IMAT 2022 · Answers & Worked Solution

IMAT 2022 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 · 20 questions

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1 Logical Reasoning

Q1. We have two standard forms of treatment for depression: antidepressant medication and psychological therapy….

We have two standard forms of treatment for depression: antidepressant medication and psychological therapy. But over the last 30 years these treatments have not reduced either the prevalence of, or the disability caused by, depression: it is likely to remain a significant and largely intractable mental health problem. There are three key issues here: access, compliance and relapse. Access to treatment tends to be restricted to the minority of people who live in urban areas of wealthy countries. But even those who have access to care do not always comply with treatment recommendations — for many understandable reasons. To compound all this, high numbers of people who respond well to treatment later relapse: this is one of the reasons why depression remains so widespread.

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

AOne of the reasons why depression remains so widespread is the high rate of relapse.
BAccess, compliance and relapse are the three key issues in the treatment of depression.
CDepression is likely to remain a significant and largely intractable mental health problem.
DAccess to treatment for depression tends to be restricted to people in urban areas of wealthy countries.
EOver the past 30 years, treatments have not reduced the prevalence of or disability caused by depression.

Correct answer: C Depression is likely to remain a significant and largely intractable mental health problem.

Full explanation

To identify the conclusion of the passage, let’s first break it down into its key components.

The passage discusses the treatment of depression, as indicated by the introductory sentence. It then highlights that despite advancements in treatment, the prevalence of depression remains high. The passage attributes this persistence to three key issues.

A closer look at these issues reveals the phrase “for many understandable reasons” suggesting that these challenges arise from valid, inherent factors that may be difficult to alter through external intervention. Consequently, this implies that the prevalence of depression may not decrease in the future.

Option A Explanation:

A) One of the reasons why depression remains so widespread is the high rate of relapse.

This option presents a fact rather than the conclusion of the entire paragraph.

Option B Explanation:

B) Access, compliance and relapse are the three key issues in the treatment of depression.

This option presents a fact rather than the conclusion of the entire paragraph.

Option C Explanation:

C) Depression is likely to remain a significant and largely intractable mental health problem.

This option correctly states the conclusion of the paragraph as it is derived before.

Option D Explanation:

D) Access to treatment for depression tends to be restricted to people in urban areas of wealthy countries.

This option presents a fact rather than the conclusion of the entire paragraph.

Option E Explanation:

E) Over the past 30 years, treatments have not reduced the prevalence of or disability caused by depression.

This option presents a fact rather than the conclusion of the entire paragraph.

Summary to learn

In a passage that presents several factual claims building toward a broader point, the argument’s main conclusion is the single overall claim that every other sentence exists to support — it is identified by its logical role, not by how vividly it’s worded or where it sits in the passage. A supporting fact (even a striking one, like a statistic about relapse rates) is still just a premise if the passage goes on to use it to justify a further, more general claim.

2 Logical Reasoning

Q2. In many countries of the world, religious and political institutions have been the main providers of mass…

In many countries of the world, religious and political institutions have been the main providers of mass education for children. Their motivation for founding schools has, of course, been to promote their own ideologies and recruit followers. But children at school are vulnerable and impressionable, and therefore need to be protected from having ideologies imposed upon them.

Education is fundamentally incompatible with indoctrination and the promotion of particular worldviews. So the education provided in schools should be based on scientific atheism rather than religion or politics.

Which one of the following is an underlying assumption of the above argument?

AEveryone needs a belief system to guide them in life.
BMany adults reject the beliefs they were taught at school.
CSome governments cannot afford to fund universal education.
DScientific atheism is not an ideology.
EThe aim of education is to offer a vision of life.

Correct answer: D Scientific atheism is not an ideology.

Full explanation

Assumptions are unstated facts within a paragraph that relate the argument to the conclusion.

To answer this question, we must first identify the conclusion of the paragraph. The argument says that children, being at a vulnerable age, should not be subjected to the promotion of the ideologies of religion or political institutions. The conclusion is explicitly stated at the end: “education provided in schools should be based on scientific atheism”. From these facts, we can assume that scientific atheism is permitted in schools because it is not considered an ideology.

Option A Explanation:

A) Everyone needs a belief system to guide them in life.

This is not stated in the paragraph (could be an assumption) but it does not relate the argument with the conclusion. Thus, this is not an assumption.

Option B Explanation:

B) Many adults reject the beliefs they were taught at school.

It does not relate the argument with the conclusion. Thus, this is not an assumption.

Option C Explanation:

C) Some governments cannot afford to fund universal education.

It does not relate the argument with the conclusion. Thus, this is not an assumption.

Option D Explanation:

D) Scientific atheism is not an ideology.

This relates the argument with the conclusion. Thus, this is the correct underlying assumption of the above argument.

Option E Explanation:

E) The aim of education is to offer a vision of life.

It does not relate the argument with the conclusion. Thus, this is not an assumption.

Summary to learn

An argument’s assumption is an unstated premise that the argument needs in order for its stated evidence to actually support its conclusion — it is the missing logical link, not merely any fact that happens to be true or unstated. The standard way to test a candidate assumption is the negation test: assume it is false and check whether the conclusion still follows from the evidence; if the conclusion collapses, the statement was a required assumption.

3 Logical Reasoning

Q3. What is the secret of success? The question is as old as philosophy itself. The Greeks argued that it boiled…

What is the secret of success? The question is as old as philosophy itself. The Greeks argued that it boiled down to the possession and exercise of certain character traits, such as generosity and bravery. But new research emerging from social psychology suggests you have to be self-confident to be successful. The study, involving over 200 successful people from all walks of life, comprised detailed interviews and the observation of mental and physical problem solving. The research found that all of the participants had a strong belief in their own abilities and persevered in the face of challenges because they thought they could do it. If you want to be successful, then, you must have faith in your own abilities.

Which one of the following is the best statement of the flaw in the above argument?

AIt assumes that self-confidence is responsible for success, and not vice versa.
BIt relies on different senses of the expression ‘self-confidence’.
CIt ignores the significance of other factors, such as luck.
DIt assumes that everyone can become self-confident.
EIt justifies a claim on the basis of how things were in the past.

Correct answer: A It assumes that self-confidence is responsible for success, and not vice versa.

Full explanation

The argument concludes that self-confidence leads to success based on a study of successful people. However, it fails to consider the possibility that success itself might have contributed to their self-confidence rather than the other way around. This is a causation vs. correlation fallacy — just because successful people tend to have self-confidence does not mean self-confidence caused their success.

Option A Explanation:

A) It assumes that self-confidence is responsible for success, and not vice versa.

This is the best statement that points out the flaw in the argument.

Option B Explanation:

B) It relies on different senses of the expression ‘self-confidence’.

