅₀O₆

Summary to learn

Esterification joins a fatty acid's carboxyl group to one of glycerol's hydroxyl groups, releasing one water molecule per bond formed; building a triglyceride from glycerol and three fatty acids therefore forms three ester bonds and releases three water molecules overall. The triglyceride's formula is found by adding the atoms from glycerol and all three fatty acids together, then subtracting the atoms of the three released water molecules (3 × H₂O, i.e. 6 H and 3 O) from that sum.

A cell containing four pairs of homologous chromosomes divides by meiosis. Which row shows the cells produced and the number of chromosomes that they contain?

Each number below is the chromosome count of one cell; more than one number in a column means more than one cell was produced at that stage.

rowparent cellend of meiosis Iafter meiosis II
142, 22, 2, 2, 2
244, 42, 2, 2, 2
384, 44, 4, 4, 4
488, 84, 4, 4, 4
5816, 168, 8, 8, 8
  • Arow 1
  • Brow 4
  • Crow 3
  • Drow 5
  • Erow 2
Correct answer: C row 3

Full explanation

The question mentions a cell containing four pairs of homologous chromosomes divides by meiosis.

Meiosis is composed of 2 stages of cell division.

- Meiosis 1 is reductional division (homologous chromosomes separation)

- Meiosis 2 is equational division (sister chromatids separation)

For a cell with 4 homologous chromosomes, there will be 8 chromosomes. 2 cells; each with 4 chromosomes will result from Meiosis 1. After meiosis 2, 4 cells with 4 chromosomes each will result.

Thus, the correct option is option C) row 3.

Summary to learn

Meiosis is two sequential divisions of one diploid cell. Meiosis I is the reductional division: homologous chromosome pairs separate, so the starting chromosome number is halved, but each chromosome still consists of two sister chromatids, producing two cells with half the original chromosome count. Meiosis II is the equational division: sister chromatids separate in each of those two cells, doubling the cell count to four but leaving the chromosome count per cell unchanged from the end of meiosis I — so across the whole process, a cell with n pairs of homologous chromosomes (2n chromosomes) ends up as four haploid cells, each with n chromosomes.

The sequence of bases in part of a DNA strand is:

TATGATCTTAGGCAACAT

A strand of mRNA is transcribed using this sequence of bases. Which one of the following charts shows the correct proportions of the bases in the mRNA?

  • A
    IMAT 2021 question 32 mRNA base pie chart option A
  • B
    IMAT 2021 question 32 mRNA base pie chart option B
  • C
    IMAT 2021 question 32 mRNA base pie chart option C (correct)
  • D
    IMAT 2021 question 32 mRNA base pie chart option D
  • E
    IMAT 2021 question 32 mRNA base pie chart option E
Correct answer: C Option C (A and U each 1/3 of the circle, G and C each 1/6)

Full explanation

The sequence of bases in part of a DNA strand is:

TATGATCTTAGGCAACAT

A strand of mRNA is transcribed using this sequence of bases.

According to complementary base pairing, the sequence of mRNA is:

AUACUAGAAUCCGUUGUA (6A, 6U, 3G, 3C)

Total base number is 6+6+3+3 = 18

Adenine and Uracil each will occupy one-third of circle and Guanine and Cytosine will occupy one-sixth of the circle.

Thus, the correct option is option C.

Summary to learn

Transcription copies a DNA template strand into a complementary mRNA strand using standard base-pairing rules, but with uracil (U) replacing thymine (T): DNA's A pairs with mRNA's U, DNA's T pairs with mRNA's A, and DNA's G and C pair with mRNA's C and G respectively. Once the mRNA sequence is known, the proportion of each base is simply that base's count divided by the total number of bases in the strand — two bases occurring in equal numbers will occupy equal-sized slices of a pie chart representing those proportions.

The diagram represents an animal cell with five organelles labelled P, Q, R, S and T.

IMAT 2021 question 33 labelled animal cell diagram, organelles P to T

Which row correctly matches the label with the name and function of the cell organelle?

labelname of cell organellefunction of cell organelle
row 1Pmitochondrionprotein synthesis
row 2Qcentriolesholds sister chromatids together
row 3Rribosomeformation of lysosomes
row 4SGolgi apparatusanaerobic respiration
row 5Tnucleolusformation of ribosomal sub-units
  • Arow 2
  • Brow 4
  • Crow 1
  • Drow 5
  • Erow 3
Correct answer: D row 5

Full explanation

Label P represents Golgi apparatus, which can be identified by their stacks of associated, flattened sacs, or cisternae. The main function of the Golgi apparatus is to receive, modify and send proteins to other destinations. Golgi has different numbers of cistenae, but in this picture may appear connected under a microscope, but biochemically and structurally, each cisterna is an individual unit.

Label Q represents centrosome, which is composed of 2 centrioles. It helps organize microtubule assembly in animal cells.

Label R represents rough endoplasmic reticulum, which can be identified by network of membranous tubules and sacs called cisternae studded by ribosomes. Their main function is the production of secretory proteins.

Label S represents the mitochondrion, identifiable by its double-membrane structure. Its primary function is to carry out aerobic respiration and produce ATP, the cell's main energy source.

Label T represents the nucleolus, which is the prominent structure inside the nucleus. It synthesizes rRNA.

Among 5 rows mentioned in the table, the only correct row is row 5.

Summary to learn

Several membrane-bound and non-membrane-bound organelles each have a distinct primary role: the Golgi apparatus (recognisable by its stacked, flattened cisternae) receives, modifies and packages proteins for their final destinations; the centrosome, composed of two centrioles, organises microtubule assembly; rough endoplasmic reticulum, studded with ribosomes, produces secretory proteins; the mitochondrion, identifiable by its double membrane, carries out aerobic respiration to generate ATP; and the nucleolus, a dense structure inside the nucleus, synthesises rRNA and assembles ribosomal sub-units.

The diagram shows the relationship between the features of two substances involved in digestion: bile and amylase.

IMAT 2021 question 34 Venn diagram of bile and amylase features, regions X, Y and Z

Which of the following rows is correct for X, Y and Z?