The argument does not shift between different meanings of “self- confidence”; it consistently refers to belief in one’s own abilities.

Option C Explanation:

C) It ignores the significance of other factors, such as luck.

While other factors like luck may contribute to success, the main flaw here is the assumption about causation, not the exclusion of other factors.

Option D Explanation:

D) It assumes that everyone can become self-confident.

The argument does not claim that everyone can develop self- confidence; it simply states that self-confidence is necessary for success.

Option E Explanation:

E) It justifies a claim on the basis of how things were in the past.

The study is based on contemporary research, not historical analysis, so this does not apply.

Summary to learn

An argument that concludes ‘A causes B’ purely from observing that A and B tend to occur together commits the classic correlation-is-not-causation flaw: the data is equally consistent with B causing A, with a third factor causing both, or with mere coincidence. Spotting this flaw means asking whether the argument has actually ruled out the reverse causal direction, not just assumed the direction that suits its conclusion.

4 Logical Reasoning

Q4. The presence of a mind requires the presence of self-consciousness. Machines do not have self-consciousness;…

The presence of a mind requires the presence of self-consciousness. Machines do not have self-consciousness; therefore machines do not have minds.

Which one of the following most closely parallels the reasoning used in the above argument?

AThe morally best option is that which maximizes benefit. Larger charities can provide the most benefit from donations, therefore it is morally best to choose larger charities to donate to.
BTo count as an emotion, a mental state needs to have representational content. Depression does not have representational content; therefore depression is not an emotion.
CTrust and reliance are not the same thing, because trust is a mental attitude, whereas reliance is not.
DOnly true beliefs can be knowledge. My belief that the world is spherical is true, therefore I know that the world is spherical.
EThere is no obligation to keep promises to someone after they have died, since the virtue of keeping promises is to promote the promisee’s wellbeing, and their capacity for wellbeing ceases upon death.

Correct answer: B To count as an emotion, a mental state needs to have representational content. Depression does not have representational content, therefore, depression is not an emotion.

Full explanation

The original argument follows this logical structure:

1. Premise: A mind requires self-consciousness.

2. Premise: Machines do not have self-consciousness.

3. Conclusion: Therefore, machines do not have minds.

In other words: if A (mind) requires B (self-consciousness), and X (machines) do not have B (self-consciousness), then X (machines) do not have A (minds).

Option A Explanation:

A) The morally best option is that which maximises benefit. Larger charities can provide the most benefit from donations, therefore it is morally best to choose larger charities to donate to.

Premise 1: If an option is morally best, then it maximizes benefit. (If A → B)

Premise 2: Larger charities maximize benefit. (B is true)

Conclusion: Therefore, larger charities are morally best. (A is true)

It does not follow the same structure the original argument, because there is no negation of a premise.

Option B Explanation:

B) To count as an emotion, a mental state needs to have representational content. Depression does not have representational content, therefore depression is not an emotion.

Premise 1: If something is an emotion, then it must have representational content.

(If A → B)

Premise 2: Depression does not have representational content. (Not B) Conclusion: Therefore, depression is not an emotion. (Not A)

This follows the same structure as the original argument.

Option C Explanation:

C) Trust and reliance are not the same thing, because trust is a mental attitude, whereas reliance is not.

This is a definitional argument, not a conditional statement. There is no “If A → B” structure.

Option D Explanation:

D) Only true beliefs can be knowledge. My belief that the world is spherical is true, therefore I know that the world is spherical.

Premise 1: If something is knowledge, then it must be a true belief. (If A → B)

Premise 2: My belief is true. (B is true)

Conclusion: Therefore, I have knowledge. (A is true)

It does not follow the same structure the original argument.

Option E Explanation:

E) There is no obligation to keep promises to someone after they have died, since the virtue of keeping promises is to promote the promisee’s wellbeing, and their capacity for wellbeing ceases upon death.

Premise 1: If there is an obligation to keep promises, then the promisee must have well-being. (If A → B)

Premise 2: The promisee no longer has well-being. (Not B)

Conclusion: Therefore, there is no obligation to keep promises. (Not A)

This has the same A→B, not B, therefore not A skeleton as the original, but it gets there by arguing that an obligation lapses once the purpose behind it can no longer be served — not by testing whether something belongs to a category defined by a required property.

Option B is the closer match: like the original argument, it asks whether something belongs to a category (a mind, an emotion) that is defined by a property it must have, and denies membership because that property is missing. Option E reaches a similar conclusion, but through a purpose-based justification rather than a category test, which makes it a good decoy but not as close a parallel.

Hence, the correct answer is (B).

Summary to learn

Two arguments share the same underlying logical structure only if they use identical roles for their premises and conclusion, not merely a similar topic. A common pattern here is denying a necessary condition: ‘A requires B; this case lacks B; therefore this case lacks A.’ An option that swaps in a different logical form — for example affirming a condition instead of denying one, or reaching its conclusion by a different route such as arguing from purpose rather than from category membership — is not a genuine parallel, however similar its subject matter looks on the surface.

5 Logical Reasoning

Q5. Individuals accept deliberate harm being done to human beings and other living creatures for a variety of…

Individuals accept deliberate harm being done to human beings and other living creatures for a variety of reasons. Whether it is self-defence, the need to kill animals for food, or some other reason, many — if not most — people who consider themselves to have ‘good morals’ will generally agree to the intentional killing of other beings if there is adequate justification for doing so. However, one cannot justify killing without complete knowledge of what those who are killed go through. Thus, people who choose to eat meat should find out about how the animals they consume are reared and killed. Otherwise, people cannot truly accept full responsibility for their decision-making.

Which one of the following best illustrates the principle used in the above argument?

AFarmers who need to kill crop-eating insects should find out which pesticides are the least harmful to other kinds of wildlife.
BA police officer who accidentally kills someone in the line of duty should be willing to tell the victim’s family about the circumstances of the death.
CA lawyer prosecuting an individual for murder should be aware of any serious difficulties in the life of the defendant in the years leading up to the crime.
DScientists who use dead animal specimens for the purpose of an experiment should be certain there are no alternative research methods available.
ECitizens who support imposing the death penalty in some criminal cases should educate themselves about the procedures used to administer it.

Correct answer: E Citizens who support imposing the death penalty in some criminal cases should educate themselves about the procedures used to administer it.

Full explanation

The passage argues that people who accept or support intentional harm (e.g., eating meat) must fully understand the consequences of that harm (e.g., how animals are reared and killed) in order to take full responsibility for their decisions. And if a person supports an action that causes harm, they must educate themselves about the details of that harm to fully take responsibility.

Option A Explanation:

A) Farmers who need to kill crop-eating insects should find out which pesticides are the least harmful to other kinds of wildlife.

This is about minimizing harm rather than accepting responsibility for a harmful choice.

Option B Explanation:

B) A police officer who accidentally kills someone in the line of duty should be willing to tell the victim’s family about the circumstances of the death.

The focus here is on informing others rather than educating oneself about harm before making a decision.

Option C Explanation:

C) A lawyer prosecuting an individual for murder should be aware of any serious difficulties in the life of the defendant in the years leading up to the crime.

This is about understanding the defendant’s background, not about taking responsibility for supporting harm.

Option D Explanation:

D) Scientists who use dead animal specimens for the purpose of an experiment should be certain there are no alternative research methods available.

This is about avoiding harm, if possible, not about educating oneself about harm before accepting it.

Option E Explanation:

E) Citizens who support imposing the death penalty in some criminal cases should educate themselves about the procedures used to administer it.

This is the best match to the principle used in the argument.

Summary to learn

A ‘principle’ question asks you to extract the general rule an argument relies on and then find a different, concrete scenario that applies that exact same rule. Here the principle is: anyone who accepts or supports an action that causes deliberate harm has a responsibility to understand fully what that harm actually involves before they can be said to take responsibility for it. The correct match applies this same ‘know what you’re supporting before you support it’ logic to an unrelated scenario, rather than merely sharing a surface theme like harm-avoidance or informing others after the fact.

6 Problem Solving

Q6. Six sacks each consist of one kind of fruit: apples, oranges or limes. The weights of the sacks are:8kg, 13…

Six sacks each consist of one kind of fruit: apples, oranges or limes. The weights of the sacks are:

8kg, 13 kg, 17 kg, 18 kg, 22 kg, 24 kg

The total weight of all the apples is twice the total weight of all the limes, and there is only one sack of oranges.

What is the weight of the sack of oranges?

A24 kg
B22 kg
C18 kg
D17 kg
E13 kg

Correct answer: A 24 kg

Full explanation

Let:

A be the total weight of apples. L be the total weight of limes.

O be the weight of the single sack of oranges. Given: A = 2L

The total weight of all sacks;

8+13+17+18+22+24 = 102 kg A + L + O = 102 kg

2L + L + O = 102 kg

3L + O = 102 kg

Substitute possible values of O from the options and check whether the resultant L is an integer.

It can be determined that only the 18 kg and 24 kg options yield integer values.

If O = 18,

3L + 18 = 102

3L = 84

L = 28 (Integer, possible)

Check if L (Total weight of lime) = 28 can be formed by the remaining weights: 8, 13, 17, 22, 24. No valid combination.

If O = 24,

3L + 24 = 102

3L = 78

L = 26

Check if L (Total weight of lime) = 26 can be formed by the remaining weights: 8, 13, 17, 18, 22.

Possible combination: 8 + 18 = 26. This is valid.

Therefore, total weight of lime (L) = 26 kg (8 + 18),

total weight of apple (A) = 2L = 52 kg (13+17+22), and total weight of orange (O) = 24 kg.

– Verify total: 52+26+24 = 102 kg.

– Thus, the weight of the sack of oranges is A) 24kg

Summary to learn

Constraint puzzles with only a handful of given values are often best solved by turning each stated relationship into an algebraic equation (here, total weight = apples + limes + oranges, with apples = 2 × limes), then testing each candidate value for the unknown you’re solving for and checking whether the rest of the equation resolves to a valid, integer answer that can actually be built from the remaining given numbers.

7 Problem Solving

Q7. There are 10 students in a class and they like visiting each other. A visit means that one student visits the…

There are 10 students in a class and they like visiting each other. A visit means that one student visits the home of another student. We know that each student in the class has visited the same number of students. No two students in the class have both visited each other.

What is the maximum number of students that a student in this class could have visited?

Correct answer: B 4

Full explanation

This question can be solved by using the combination formula because it is about selection of objects (homes) where the order does not matter (no two students in the class have both visited each other).

The number of ways to choose ‘r’ (2 homes) out of ‘n’ distinct objects (10 homes) is given by:

nCr = n!/[r!(n−r)!]

10C2 = 10!/[2!(10−2)!] = 10!/(2!8!) = 9 × 5 = 45 total visits

For each student: 45/10 = 4.5 visits

Since the answer must be an integer, each student visits a maximum of 4 other students.

Thus, the correct option is option B) 4.

Summary to learn

When choosing an unordered pair of items from a larger set (here, pairs of students who visit each other, where order doesn’t matter and no pair repeats), the total number of possible pairs is given by the combination formula nCr = n!/[r!(n−r)!]. Dividing that total number of pairs evenly across every individual in the set gives the average number of pairings per person; when that average isn’t a whole number, the true per-person maximum is the largest whole number that average could support, found by rounding down.

8 Problem Solving

Q8. I am planning a one-way flight and I can fly with one of the following five companies.None of the three…

I am planning a one-way flight and I can fly with one of the following five companies.

None of the three maximum dimensions can be exceeded.

I have two bags, one of size 52 x 40 x 22 cm and one of size 40 x 30 x 20 cm.

I am happy to take either bag with me. I need to have priority boarding. Which company should I choose if I wish to spend as little as possible?

AWassAir
BBritAir
CMistAir
DTowAir
EEasAir

Correct answer: A WassAir

Full explanation

To answer this question, we can first eliminate the airline that does not have priority boarding, which is EasAir.

Next, we can rule out any airlines with a maximum cabin bag size smaller than what is required. With priority boarding, the passenger’s smaller bag, measuring 40 x 30 x 20 cm, is acceptable for all four remaining airlines.

We can calculate the cost now.

BritAir costs 53+25 = 78

WassAir costs 59+15 = 74

TowAir costs 72+5 = 77

MistAir costs 60+20 = 80

Therefore, the most affordable option for the passenger would be WassAir.

Summary to learn

When a choice must satisfy several separate hard requirements at once (a maximum bag size, a required extra service), any option that fails even a single one of those requirements is eliminated outright, regardless of how well it performs elsewhere. Only after every option has been checked against every hard requirement does it make sense to compare the survivors on a softer criterion like total cost.

9 Problem Solving

Q9. Volunteers for a coastal conservation charity have cleaned beaches since the late 1990s and have recorded the…

Volunteers for a coastal conservation charity have cleaned beaches since the late 1990s and have recorded the number of items collected. Three items found on the beach by volunteers which have seen an increase are shown in the table below.

Year	Cigarette butts	Plastic bottles	Straws and stirrers
1997	1,547,346	263,982	249,202
2017	2,412,151	1,578,834	749,360

Which one of the following graphs could show the percentage increase in items collected between 1997 and 2017?