XYZ
row 1assimilates lipidstored in the gall bladderdigests maltose
row 2digests lipidworks in the small intestinedigests starch
row 3digests lipidproduced by the pancreasproduces maltose
row 4emulsifies lipidproduced by the pancreasdigests maltose
row 5emulsifies lipidworks in the small intestinedigests starch
  • Arow 5
  • Brow 2
  • Crow 1
  • Drow 4
  • Erow 3
Correct answer: A row 5

Full explanation

Bile is digestive fluid produced by the liver and stored in the gall bladder. Bile aids digestion by emulsifying fats in the small intestine, breaking large fat droplets into smaller ones to increase the surface area for lipase enzymes to act, making fat digestion more efficient.

Amylase is an enzyme that breaks down polysaccharides (like starch and glycogen) into smaller sugars. It is produced by the pancrease and released into the duodenum. Specifically, amylase hydrolyzes the α-1,4-glycosidic bonds between glucose units in long polysaccharide chains. It breaks them down into smaller chains, mainly maltose (a disaccharide made of two glucose units), but it cannot digest maltose. Maltose is broken into the glucose by maltase.

The similar feature between bile and pancreatic amylase is the site of action. Both of them act in the small intestine.

Thus, the correct role that shows the relationship between the features of bile and amylase is row 5.

Summary to learn

Bile and amylase are both digestive secretions that act in the small intestine, but they play very different roles there: bile, produced by the liver and stored in the gallbladder, emulsifies (physically breaks up) fat droplets to increase their surface area for lipase, while amylase, produced by the pancreas, chemically hydrolyses the bonds in starch to break it down into maltose (but cannot itself break maltose down further into glucose — that is maltase's job). Comparing two processes described only abstractly, as "X", "Y" and "Z", means matching each label to the specific verb and location that the biology actually supports, rather than to whichever answer sounds most familiar.

Organ or tissue transplants normally require that the donor's antigens must be closely matched to those of the recipient. Which one of the following types of transplant can typically be carried out WITHOUT the need for a match between donor and recipient?

  • Aliver
  • Blung
  • Ccornea
  • Dkidney
  • Eheart
Correct answer: C cornea

Full explanation

Any substance that elicits a B or T cell response is called an antigen. In adaptive immunity, recognition occurs when a B cell or T cell binds to an antigen, such as a bacterial or viral protein, via a protein called an antigen receptor. For immune cells to have access to the particular antigen ; in this case, the donor's antigen; a transportation system (blood supply) is required. Among the given 4 organs, the cornea is the only avascular organ. Thus, immune cells and antibodies have limited access to it and transplant can be carried out without the need for a match between donor and recipient.

Thus, the correct option is option C) cornea.

Summary to learn

Organ and tissue transplants normally require close antigen matching because the immune system's B and T cells recognise foreign antigens via blood-borne immune cells and antibodies reaching the transplanted tissue. The cornea is the one major exception: it is avascular (has no blood supply of its own), so the immune system's cells and antibodies have essentially no access to it, which is why corneal transplants can typically be performed without needing to match donor and recipient.

The SRY gene is normally located on the human Y chromosome. This gene initiates the development of male characteristics. Using this information, which of the following statements about the SRY gene is/are correct?

1. Insertion of the SRY gene into an X chromosome of a female zygote could give it male characteristics

2. A sperm cell arising from incorrect division, which has a functional SRY gene, could give rise to a female with a sex chromosome trisomy following fertilisation with a normal ova

3. During meiosis, crossing over could result in the formation of 'X' sperm with the SRY gene, which could cause male characteristics after fertilisation

  • A3 only
  • B1 and 3 only
  • C2 only
  • D1 and 2 only
  • E1 only
Correct answer: B 1 and 3 only

Full explanation

SRY gene (Sex-determining Region Y) is located on Y chromosome. It is required for testis development. Without SRY gene, gonads develop into ovaries, even in XY embryos.

Analysis of the given statements about SRY gene

1. Insertion of the SRY gene into an X chromosome of a female zygote could give it male characteristics This statement is correct. Since the SRY gene is responsible for initiating the male developmental pathway, If inserted into an X chromosome in a zygote, it could lead to male characteristics despite the absence of a Y chromosome.

2. A sperm cell arising from incorrect division, which has a functional SRY gene, could give rise to a female with a sex chromosome trisomy following fertilisation with a normal ova This statement is false. If the sperm carries an SRY-containing chromosome, the individual is unlikely to be phenotypically female because the presence of the SRY gene typically leads to male development.

3. During meiosis, crossing over could result in the formation of 'X' sperm with the SRY gene, which could cause male characteristics after fertilisation This statement is correct. If the SRY gene is transferred onto the X chromosome and an X-bearing sperm fertilizes an egg, the resulting XX individual could develop male characteristics due to the presence of SRY.

Thus, the correct option is option B) 1 and 3 only.

Summary to learn

The SRY gene, normally carried on the Y chromosome, is the single gene responsible for initiating male sexual development — without it, even an XY embryo's gonads develop as ovaries. Because male development follows SRY specifically, rather than the presence of a Y chromosome as such, SRY relocating onto an X chromosome (through insertion, or through crossing over between the X and Y during meiosis) can trigger male characteristics in an individual who is chromosomally XX, while a Y-bearing sperm without a functional SRY gene would not.

The diagram shows a cross section through a human eye. Some parts of the eye are labelled 1 to 5 with notes. Which one of the following notes is correct?

IMAT 2021 question 37 figure
  • Anote 3
  • Bnote 1
  • Cnote 2
  • Dnote 4
  • Enote 5
Correct answer: D note 4

Full explanation

Note 1 is false because The retina is primarily composed of sensory neurons, specifically photoreceptors (rods and cones), and interneurons that process visual information before sending it to the brain.

Note 2 is false because fovea is densely packed with cone photoreceptors.

Note 3 is false because pupil constricts to reduce the light entering the eye in the light, not in the dark.

Note 4 is true because the cornea is avascular (lacks blood vessels), so it relies on the aqueous humor for nutrients, including glucose and oxygen.