Correct answer: B Option B

Full explanation

The percentage increase in each item collected between 1997 and 2017 must be calculated: percentage increase = [(new value − old value) / old value] × 100%.

Item	1997	2017	% increase
Cigarette butts	1,547,346	2,412,151	≈ 60%
Plastic bottles	263,982	1,578,834	≈ 500%
Straws and stirrers	249,202	749,360	≈ 200%

The only chart whose bars correctly reflect this pattern — cigarette butts increasing the least, plastic bottles increasing roughly 8–9 times as much as cigarette butts, and straws/stirrers increasing to a level clearly between the other two — is option B.

Hence, the correct answer is (B).

Summary to learn

Percentage increase is calculated as [(new value − old value) / old value] × 100%, always measured against the original (old) value, not the new one and not the raw difference between them. When comparing several quantities’ percentage changes on a graph, it’s the relative change — not the absolute size of the numbers — that determines which bar should be tallest.

10 Problem Solving

Q10. On a volcanic island, scientists plan to install sensors to monitor ground motions and predict volcanic…

On a volcanic island, scientists plan to install sensors to monitor ground motions and predict volcanic activity. The outline of the island is shown below. The shaded area in the middle is the volcano.

A sensor cannot be installed on the volcano itself but can be installed on any one of the other squares. Each sensor takes measurements from the square on which it is installed and the surrounding squares. See an example below.

What is the minimum number of sensors that need to be installed to take measurements of the entire area of the island (excluding the volcano)?

Correct answer: C 20

Full explanation

Look back at the second diagram in the question: a sensor placed at S measures its own square plus the four squares that share an edge with it — up, down, left, right — forming a plus shape of 5 squares. The 4 diagonal corners are left white in that example, so they’re NOT covered. That plus shape is the whole puzzle.

The island itself is a 9×9 grid of 81 squares, with the volcano sitting as a solid 3×3 block right in the centre (9 squares). So the area that actually needs a sensor’s reach is 81 − 9 = 72 squares.

Two options can be thrown out immediately just on capacity, without placing a single sensor. Each sensor reaches at most 5 squares, so 6 sensors (option A) can reach at most 6 × 5 = 30 squares, and 10 sensors (option E) at most 10 × 5 = 50 — both well short of the 72 that need measuring, no matter how cleverly they’re placed.

That leaves 16, 20 and 22. Here’s the tempting trap: 72 ÷ 5 = 14.4, so if every single sensor’s cross landed perfectly on the island with no overlap and no waste, you’d need only 15. But look at the shape of this board — a square doughnut, basically. A sensor placed against the island’s outer edge always loses at least one arm of its cross off the grid, where there’s nothing to measure. A sensor placed against any of the volcano’s four sides loses an arm onto the volcano, which also doesn’t count. Between the island’s own boundary and the volcano’s boundary, a large share of the useful squares to place a sensor on are edge-adjacent one way or the other, so that idealised 15 — and 16 (option D) right after it — is never actually reachable once you try to build a real, gap-free layout.

The diagram above shows the layout that does work: the sensors sit in offset rows, staggered so each row’s crosses slot into the gaps left by the row above, tiling the board almost edge-to-edge. The middle row (level with the volcano) only has 4 sensors, pushed out to the sides, because the centre of that row is blocked by the volcano itself; the two rows immediately above and below the volcano have none at all, since the crosses from the rows further out already reach in and cover them. Counting the marked squares row by row — 3, 2, 3, 0, 4, 0, 3, 2, 3 — gives 20 sensors in total, and every one of the 72 island squares ends up covered, with only a modest amount of overlap where neighbouring crosses touch.

22 (option B) would also fully cover the island — it’s just 2 sensors more than the minimum actually needed. 20 is the smallest number for which a complete, gap-free layout exists, so the correct answer is (C).

Summary to learn

In a coverage puzzle, each placed item’s ‘reach’ has a specific fixed shape — here, a plus-shaped footprint of 5 squares (the square it sits on plus its four edge-touching neighbours, not its diagonal neighbours). Dividing the total area to be covered by the area one item can reach gives a theoretical lower bound on how many items are needed, but that bound usually isn’t achievable in practice: items placed near a boundary (an outer edge, or the edge of an excluded region) inevitably waste part of their reach off the area that needs covering, so the true minimum is typically higher than the naive division suggests.

11 General Knowledge

Q11. Which one of the following spoke to the United Nations on 12th July 2013 to call for a worldwide access to…

Which one of the following spoke to the United Nations on 12th July 2013 to call for a worldwide access to education ?

AMalala Yousafzai
BBenazir Bhutto
CKofi Annan
DBarack Obama
EAung San Suu Kyi

Correct answer: A Malala Yousafzai

Full explanation

Option A Explanation:

On 12th July 2013, Malala Yousafzai delivered a powerful speech at the United Nations calling for worldwide access to education, particularly for girls. This day, her 16th birthday, was later declared “Malala Day” by the UN in recognition of her advocacy.

Option B Explanation:

Former Prime Minister of Pakistan, but was assassinated in 2007.

Option C Explanation:

Former UN Secretary-General, but not known for a speech on this date.

Option D Explanation:

Former US President, but did not give this speech.

Option E Explanation:

Burmese activist and Nobel laureate, but not linked to this UN speech.

Summary to learn

On 12th July 2013 — her 16th birthday — Malala Yousafzai addressed the United Nations, calling for worldwide access to education, particularly for girls. The UN later named the date ‘Malala Day’ in recognition of her advocacy for education rights.

12 General Knowledge

Q12. Which of the following dancing traditions is NOT correctly matched to its place of origin?

Which of the following dancing traditions is NOT correctly matched to its place of origin?

AHaka – New Zealand
BSamba — Brazil
CFlamenco – Argentina
DBharatnatyam – India
EMambo – Cuba

Correct answer: C Flamenco – Argentina

Full explanation

Option A Explanation:

The Haka is a traditional war dance of the Māori people of New Zealand.

Option B Explanation:

Samba is a famous Brazilian dance and music genre, closely associated with Carnival.

Option C Explanation:

Flamenco originated in Spain, particularly in the Andalusia region, not Argentina.

Option D Explanation:

Bharatanatyam is a classical Indian dance form originating from Tamil Nadu, India.

Option E Explanation:

Mambo originated in Cuba, blending Afro-Cuban and jazz influences.

Summary to learn

Several traditional dances are strongly tied to a specific place of origin: the Haka to the Māori people of New Zealand, samba to Brazil, Bharatanatyam to Tamil Nadu in India, and mambo to Cuba. Flamenco, however, originated in Spain (specifically Andalusia), not Argentina — Argentina’s own signature dance is the tango.

13 General Knowledge

Q13. Which one of the following novels was awarded the Pulitzer Prize for Fiction in 1953?

Which one of the following novels was awarded the Pulitzer Prize for Fiction in 1953?

AThe Old Man and the Sea by Ernest Hemingway
BThe Great Gatsby by Francis Scott Fitzgerald
CThe Catcher in the Rye by J. D. Salinger
DOn the Road by Jack Kerouac
EMoby Dick by Herman Melville

Correct answer: A The Old Man and the Sea by Ernest Hemingway

Full explanation

Option A Explanation:

The Old Man and the Sea (1952) was awarded the Pulitzer Prize for Fiction in 1953. It is one of Hemingwayʼs most famous works and contributed to his Nobel Prize in Literature in 1954.

Option B Explanation:

The Great Gatsby (1925) by F. Scott Fitzgerald was not recognized with a Pulitzer and gained major recognition only later.

Option C Explanation:

The Catcher in the Rye (1951) by J.D. Salinger did not win a Pulitzer Prize.

Option D Explanation:

On the Road (1957) by Jack Kerouac Did not win a Pulitzer Prize.

Option E Explanation:

Moby-Dick (1851) by Herman Melville Published long before the Pulitzer Prize existed (established in 1917).

Summary to learn

Ernest Hemingway’s short novel The Old Man and the Sea (1952) won the Pulitzer Prize for Fiction in 1953 and contributed to Hemingway later being awarded the Nobel Prize in Literature in 1954. Other celebrated American novels of the era, such as The Great Gatsby, The Catcher in the Rye and On the Road, never won a Pulitzer, while Moby-Dick predates the prize’s creation in 1917 entirely.

14 General Knowledge

Q14. Which of the following European languages is NOT categorised as a Slavic language?

Which of the following European languages is NOT categorised as a Slavic language?

ACzech
BUkrainian
CLithuanian
DSlovene
EPolish

Correct answer: C Lithuanian

Full explanation

Slavic languages belong to the Indo-European language family and are divided into three branches:

1. West Slavic: Czech, Slovak, Polish

2. East Slavic: Russian, Ukrainian, Belarusian

3. South Slavic: Slovene, Serbian, Croatian, Bulgarian, etc.

Among the given options, only Lithuanian is NOT a Slavic language. It belongs to the Baltic language family, which is also part of the Indo-European family but forms a separate branch alongside Latvian.

Summary to learn

The Slavic language family (part of the broader Indo-European family) splits into three branches: West Slavic (Czech, Slovak, Polish), East Slavic (Russian, Ukrainian, Belarusian), and South Slavic (Slovene, Serbian, Croatian, Bulgarian, and others). Lithuanian is not part of this family at all — it belongs to the separate Baltic branch of Indo-European, alongside Latvian.

15 General Knowledge

Q15. Which of the following philosophers is considered one of the founders of analytic philosophy?

Which of the following philosophers is considered one of the founders of analytic philosophy?

AHans Jonas
BGottfried Wilhelm Leibniz
CMichael Foucault
DBertrand Russell
EFrancis Bacon

Correct answer: D Bertrand Russell

Full explanation

Analytic philosophy is a tradition that emphasizes logical analysis,

language, and clarity of argument, emerging in the late 19th and early 20th centuries.

Option A Explanation:

Hans Jonas was a philosopher of existentialism and bioethics, not analytic philosophy.

Option B Explanation:

Gottfried Wilhelm Leibniz (B) was an early modern philosopher and mathematician but lived long before analytic philosophy emerged.

Option C Explanation:

Michel Foucault was a continental philosopher, associated with postmodernism and critical theory.

Option D Explanation:

Bertrand Russell (D) is one of the founders of analytic philosophy, along with G.E. Moore and Ludwig Wittgenstein. His work in logic, philosophy of language, and epistemology—especially in Principia Mathematica (co- authored with Alfred North Whitehead)—laid the foundation for analytic philosophy.

Option E Explanation:

Francis Bacon (E) was a Renaissance philosopher, known for developing the scientific method, not analytic philosophy.

Summary to learn

Analytic philosophy, a tradition emphasising logical analysis, precise language and rigorous argument, emerged in the late 19th and early 20th centuries. Bertrand Russell, together with G.E. Moore and Ludwig Wittgenstein, is considered one of its founders — his work in logic and philosophy of language, including Principia Mathematica with Alfred North Whitehead, laid much of its foundation, in contrast to continental or earlier philosophical traditions represented by figures like Foucault, Leibniz or Bacon.

16 General Knowledge

Q16. Amongst the following modern-day countries, which never had any region form part of the Roman Empire?

Amongst the following modern-day countries, which never had any region form part of the Roman Empire?

APortugal
BEgypt
CBelgium
DSlovenia
EDenmark

Correct answer: E Denmark

Full explanation

Option A Explanation:

Portugal (A) was part of the Roman province Lusitania.

Option B Explanation:

Egypt (E) was a key Roman province after being annexed by Augustus in 30 BCE.

Option C Explanation:

Belgium (C) was part of the province Gallia Belgica.

Option D Explanation:

Slovenia (D) was part of Pannonia and Noricum.

Option E Explanation:

The Roman Empire expanded across Europe, North Africa, and the Middle East, but it never fully incorporated Denmark into its territory.

Summary to learn

At its greatest extent, the Roman Empire spanned most of continental Europe, North Africa and the Middle East — including regions that are now Portugal (Lusitania), Belgium (Gallia Belgica), and Slovenia (Pannonia/Noricum). Denmark, however, was never incorporated into Roman territory, remaining outside the empire’s northern frontier.

17 General Knowledge

Q17. Which one of the following chemical elements was discovered by Marie and Pierre Curie?

Which one of the following chemical elements was discovered by Marie and Pierre Curie?

APolonium
BUranium
CBoron
DHydrogen
ENitrogen

Correct answer: A Polonium

Full explanation

Option A Explanation:

Marie and Pierre Curie discovered Polonium (Po) in 1898 while researching radioactivity in uranium ores. They named it after Poland, Marie Curie’s

homeland, as a symbolic gesture for Polish independence.

Option B Explanation:

Uranium (B) was discovered by Martin Heinrich Klaproth in 1789.

Option C Explanation:

Boron (C) was discovered by Joseph Louis Gay-Lussac and Louis-Jacques Thénard in 1808.

Option D Explanation:

Hydrogen was discovered by Henry Cavendish in 1766.

Option E Explanation:

Nitrogen (E) was discovered by Daniel Rutherford in 1772.

Summary to learn

Marie and Pierre Curie discovered polonium in 1898 while investigating the radioactivity of uranium ores, naming it after Poland (Marie Curie’s homeland) as a gesture toward Polish independence. Other elements sometimes confused with their work — uranium, boron, hydrogen, nitrogen — were each discovered by different scientists decades earlier.