Note 5 is false because cornea cannot be adjusted. Only lens can adjust their curvature for fine focus.

Thus, the correct option is option D) note 4.

Summary to learn

Different structures in the human eye have distinct, non-interchangeable roles: the retina is composed of photoreceptors (rods and cones) and interneurons that process visual signals; the fovea is densely packed specifically with cone photoreceptors, giving it high visual acuity; the pupil constricts in bright light (not in the dark) to limit how much light enters; the cornea is avascular and so relies on the aqueous humor, rather than blood, to supply its nutrients and oxygen; and fine focusing is achieved by the lens changing its curvature, not by any adjustment of the fixed-shape cornea.

Which row could be correct for directional selection?

a low-frequency phenotype is selecteda predator could be the causethe frequency of a recessive allele increases
row 1YesNoNo
row 2NoYesNo
row 3NoNoYes
row 4NoYesYes
row 5YesYesYes
  • Arow 3
  • Brow 1
  • Crow 2
  • Drow 5
  • Erow 4
Correct answer: D row 5

Full explanation

Natural selection can alter the frequency distribution of heritable traits in three ways, depending on which phenotypes in a population are favored: through directional selection, disruptive selection, and stabilizing selection.

Directional selection occurs when conditions favor individuals exhibiting one extreme of a phenotypic range.

Disruptive selection occurs when conditions favor individuals at both extremes of a phenotypic range over individuals with intermediate phenotypes.

Stabilizing selection acts against both extreme phenotypes and favors intermediate variants

Among the given information on the table, only the row 5 represents the correct pattern of directional selection because a low frequency phenotype is selected and it could be the case that the frequency of a recessive allele increases and a predator could be the cause.

Summary to learn

Natural selection can reshape a population's traits in three characteristic ways depending on which phenotypes are favoured: directional selection favours one extreme of a phenotypic range (shifting the population toward it over time), disruptive selection favours both extremes over the intermediate form, and stabilising selection favours the intermediate form over both extremes. A scenario where a previously rare, extreme phenotype becomes favoured — for instance because a predator selectively targets the more common form — and the allele behind that rare phenotype consequently rises in frequency is the signature of directional selection specifically.

Which one of the following statements is correct about the cardiac cycle of a healthy human?

  • AWhen the left ventricle relaxes, the aortic valve closes.
  • BWhen the right atrium contracts, the left ventricle contracts.
  • CWhen the right ventricle contracts, the right atrio-ventricular valve opens.
  • DWhen the right atrio-ventricular valve closes, the left atrio-ventricular valve opens.
  • EWhen the left atrium contracts, the aortic valve opens.
Correct answer: A When the left ventricle relaxes, the aortic valve closes.

Full explanation

For an adult human at rest with a heart rate of about 72 beats per minute, one complete cardiac cycle takes about 0.8 second. 3 general phases are involved.

1. Atrial and ventricular diastole : AV valves open and semilunar valves close.

2. Atrial systole and ventricular diastole : AV valves open and semilunar valves close.

3. Ventricular systole and atrial diastole : AV valves close and semilunar valves open.

Option A Explanation:

A) When the left ventricle relaxes, the aortic valve closes.

During ventricular diastole, semilunar valves (aortic valve) close.

Thus, this option is correct.

Option B Explanation:

B) When the right atrium contracts, the left ventricle contracts.

During atrial systole phase, ventricles relax.

Thus, this option is false.

Option C Explanation:

C) When the right ventricle contracts, the right atrio-ventricular valve opens.

During ventricular systole, AV valves close and semilunar valves open.

Thus, this option is false.

Option D Explanation:

D) When the right atrio-ventricular valve closes, the left atrio-ventricular valve opens.

AV valves close and open simultaneously.

Thus, this option is false.

Option E Explanation:

E) When the left atrium contracts, the aortic valve opens.

During atrial systole phase, AV valves open and semilunar valves (aortic valve) close.

Thus, this option is false

Summary to learn

The cardiac cycle alternates between two valve states that never occur in any other combination: during ventricular diastole (relaxation), the atrioventricular (AV) valves are open and the semilunar valves (including the aortic valve) are closed, while during ventricular systole (contraction), the AV valves close and the semilunar valves open. Because the two AV valves (and the two semilunar valves) always open and close together as pairs, and the whole heart alternates between just these two valve configurations, most "which valve does what" distractors can be eliminated just by tracking which single phase the heart is actually in.

Which of the following cell structures contain(s) biological catalysts

1. Cytoplasm

2. Nucleus

3. Mitochondria

  • A2 only
  • B1, 2 and 3
  • C3 only
  • D2 and 3 only
  • E1 only
Correct answer: B 1, 2 and 3

Full explanation

Biological catalysts are enzymes that control the rate of reaction of metabolic processes occurring in the living cells. Metabolic process usually occur in all of the 3 mentioned cellular structures.

All three structures listed --- cytoplasm, nucleus, and mitochondria --- contain enzymes and thus biological catalysts. In the cytoplasm, enzymes are involved in pathways like glycolysis, where glucose is broken down to produce energy. In the nucleus, enzymes are essential for DNA replication and transcription processes, such as DNA polymerase and RNA polymerase. In the mitochondria, enzymes drive the reactions of the citric acid cycle (Krebs cycle) and the electron transport chain, both critical for aerobic respiration and ATP synthesis. Therefore, all three structures (1, 2, and 3) contain biological catalysts.

Summary to learn

Biological catalysts (enzymes) are proteins that speed up the metabolic reactions occurring throughout a cell, and since metabolism happens in many compartments at once, so do enzymes: the cytoplasm hosts glycolysis enzymes that break down glucose, the nucleus hosts DNA polymerase and RNA polymerase for replication and transcription, and mitochondria host the enzymes of the citric acid cycle and the electron transport chain that drive aerobic ATP production.

Chemistry

General, inorganic, organic & biochemistry · 12 questions
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The general formula of an oxoacid is HₘXOₙ Which of the following expressions gives the oxidation state of element X?

  • An - 2m
  • Bm- 2n
  • C2m - n
  • D2n - m
  • Em + 2n
Correct answer: D 2n - m

Full explanation

The general formula of a molecule is given : HₘXOₙ

First, assign Oxidation Numbers to Known Elements.

- Hydrogen (H): Usually +1.

- Oxygen (O): Usually 2.

- X: Unknown (we need to determine it).

The sum of oxidation states in a neutral molecule must be 0.

Oxidation state of H + Oxidation state of X + Oxidation state of O = 0

(m × (+1)) + (Oxidation state of X) + (n × (−2)) = 0

m + (Oxidation state of X) − 2n = 0

Oxidation state of X = 2n−m

Thus, the correct option is option D) 2n - m

Summary to learn

In any neutral molecule, the oxidation numbers of every atom must sum to zero once each atom's contribution is multiplied by how many of that atom are present. For an oxoacid HmXOn, using hydrogen's standard oxidation state of +1 and oxygen's standard oxidation state of −2, setting up that sum — m(+1) + (oxidation state of X) + n(−2) = 0 — and rearranging for the one unknown gives the oxidation state of X directly in terms of m and n.

As Group VII of the Periodic Tables (F to I) is descended, which of the following properties of the elements DECREASE?

1. Melting points

2. Electronegativies

3. First ionisation energies

  • A2 and 3 only
  • B1 only
  • C2 only
  • D1 and 3 only
  • E1, 2 and 3
Correct answer: A 2 and 3 only

Full explanation

Group VII (Group 17 in modern IUPAC notation) consists of the halogens: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).

As we move down the group;

- Melting point increases because the size of the molecules increases and London dispersion force become stronger with increasing atomic size.

- Electronegativity decreases because as atomic size increases, reducing the effective nuclear affinity on bonding electrons. Fluorine is the most electronegative element.

- First ionizing energy decreases because as the atomic radius increases, the outermost electrons are further from the nucleus and less energy is needed to remove the outermost electron.

Thus, only properties 2 and 3 decrease down the group. The correct option is option A) 2 and 3 only

Summary to learn

Moving down Group VII (the halogens: F, Cl, Br, I, At), several periodic trends move in opposite directions. Melting point increases down the group, because larger atoms/molecules have stronger London dispersion forces holding them together. Electronegativity and first ionisation energy both decrease down the group, because the increasing atomic radius places the outermost (bonding or valence) electrons further from the nucleus, weakening the nucleus's pull on them and making those electrons both less strongly attracted to a bonding partner and easier to remove entirely.

100mL of a solution contained 3.2g of potassium nitrate. 25mL of this solution was added to an empty 250mL volumetric flask. Distilled water was added up to the 250mL mark and the flask was shaken to ensure that mixing was complete. A pipette was used to transfer 25mL of the resulting solution from the volumetric flask to an empty conical flask. What is the concentration of the potassium nitrate solution, in g L⁻¹, in the conical flask?

  • A0.32 gL⁻¹
  • B3.20 gL⁻¹
  • C0.08 gL⁻¹
  • D0.80 gL⁻¹
  • E8.00 gL⁻¹
Correct answer: B 3.20 gL⁻¹

Full explanation

Given :

- Mass of KNO₃ = 3.2 g

- Volume of solution = 100 mL = 0.100 L

Initial concentration =massvolume=3.2 g0.1 L= 32 gL⁻¹

After dilution in the volumetric flask,

25 mL of the initial solution is taken and diluted to 250 mL.

Dilution formula : C1V1 = C2V2

where : C1 = 32 gL- 1, V1 = 25 ml, V2 = 250 ml, C2 = ?

( 32 gL- 1 )(25ml) = C2 (250ml)

C2 =32 × 25250=800250= 3.2 gL⁻¹

Thus, the correct option is option B) 3.20 gL⁻¹

Summary to learn

A serial dilution problem is solved one step at a time, converting mass into concentration first (mass ÷ volume), then applying the dilution formula C1V1 = C2V2 whenever a known volume of solution is diluted up to a new, larger volume. Once a diluted solution has been mixed thoroughly, taking any smaller sample of it with a pipette does not change its concentration further — pipetting removes a portion of the solution, not more solvent, so the sample's concentration matches the flask it was drawn from.

At room temperature and pressure, which of the following substances has the strongest hydrogen bonds between their molecules?

  • APropanal, CH₃CH₃CHO
  • BFluoromethane, CH₃F
  • CEthanoic acid, CH₃СООН
  • DTrimethylamine, (CH₃)₃N
  • EHydrogen sulfide, H₃S
Correct answer: C Ethanoic acid, CH₃СООН

Full explanation

Hydrogen bonding occurs when hydrogen is directly bonded to highly electronegative atoms (N, O, or F).

Option A Explanation:

A) Propanal, CH₃CH₃CHO

- No strong hydrogen bonding because C=O (carbonyl) does not have an H directly attached to O.

- Only dipole-dipole and Van der Waals forces.

Option B Explanation:

B) Fluoromethane, CH₃F

- No strong hydrogen bonding because H is not directly bonded to F.

- Only dipole-dipole interactions due to polar C-F bonds.

Option C Explanation:

C) Ethanoic acid, CH₃СООН

Forms strong hydrogen bonds due to --OH in the carboxyl group.

Option D Explanation:

D) Trimethylamine, (CH₃)₃N

- No hydrogen bonding because there is no H attached to N.

- Only weak dipole-dipole interactions.

Option E Explanation:

E) Hydrogen sulfide, H₃S

- No significant hydrogen bonding because H is not attached to N, F or O.

- Only weak dipole-dipole and Van der Waals forces.

Summary to learn

Hydrogen bonding, the strongest common intermolecular force, requires a hydrogen atom directly bonded to a small, highly electronegative atom — nitrogen, oxygen, or fluorine (N, O or F) — on one molecule, positioned to interact with a lone pair on another. A carbonyl group's oxygen (as in an aldehyde), a C−F bond, an amine nitrogen with no attached H, and hydrogen bonded to sulfur (which is not electronegative enough) all fail this test and so rely only on weaker dipole-dipole or dispersion forces; a carboxylic acid's −OH group, with hydrogen bonded directly to oxygen, is a textbook case that does hydrogen-bond strongly.