18 General Knowledge

Q18. Which of the following European countries does NOT recognise a denomination of Christianity as its state…

Which of the following European countries does NOT recognise a denomination of Christianity as its state religion?

AMalta
BGreece
CSpain
DDenmark
EEngland

Correct answer: C Spain

Full explanation

Option A Explanation:

Malta recognizes Roman Catholicism as the state religion, as stated in its Constitution.

Option B Explanation:

Greece recognizes Eastern Orthodoxy (Greek Orthodox Church) as the prevailing religion in its Constitution.

Option C Explanation:

Spain does NOT have an official state religion. While Catholicism is historically dominant, Spain’s 1978 Constitution established secularism, meaning the state does not officially recognize any religion.

Option D Explanation:

Denmark has the Evangelical Lutheran Church as the state church, which is supported by the government.

Option E Explanation:

England has the Church of England (Anglicanism) as the official state church, with the British monarch as its Supreme Governor.

Summary to learn

Several European countries formally recognise a specific Christian denomination as their state religion: Malta (Roman Catholicism), Greece (Greek Orthodoxy), Denmark (the Evangelical Lutheran Church) and England (the Church of England, with the monarch as Supreme Governor). Spain, despite Catholicism’s historical dominance there, has no official state religion — its 1978 Constitution established a secular state.

19 General Knowledge

Q19. Which one of the following succeeded Jean-Claude Juncker as President of the European Commission on 1…

Which one of the following succeeded Jean-Claude Juncker as President of the European Commission on 1 December 2019?

AUrsula von der Leyen
BChristine Legarde
CAlexis Tsipras
DMario Draghi
EJosé Manuel Barroso

Correct answer: A Ursula von der Leyen

Full explanation

Option A Explanation:

Jean-Claude Juncker served as President of the European Commission from 1 November 2014 to 30 November 2019. He was

succeeded by Ursula von der Leyen, who took office on 1 December 2019.

Option B Explanation:

Christine Lagarde became President of the European Central Bank (ECB) in 2019, not the president of the European Commission.

Option C Explanation:

Alexis Tsipras was the Prime Minister of Greece (2015–2019).

Option D Explanation:

Mario Draghi was the President of the ECB (2011–2019) and later Prime Minister of Italy (2021–2022).

Option E Explanation:

José Manuel Barroso (E) was the President of the European Commission before Juncker (2004–2014).

Summary to learn

Jean-Claude Juncker served as President of the European Commission from November 2014 until 30 November 2019, when he was succeeded by Ursula von der Leyen on 1 December 2019. This role is distinct from the presidency of the European Central Bank (held around that time by Mario Draghi, then Christine Lagarde) and from national head-of-government positions.

20 General Knowledge

Q20. Which of the following countries never had a female prime minister in the 20th century?

Which of the following countries never had a female prime minister in the 20th century?

AIndia
BUnited Kingdom
CPakistan
DSweden
EIsrael

Correct answer: D Sweden

Full explanation

Option A Explanation:

India elected Indira Gandhi as its first female Prime Minister in 1966.

Option B Explanation:

Margaret Thatcher became the first female Prime Minister in 1979.

Option C Explanation:

Benazir Bhutto became the first female Prime Minister in 1988.

Option D Explanation:

Sweden never had a female Prime Minister in the 20th century — its first, Magdalena Andersson, only took office in 2021.

Option E Explanation:

Golda Meir became the first female Prime Minister in 1969.

Summary to learn

Several countries had their first female prime minister at different points in the 20th century: India (Indira Gandhi, 1966), the UK (Margaret Thatcher, 1979), Pakistan (Benazir Bhutto, 1988) and Israel (Golda Meir, 1969). Sweden did not have a female prime minister at all during the 20th century — its first, Magdalena Andersson, only took office in 2021.

Biology

Cell biology, genetics, molecular biology & human physiology · 15 questions

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21 Nucleic acids and inheritance

Q21. Which diagram shows the correct hydrogen bonds between bases of a section of DNA?

Which diagram shows the correct hydrogen bonds between bases of a section of DNA?

Correct answer: D Option D

Full explanation

According to the Watson-Crick model of DNA, adenine (A) forms two hydrogen bonds with thymine (T) and only thymine, while guanine (G) forms three hydrogen bonds with cytosine (C) and only cytosine. In shorthand, A pairs with T and G pairs with C. Additionally, the phosphate groups and deoxyribose sugars are positioned alternately along the sugar-phosphate backbone on the outside of the double helix, with the nitrogenous bases facing inward, pairing specifically. The only option that features the correct hydrogen bonding pattern and correct sugar- phosphate positioning is option D.

Summary to learn

Under the Watson-Crick base-pairing model, adenine (A) pairs with thymine (T) through two hydrogen bonds, while guanine (G) pairs with cytosine (C) through three hydrogen bonds — a pattern often remembered as ‘A-T, 2 bonds; G-C, 3 bonds’. Along the DNA double helix, the sugar-phosphate backbones run along the outside, with the paired bases facing inward and hydrogen-bonded to each other across the middle.

22 Enzymes

Q22. The effect of temperature and pH on the activity of each of the enzymes P and Q was investigated.When…

The effect of temperature and pH on the activity of each of the enzymes P and Q was investigated.

When investigating the effect of temperature, the optimum pH for each enzyme was used. This was 4.5 for P and 9.5 for Q.

When investigating the effect of pH, the optimum temperature for each enzyme was used. This was 55°C for P and 25°C for Q.

Using this information, which graph could show the results from one of these investigations?

Correct answer: C Option C

Full explanation

Five graphs are given and the task is to find the one whose plotted peaks match the enzymes’ actual optimal pH or temperature values given in the question.

Option A (activity vs temperature): shows optimal temperatures of around 45°C for P and 35°C for Q. This does not match the given data (55°C for P, 25°C for Q). False.

Option B (activity vs temperature): shows optimal temperatures of around 25°C for P and 50°C for Q. This does not match the given data. False.

Option C (activity vs temperature): shows optimal temperatures of around 55°C for P and 25°C for Q. This correctly matches the given data. True.

Option D (activity vs pH): shows an optimal pH of around 9 for P and 5 for Q. This does not match the given data (4.5 for P, 9.5 for Q). False.

Option E (activity vs pH): shows an optimal pH of around 4.5 for P and 10.5 for Q. This does not match the given data. False.

Hence, the correct answer is (C).