Vitamin B5 has the structure:

IMAT 2021 question 45 figure

Which of the following functional groups are contained in a molecule of vitamin B5?

1. alcohol

2. aldehyde

3. amide

4. amine

5. carboxylic acid

6. ketone

  • A1, 3 and 6 only
  • B1, 2 and 4 only
  • C1, 3 and 5 only
  • D4, 5 and 6 only
  • E2, 5 and 6 only
Correct answer: C 1, 3 and 5 only

Full explanation

In the given Vitamin B5 structure, hydroxy group (-OH) can be identified on one end of the structure, contributing to its solubility in water. Amide group (-CONH-) can be identified in the central part of the structure. Carboxyl group (-COOH) can be identified on another end of the structure, making it acidic.

Thus, the correct option is C) 1, 3 and 5 only

Summary to learn

Identifying every functional group in a molecule means examining its full structure piece by piece rather than judging it by its overall category: a hydroxyl group (−OH) marks an alcohol, a carbonyl carbon bonded to both a nitrogen and an oxygen (−CONH−) marks an amide, and a carbon bearing both a C=O and an −OH (−COOH) marks a carboxylic acid — three chemically distinct groups that can all be present in the same molecule at once, as they are here.

Which of the following hydrocarbons are structural isomers of hexane?

IMAT 2021 question 46 figure
  • A2 only
  • B1 and 2 only
  • C1 and 3 only
  • D3 only
  • E1 only
Correct answer: A 2 only

Full explanation

Structural isomers are molecules that have the same molecular formula with different connectivity of atoms or different functional groups.

Hexane has the molecular formula C₆H₁₄

Among the given hydrocarbons, only the hydrocarbon number 2 has the same molecular formula as hexane. It also features the connectivity difference with the linear hexane. Thus, this is the correct structural isomer of hexane.

The correct option is option A) 2 only

Checking the other two against hexane's own formula (C₆H₁₄) makes this concrete. Structure 1 is drawn as a closed six-carbon ring rather than an open chain — that's cyclohexane, C₆H₁₂, a different molecular formula from hexane altogether, so it can't be an isomer of it no matter how the atoms are arranged. Structure 3 is a straight chain of only five carbons — that's pentane, C₅H₁₂, one carbon short of hexane's formula, so it's simply a smaller molecule, not an isomer. Only structure 2, a five-carbon backbone with one methyl branch (2-methylpentane), keeps hexane's exact formula, C₆H₁₄, while rearranging how the atoms connect — which is precisely what makes it a genuine structural isomer.

Summary to learn

Structural isomers share an identical molecular formula but differ in how their atoms are connected. Confirming a candidate isomer therefore starts with counting atoms, not just eyeballing the shape: a closed ring of the same number of carbons as a straight-chain alkane has two fewer hydrogens (a ring bonds an extra pair of carbons together, costing two C−H bonds) and so is a different formula entirely, a shorter chain is simply a different, smaller molecule, and only a chain with the same total carbon and hydrogen count, rearranged into a branched structure, counts as a true structural isomer.

Which row gives the correct shapes around the aluminium centres in AlCl₃ and Al₂Cl₆ molecules? [Atomic numbers: Al = 13; Cl = 17]

IMAT 2021 question 47 structural diagrams of AlCl3 and Al2Cl6
AlCl₃Al₂Cl₆
row 1trigonal planarsquare planar
row 2trigonal pyramidaltetrahedral
row 3tetrahedralsquare planar
row 4trigonal planartetrahedral
row 5trigonal pyramidalsquare planar
  • ARow 2
  • BRow 5
  • CRow 4
  • DRow 1
  • ERow 3
Correct answer: C Row 4

Full explanation

In AlCl₃ , Aluminium has 3 valence electrons and forms 3 single bonds with chlorine atoms. No lone pairs on Al express sp² hybridization, contributing to Trigonal planar shape.

In dimeric Al₂Cl₆, two AlCl₃ units link. Each Al forms three normal Al-Cl bonds + one additional Al-Cl coordinate bond with a bridging Cl. This gives each Al four bonding regions and express sp³ hybridization, contributing to Tetrahedral shape.

Thus, the correct option is option C) row 4

Summary to learn

A central atom's molecular shape follows directly from its number of bonding electron regions and lone pairs (VSEPR theory): three bonding regions and no lone pairs gives a trigonal planar shape (sp²), while four bonding regions and no lone pairs gives a tetrahedral shape (sp³). Aluminium trichloride, AlCl₃, is electron-deficient with only 3 bonds and no lone pair on Al, giving trigonal planar; in its dimer Al₂Cl₆, each Al gains a fourth bonding region by forming a coordinate (dative) bond to a bridging chlorine atom, giving each aluminium centre a tetrahedral shape instead.

An atom has a mass number of 18 and contains 10 neutrons. A common ion of this atom has a charge of -2. What is the electron configuration of this ion in its lowest energy state?

  • A1s²2s²2p⁶3s²3p⁴
  • B1s²2s²2p⁶3s²
  • C1s²2s²2p²
  • D1s²2s²2p⁴
  • E1s²2s²2p⁶
Correct answer: E 1s²2s²2p⁶

Full explanation

Given atom has a mass number of 18 and contains 10 neutrons.

atomic number (Z) = Mass number (A) - Number of neutrons = 18 - 10 = 8

Electron configuration for neutral atom is 1s²2s²2p⁴

Electron configuration for ion with a charge of -2 would be 1s²2s²2p⁶ (add 2 electrons to the outermost shell)

Thus, the correct option is option E) 1s²2s²2p⁶

Summary to learn

An atom's identity (its atomic number, and hence its neutral electron configuration) is found by subtracting its neutron count from its mass number; forming a common ion then means adding or removing electrons from that neutral configuration to match the ion's charge — a negative charge of magnitude n means n extra electrons added to the outermost shell, filling it toward the next noble-gas configuration, while a positive charge means electrons removed.

A sample of an oxide of iron contains 1.68g of iron and 0.64g of oxygen only. What is the formula of this oxide?

[Ar values: Fe = 56; 0 = 16]

  • AFe₃O₄
  • BFeO
  • CFe₄O₃
  • DFe₂O₃
  • EFe₃O₂
Correct answer: A Fe₃O₄

Full explanation

Given : mass of Fe = 1.68 g, mass of O = 0.64g

First, determine the Moles of Iron and Oxygen

Mole of Fe = 1.68g/56 = 0.03 mol

Mole of O = 0.64/16 = 0.04 mol

Then, find the simplest whole number ratio of the moles of Fe and O by dividing by the smaller number of mole.

mole of Fe : mole of O

(0.03)/(0.03) :(0.04)/(0.03)

1:1.33

To get a whole number ratio, multiply both side with 3.

1 x 3 : 1.33 x 3

3 : 4

Thus, the empirical formula is Fe₃O₄.

The correct option is option A) Fe₃O₄

Summary to learn

Finding an empirical formula from elemental masses is a fixed three-step process: convert each element's mass into moles by dividing by its atomic mass, divide every mole value by the smallest one among them to get the simplest ratio, and then, if that ratio isn't yet made of whole numbers, multiply every value by whatever small integer converts it into one — the resulting whole-number ratio gives the empirical formula's subscripts directly.

Which of the following equations is associated with the first electron affinity of chlorine?

  • ACI⁻(g) + e⁻ → CI (g)
  • B2CI⁻(g) - 2e⁻ → Cl₂ (g)
  • CCI (g) + e⁻ → CI⁻(g)
  • DCl₂ (g) + 2e⁻ → Cl₂ (g)
  • ECI (g) → CI⁻(g) + e⁻
Correct answer: C CI (g) + e⁻ → CI⁻(g)

Full explanation

The first electron affinity of an element is the energy change when one mole of electrons is added to one mole of gaseous atoms to form one mole of gaseous ions:

X(g) + e⁻ → X⁻(g)

Option A Explanation:

A) CI⁻(g) + e⁻ → CI (g)

Incorrect. This is the reverse of electron affinity, representing electron loss.

Option B Explanation:

B) 2CI⁻(g) - 2e⁻ → Cl₂ (g)

Incorrect. This represents the formation of Cl₂ from Cl⁻ ions, not a single-atom process.

Option C Explanation:

C) CI (g) + e⁻ → CI⁻(g)

Correct. This follows the form: X(g) + e⁻ → X⁻(g)

Option D Explanation:

D) Cl₂ (g) + 2e⁻ → Cl₂ (g)

Incorrect. This doesn't show the formation of Cl⁻ from Cl atoms

Option E Explanation:

E) CI (g) → CI⁻(g) + e⁻

Incorrect. This represents electron loss, not gain.

Summary to learn

The first electron affinity of an element is defined as the energy change when exactly one mole of electrons is added to one mole of its gaseous atoms to form one mole of singly-charged gaseous anions: X(g) + e⁻ → X⁻(g). Reversing that direction (an ion losing an electron to become a neutral atom), starting from an ion rather than a neutral atom, or describing a multi-atom or multi-electron process are all different quantities entirely, not the first electron affinity.

X is 50.0 mL of a 0.050 mol L⁻¹ aqueous solution of nitric acid (HNO₃). Y is 100mL of a 0.050 mol L⁻¹ aqueous solution of sulfuric acid (H₂SO₄). Which of the following statements about these solutions is/are correct

1. The hydrogen ion concentration in Y is four times greater than the hydrogen ion concentration in X

2. Only the acid in Y will be completely dissociated into ions

3. Y has a pH value of less than 2 at 25°C

  • A3 only
  • B1 only
  • C1 and 3 only
  • Dnone of them
  • E2 and 3 only
Correct answer: A 3 only

Full explanation

2 solutions of nitric acid and sulfuric acids are given. Both are strong acids.

Analysis of the given statements

1. The hydrogen ion concentration in Y is four times greater than the hydrogen ion concentration in X

X : HNO₃ fully dissociates as HNO₃ → H⁺ + NO₃⁻ [H⁺] of given Nitric acid solution = 0.050 mol L⁻¹ (same as the acid concentration)

Y : H₂SO₄ fully dissociates as H₂SO₄ → 2H⁺ + SO₄⁻ [H⁺] of given Sulfuric acid solution = 2 x 0.050 mol L⁻¹ = 0.1 mol L⁻¹ Thus, the hydrogen ion concentration in Y is two times greater than the hydrogen ion concentration in X, not four time. This statement is incorrect.

2. Only the acid in Y will be completely dissociated into ions

Since both of the given solutions are strong acids, both will completely dissociate into ions. Thus, this statement is incorrect.

3. Y has a pH value of less than 2 at 25°C

Solution Y has hydrogen concentration of 0.1 mol L⁻¹ pH = -log [H⁺] = -log [10⁻¹] = 1 Since pH = 1 is less than 2, this statement is correct.

Thus, the correct option is option A) 3 only.

Summary to learn

For a strong acid, the concentration of H⁺ ions in solution is the acid's own concentration multiplied by how many H⁺ ions each formula unit releases on complete dissociation (1 for a monoprotic acid like HNO₃, 2 for a diprotic acid like H₂SO₄) — not simply the acid's molar concentration on its own, and not affected by whether the two solutions being compared have different total volumes, since concentration is already a per-litre quantity. Once [H⁺] is known, pH = −log[H⁺] follows directly.

Which of the following changes is/are correct?

1. The addition of 1 g of salt to 100 g water will increase the freezing point

2. A change in temperature from 150°C to 120°C will increase the average kinetic energy of water molecules

3. A change in the surrounding air pressure from 100kPa to 120kPa will increase the boiling point of water

  • A1 only
  • B1 and 3 only
  • C2 only
  • D3 only
  • E1, 2 and 3
Correct answer: D 3 only

Full explanation

Analysis of the given statements

1. The addition of 1 g of salt to 100 g water will increase the freezing point This statement is false. Adding salt (a solute) to water causes freezing point depression, meaning the freezing point decreases rather than increases.