Summary to learn

Enzymes each have their own optimum temperature and optimum pH at which their activity (reaction rate) peaks, falling off on either side of that optimum as the enzyme’s shape is disrupted by heat or by pH-driven changes to charged side chains. Reading an activity-vs-temperature or activity-vs-pH graph means identifying exactly where each curve peaks and comparing that peak value against the enzyme’s actual known optimum, rather than just checking that a curve has ‘a’ peak somewhere.

23 Gene expression : Transcription

Q23. Which of the following could be found within a molecule that has just been made by transcription in a healthy…

Which of the following could be found within a molecule that has just been made by transcription in a healthy human pancreatic cell?

1. adenine

2. peptide bonds

3. phosphodiester bonds

4. ribose

A2 and 4 only
B1,2 and 3 only
C1, 3 and 4 only
D1, 2, 3 and 4
E2 and 3 only

Correct answer: C 1, 3 and 4 only

Full explanation

Transcription is the synthesis of RNA using information in the DNA.

RNA is composed of ribose sugar attached to nitrogenous base (through N-glycosidic bond) and phosphate group (through phosphodiester bond). Nitrogenous bases can be adenine, guanine, cytosine or uracil.

The only correct choices among the given options are:

1. Adenine, 3. Phosphodiester bonds and 4. Ribose Thus, the correct option is C) 1, 3 and 4 only

Summary to learn

Transcription produces messenger RNA, built from ribose sugar, phosphate groups linked by phosphodiester bonds, and the nitrogenous bases adenine, guanine, cytosine and uracil (not thymine, which is DNA-only). Peptide bonds have nothing to do with transcription — they link amino acids together during translation, a completely separate later stage of gene expression.

24 Cellular transport : Diffusion

Q24. The following diagram shows a U-tube at the start of an experiment. It contains two solutions, separated by a…

The following diagram shows a U-tube at the start of an experiment. It contains two solutions, separated by a membrane. Both solutions contain sucrose, glucose and maltose in water. The membrane allows the passage of water and all three sugars.

Which option correctly identifies what happens within the first few seconds?

AThere will be net movement of maltose from side A to B.
BThere will be net movement of sucrose from side A to B.
CThere will be net movement of glucose from side B to A.
DSolution level will increase in side B and decrease in side A.
EThere will be no net movement of sugars.

Correct answer: A There will be net movement of maltose from side A to B.

Full explanation

Since the membrane in this case is permeable to both water and sugars, diffusion of sugars will occur until equilibrium is reached, rather than osmosis being the dominant process. Osmosis (water movement) occurs primarily when the membrane is selectively permeable, meaning it allows water to pass but restricts solute movement.

Option A Explanation:

Maltose is more concentrated on side A than on side B. Therefore, it will move from side A to side B. This option accurately describes the process.

Option B Explanation:

Sucrose is more concentrated on side B than on side A. Therefore, it will

move from side B to A. However, the option says it will move from side A to

B. Thus, this option is false.

Option C Explanation:

Glucose is more concentrated on side A than on side B. Therefore, it will

move from side A to side B. However, the option says it will move from side B to A. Thus, this option is false.

Option D Explanation:

Osmosis (water movement) occurs primarily when the membrane

is selectively permeable, meaning it allows water to pass but restricts solute movement. Since only water movement can change the solution level and osmosis is not the primary process, this option is false.

Option E Explanation:

Since 2 solutions are separated by a membrane which allows the passage of water and all three sugars and there is the concentration gradient, the solutes (primarily) will move down the concentration gradient until equilibrium is reached.

Summary to learn

Diffusion is the net movement of any dissolved particle (a solute) down its own concentration gradient, and it can happen across any membrane the solute can actually pass through. Osmosis is a special case describing only water’s movement, and it becomes the dominant, visible process specifically when a membrane is selectively permeable — letting water through while blocking solutes. When a membrane freely allows both water and every solute to pass, as here, each individual solute simply diffuses down its own gradient until everything reaches equilibrium, without osmosis being the main story.

25 Cellular structure and functions

Q25. Glycoproteins are formed from amino acids and carbohydrates.What is the order in which organelles are used to…

Glycoproteins are formed from amino acids and carbohydrates.

What is the order in which organelles are used to make membrane-associated glycoproteins?

AGolgi apparatus → Vesicles → Rough endoplasmic reticulum
BLysosomes → Rough endoplasmic reticulum → Golgi apparatus
CRough endoplasmic reticulum → Vesicles → Golgi apparatus
DRough endoplasmic reticulum → Golgi apparatus → Smooth endoplasmic reticulum
EGolgi apparatus → Lysosomes → Smooth endoplasmic reticulum

Correct answer: C Rough endoplasmic reticulum → Vesicles → Golgi apparatus

Full explanation

Rough endoplasmic reticulum synthesize secretory proteins like glycoproteins together with ribosomes on their surface.

Then, secretory proteins depart from the ER wrapped in the membranes of

vesicles and travel to the cis face of the Golgi apparatus where the proteins are modified and stored and then sent to other destinations.

Lysosomes arise by budding from the Golgi apparatus, containing hydrolytic enzymes and membrane proteins that were originally synthesized in the rough endoplasmic reticulum (RER). The hydrolytic enzymes are transported from the RER to the Golgi, where they are

modified and packaged into lysosomes. While the lysosomal membrane does contain glycoproteins to protect against enzyme activity, membrane- associated glycoproteins are not the primary functional component of

lysosomes. Instead, lysosomes are specialized for intracellular digestion and waste processing, not for the secretion or transport of glycoproteins

Thus, the order for the synthesis of glycoproteins is

Rough endoplasmic reticulum → Vesicles → Golgi apparatus (Option C)

Summary to learn

Secretory proteins destined to become glycoproteins are synthesised by ribosomes on the rough endoplasmic reticulum (RER), which also attaches the initial sugar chains. They then travel, packaged in vesicles, to the Golgi apparatus, where the carbohydrate portion is further modified and the finished glycoprotein is sorted and packaged for its final destination — giving the pathway RER → vesicles → Golgi apparatus.

26 Cellular respiration

Q26. Which row shows the site of alcohol fermentation in yeast and the site of lactic acid fermentation in human…

Which row shows the site of alcohol fermentation in yeast and the site of lactic acid fermentation in human muscle cells?

ARow 1
BRow 4
CRow 2
DRow 3
ERow 5

Correct answer: D Row 3

Full explanation

Fermentation is a way of harvesting chemical energy without using either oxygen or any electron transport chain—in other words, without cellular respiration. Fermentation is an extension of glycolysis along with NAD+ regeneration that allows continuous generation of ATP by the substrate- level phosphorylation of glycolysis.

There are 2 types of fermentation.

1. Lactic acid fermentation (occur in human muscle cells)

2. Alcoholic fermentation (occur in yeast)

Both occur in the cytoplasm of cells and anerobic process. Mitochondria is the site for the aerobic steps of the cellular respiration and fermentation process does not occur in it.