2. A change in temperature from 150°C to 120°C will increase the average kinetic energy of water molecules This statement is false. Kinetic energy is directly proportional to temperature. Lowering the temperature from 150°C to 120°C will decrease, not increase, the average kinetic energy of water molecules.

3. A change in the surrounding air pressure from 100kPa to 120kPa will increase the boiling point of water This statement is correct. Boiling occurs when the vapor pressure of water equals the external pressure. Increasing air pressure from 100 kPa to 120 kPa means more energy is required for water molecules to escape, leading to a higher boiling point.

Thus, the correct option is option D) 3 only.

Summary to learn

Three separate colligative and phase-behaviour rules govern how solutes, temperature and pressure affect water: dissolving a solute lowers (never raises) the freezing point — freezing-point depression; average kinetic energy of molecules is directly proportional to absolute temperature, so cooling a substance always decreases it; and boiling occurs when a liquid's vapour pressure equals the surrounding pressure, so raising the external pressure requires a higher temperature (and therefore a higher vapour pressure) before boiling can occur, raising the boiling point.

Physics & Mathematics

Mechanics, electricity, thermodynamics, algebra & geometry · 8 questions
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Find the complete set of values of x which satisfy the inequality ½(2x + 3) − ⅔(x + 1) < 2x

  • Ax > 1/2
  • Bx < −5
  • Cx > 5/14
  • Dx > 7/8
  • Ex > 5/4
Correct answer: A x > 1/2

Full explanation

Multiply through by 6 (the LCM of 2 and 3) to clear fractions: 6 × [½(2x+3) − ⅔(x+1)] < 6 × 2x ⇒ 3(2x + 3) − 4(x + 1) < 12x.

Expand: 6x + 9 − 4x − 4 < 12x ⇒ 2x + 5 < 12x ⇒ 5 < 10x ⇒ x > 1/2.

Hence, the correct answer is (A).

Summary to learn

Solving a linear inequality follows the same algebraic steps as solving an equation — clearing fractions by multiplying through by a common denominator, expanding brackets, and collecting like terms — with one crucial extra rule: multiplying or dividing both sides by a negative number reverses the direction of the inequality sign, so it's worth tracking whether that step ever occurs.

At an athletics competition, a hammer thrower swings a hammer in a horizontal circle. Immediately before releasing the hammer, the ball at the end of the hammer is moving at a constant angular velocity of 10 rad/s in a horizontal circular path of radius 2.5 m.
Which row in the table gives the speed and the magnitude of the acceleration of the ball just before release?
Row 1: speed 25 m/s, acceleration 250 m/s². Row 2: speed 25 m/s, acceleration 40 m/s². Row 3: speed 15 m/s, acceleration 50 m/s². Row 4: speed 10 m/s, acceleration 40 m/s². Row 5: speed 10 m/s, acceleration 0 m/s².

  • Arow 4
  • Brow 2
  • Crow 3
  • Drow 1
  • Erow 5
Correct answer: D row 1

Full explanation

For circular motion, speed v = ωr = 10 rad/s × 2.5 m = 25 m/s.

Centripetal acceleration a = ω²r = 10² × 2.5 = 100 × 2.5 = 250 m/s².

This matches row 1 (speed 25 m/s, acceleration 250 m/s²).

Hence, the correct answer is (D).

Summary to learn

For an object moving in a circle at constant angular velocity ω and radius r, its linear (tangential) speed is v = ωr, and the centripetal acceleration directed toward the circle's centre is a = ω²r (equivalently v²/r). Both quantities depend only on the angular velocity and the radius, so once those two values are known, speed and acceleration follow directly from these two standard formulas.

Which of the following expressions gives a quantity that can be measured in joules (J)? [Assume that all quantities are magnitudes.]

  • A(mass)² × velocity
  • Bmomentum × velocity
  • Cvoltage / (current × time)
  • D(charge)² × resistance
  • Especific heat capacity / (mass × temperature change)
Correct answer: B momentum × velocity

Full explanation

Momentum = mass × velocity, so momentum × velocity = mass × velocity². This is dimensionally the same as kinetic energy (½mv²), whose unit is the joule (J).

Checking the other options: (mass)² × velocity has units of kg²·m/s, not energy. Voltage/(current × time) has units of V/(A·s) = W/A² roughly, not joules. (charge)² × resistance has units of C²·Ω, not joules directly. Specific heat capacity/(mass × temperature change) has units of 1/(kg²·K²) roughly, not joules.

Hence, the correct answer is (B).

Summary to learn

Checking whether a combination of physical quantities has units of energy (joules) means reducing each candidate expression to its base SI units and comparing against a known energy formula, such as kinetic energy ½mv² (units kg·m²/s²) or momentum × velocity, which is dimensionally identical to mass × velocity² and therefore also has units of joules — a quick way to test any unfamiliar-looking combination is to relate it back to a formula whose units are already known.

A metal has a specific heat capacity of 500 J/(kg°C). A block of this metal has a mass of 1.20 kg and is provided with thermal energy by a heater for 5.00 minutes. The temperature of the block increases from 40.0°C to 90.0°C without a phase change.
What is the power of the heater? [Assume that no thermal energy is lost to or gained from the surroundings and that the metal is at a uniform temperature at all times.]

  • A180 W
  • B10 800 W
  • C100 W
  • D80 W
  • E6000 W
Correct answer: C 100 W

Full explanation

Thermal energy required: Q = mcΔT = 1.20 kg × 500 J/(kg°C) × (90.0 − 40.0)°C = 1.20 × 500 × 50 = 30 000 J.

Time = 5.00 minutes = 300 s. Power = energy / time = 30 000 J / 300 s = 100 W.

Hence, the correct answer is (C).

Summary to learn

The thermal energy needed to change a substance's temperature (with no phase change) is Q = mcΔT, where c is specific heat capacity; once that energy requirement is known, the power of a heater supplying it at a constant rate over a given time is simply power = energy ÷ time (with time converted into seconds to match the standard unit of power, the watt).

PQR is a right-angled triangle with angle PRQ equal to 90°. Point S is on the side PR. Point T is on the side RQ. The line ST is parallel to the line PQ. RS = 2.5 cm, PS = 1 cm, RT = 5 cm.
What is the perimeter of the trapezium PQTS in cm? [diagram not to scale]

  • A2(1 + 3√5)
  • B3(1 + 2√3)
  • C2(1 + 3√6)
  • D3(1 + 2√5)
  • E2(1 + 3√3)
Correct answer: D 3(1 + 2√5)

Full explanation

PR = PS + SR = 1 + 2.5 = 3.5 cm. Since ST ∥ PQ, triangles RST and RPQ are similar, so RS/RP = RT/RQ: 2.5/3.5 = 5/RQ, giving RQ = 5 × 3.5/2.5 = 7 cm.

QT = RQ − RT = 7 − 5 = 2 cm.

PQ (hypotenuse of the right triangle PRQ) = √(RP² + RQ²) = √(3.5² + 7²) = √(12.25 + 49) = √61.25 = (7√5)/2 cm.

Perimeter of trapezium PQTS = PS + ST + TQ + QP. Using ST/PQ = RS/RP = 2.5/3.5 = 5/7: ST = (5/7) × (7√5)/2 = (5√5)/2 cm.

Perimeter = 1 + (5√5)/2 + 2 + (7√5)/2 = 3 + (12√5)/2 = 3 + 6√5 = 3(1 + 2√5) cm.

Hence, the correct answer is (D).

Summary to learn

When a line inside a triangle is drawn parallel to one of its sides, it creates two similar triangles, and corresponding sides of similar triangles are always in the same fixed ratio. That ratio can be found from any one matching pair of known sides, and then applied to find every other unknown side — including combining it with the Pythagorean theorem on the full right-angled triangle to find a hypotenuse — before adding all four sides together for a perimeter.

PQR and PRS are right-angled triangles. Angle PRS = Angle PQR = 90°. RS = 5 cm. The area of triangle PQR is 14 cm² and tan(PRQ) = 1/7.
What is the value of cos(RPS)? [diagram not to scale]

  • A√2/4
  • B2√2/3
  • C1/3
  • D√2/2
  • E√6/3
Correct answer: B 2√2/3

Full explanation

In triangle PQR (right angle at Q), tan(PRQ) = PQ/QR = 1/7, so let PQ = x, QR = 7x. Area = ½ × PQ × QR = ½ × x × 7x = 3.5x² = 14, so x² = 4, x = 2. Thus PQ = 2 cm, QR = 14 cm.

PR (hypotenuse of PQR) = √(PQ² + QR²) = √(4 + 196) = √200 = 10√2 cm.

In triangle PRS, the right angle is at R (angle PRS = 90°), with legs PR = 10√2 cm and RS = 5 cm. The hypotenuse PS = √(PR² + RS²) = √(200 + 25) = √225 = 15 cm.

cos(RPS) = adjacent/hypotenuse = PR/PS = 10√2/15 = 2√2/3.

Hence, the correct answer is (B).

Summary to learn

A shape built from two right-angled triangles that share one side can be solved one triangle at a time: a given area and a given trigonometric ratio (like a tangent) are enough to set up two equations for that triangle's two legs, and the Pythagorean theorem then gives its hypotenuse. Because the triangles share a side, that hypotenuse becomes a known side of the second triangle, where the Pythagorean theorem and basic trig ratios (such as cosine = adjacent/hypotenuse) apply again to find the rest.

A hydraulic jack consists of a piston with a small cross-sectional area connected by a tube to a piston with a larger cross-sectional area. The cylinders of the pistons and the tube contain oil. A downward force F₁ is applied to the smaller piston, which results in an upwards resultant force F₂ being exerted on the larger piston. Points X and Y are in the oil, immediately underneath the pistons (small and large respectively), which are at the same height.
Which of the following statements about the pressure and forces in the hydraulic jack is/are correct?
1. The pressure at Y is less than the pressure at X.
2. The pressure at Y is equal to the pressure at X.
3. F₂ is greater than F₁.
4. F₂ is less than F₁.

  • A2 and 3 only
  • B1 only
  • C1 and 4 only
  • D3 only
  • E2 and 4 only
Correct answer: A 2 and 3 only

Full explanation

By Pascal's Principle, pressure applied to an enclosed fluid is transmitted equally throughout the fluid. Pressure is equal at the same height in a connected fluid, so PX = PY. This makes statement 1 false and statement 2 true.

Since pressure = force/area, and PX = PY: F₁/A₁ = F₂/A₂, where A₂ (large piston) > A₁ (small piston). For the equality to hold with a larger area, F₂ must be greater than F₁. This makes statement 3 true and statement 4 false.

So, only statements 2 and 3 are correct.

Hence, the correct answer is (A).

Summary to learn

Pascal's Principle states that pressure applied anywhere in an enclosed, connected fluid is transmitted equally throughout it, so points at the same height within that fluid are always at equal pressure — regardless of the different piston sizes above them. Since pressure = force ÷ area, equal pressure with unequal areas (F₁/A₁ = F₂/A₂) means the piston with the larger area must experience the larger force; this is the physical principle that lets a hydraulic jack multiply a small input force into a much larger output force.

Which one of the following is a simplification of (x + 2)² / (x² + x − 2)?

  • A(x + 2)² / [(x − 2)(x + 1)]
  • B(4x + 4)/(x − 2)
  • C(x + 2)/(x − 2)
  • D−4
  • E(x + 2)/(x − 1)
Correct answer: E (x + 2)/(x − 1)

Full explanation

Factorise the denominator: x² + x − 2 = x² − x + 2x − 2 = x(x − 1) + 2(x − 1) = (x + 2)(x − 1).

So the expression becomes (x + 2)² / [(x + 2)(x − 1)] = (x + 2)/(x − 1), cancelling one factor of (x + 2).

Hence, the correct answer is (E).

Summary to learn

Simplifying an algebraic fraction starts with factorising both the numerator and the denominator fully, since only identical factors appearing in both can be cancelled — factorising a quadratic like x² + x − 2 by splitting the middle term (into groups that share a common factor) reveals its two linear factors, one of which may then cancel directly against a matching factor in the numerator.

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