Both processes happen in the cytoplasm, which is exactly what Row 3 of the table shows for both columns. Thus, the correct option is Option D) Row 3

Summary to learn

Both major forms of fermentation — alcoholic fermentation in yeast and lactic acid fermentation in human muscle cells — are anaerobic extensions of glycolysis that regenerate NAD⁺ so glycolysis can keep producing ATP without oxygen. Because neither process uses the electron transport chain or any other mitochondrial machinery, both take place in the cytoplasm, not inside the mitochondria at all.

27 Photosynthesis

Q27. Which of the following statements about photosynthesis is/are correct?1. The site of the light-dependent…

Which of the following statements about photosynthesis is/are correct?

1. The site of the light-dependent reactions is the thylakoids, and the products of these reactions include ATP and oxygen.

2. The site of the light-independent reactions is the stroma, and the products of these reactions include carbohydrates and carbon dioxide.

3. Chlorophyll that is embedded in the chloroplast outer membrane uses light to split water molecules.

A2 and 3 only
B3 only
C1 only
D1,2 and 3
E1 and 2 only

Correct answer: C 1 only

Full explanation

Photosynthesis is the process in which light energy is harnessed and used to drive the synthesis of organic compounds.

Photosynthesis occurs in the chloroplasts of plants and algae.

Chloroplast structure : A chloroplast has two membranes surrounding a dense fluid called the stroma. Suspended within the stroma is a third membrane system, made up of sacs called thylakoids, which segregates the stroma from the thylakoid space inside these sacs. In some places, thylakoid sacs are stacked in columns called grana (singular, granum).

Chlorophyll, the green pigment that gives leaves their color, resides in the thylakoid membranes of the chloroplast.

Photosynthesis process involve 2 main steps;

1. the light-dependent reactions (occur in thylakoids, products : ATP, NADPH and O₂)

2. the light-independent reactions or Calvin cycle (occur in the stroma, products : Glucose)

Among the given statements, only the first one is true.

The second statement is false because carbon dioxide is not a product; rather, it is used as a reactant.

The third statement is false because chlorophyll is embedded in the thylakoid membrane, not in the outer membrane of the chloroplast.

Thus, the correct option is option C) 1 only.

Summary to learn

Photosynthesis happens in two linked stages inside the chloroplast. The light-dependent reactions occur in the thylakoid membranes and produce ATP, NADPH and oxygen (from splitting water). The light-independent reactions (the Calvin cycle) occur in the stroma, using that ATP and NADPH to fix carbon dioxide — a reactant, not a product — into glucose. Chlorophyll itself is embedded specifically in the thylakoid membranes, not in the chloroplast’s outer envelope membrane.

28 Mitosis

Q28. The photomicrograph shows a section of a plant root tip with cells showing different stages of the cell…

The photomicrograph shows a section of a plant root tip with cells showing different stages of the cell cycle. Five of the cells have been labelled.

Which cell (1-5) shows anaphase?

Correct answer: C 2

Full explanation

The photomicrograph of plant cells with different stages of cell cycle

(Mitotic phase and Interphase) is given.

Mitosis is conventionally broken down into five stages:

1. Prophase – chromosomes condense, spindle fibers form, nuclear envelope breaks down.

2. Metaphase – chromosomes align at the metaphase plate.

3. Anaphase – sister chromatids separate and move to opposite poles.

4. Telophase – nuclear envelopes reform, chromosomes decondense.

5. Cytokinesis – cytoplasm divides, forming two daughter cells. From can the given photomicrograph, it can be noted that

Label no.1 indicates the metaphase because the chromosomes are all at the metaphase plate.

Label no.2 indicates the anaphase because the chromatids of each chromosome have separated, and the daughter chromosomes are moving to the ends of the cell.

Label no.3 indicates the interphase because the nuclear envelope is intact, and no separated and condensed chromosomes can be seen.

Label no.4 indicates the cytokinesis because the cell plate, which will divide the cytoplasm in two, is growing toward the perimeter of the parent cell.

Label no. 5 indicates the prophase because the chromosomes are condensing and the nucleolus is beginning to disappear.

Thus, the correct label which indicates the anaphase is label no.2 (Option C)

Summary to learn

Mitosis is conventionally divided into stages recognisable under a microscope by the state of the chromosomes and nuclear envelope: prophase (chromosomes condensing, spindle forming, nuclear envelope breaking down), metaphase (chromosomes aligned at the cell’s equator), anaphase (sister chromatids visibly separating and moving to opposite poles), and telophase (nuclear envelopes reforming around two separated chromosome sets), followed by cytokinesis (the cytoplasm physically dividing). A cell showing an intact nuclear envelope with no condensed chromosomes is simply in interphase, not undergoing division at all.

29 Classical genetics

Q29. A male child has haemophilia. Neither parent has the condition. The parents have a second child.Which of the…

A male child has haemophilia. Neither parent has the condition. The parents have a second child.

Which of the following statements could be correct about this family?

1. There is a 25% chance that the second child is a boy with haemophilia

2. There is a 75% chance that the second child does not show the condition

3. There is a 50% chance that the mother is a carrier

[Assume no other mutations.]

A1 and 2 only
B3 only
C2 only
D2 and 3 only
E1 only

Correct answer: A 1 and 2 only

Full explanation

Hemophilia is a sex-linked recessive disorder , meaning the defective gene is located on the X chromosome.

Let Xₑ be the hemophilic gene.

For a daughter to have hemophilia, she must inherit two copies of the defective gene (XₑXₑ).

For a son, only one copy is needed (XₑY) since males have only one X chromosome.

It is given that the male child has haemophilia (XₑY). Since the father contributes the Y chromosome, the Xₑ must have come from the mother.

Thus, the parents’ genotypes can be determined as: Father: XY (unaffected)

Mother: XXₑ (carrier)

Possible genotypes of the second child

Female child: 100% chance of being XXₑ (carrier, but unaffected). Male child: 50% chance of being XY (healthy) or XₑY (hemophilic). In other words, only 1 out of 4 children will have the disease gene.

Since the probability of having a male or female child is ½, the chance that the second child is a boy with hemophilia is ½ x ½ = ¼ = 25 %

The probability that the second child does not have hemophilia is 1 — ¼ = ¾ = 75%

Since the first child has hemophilia, it is 100% certain that the mother is a carrier (XXₑ).

Thus, the correct statements are 1 and 2 (option A)

Summary to learn

Haemophilia is an X-linked recessive condition, so an affected son (XᵇY) must have inherited his single defective allele from his mother, making her an obligate carrier (XXᵇ) even though she shows no symptoms herself, while an unaffected father contributes a normal X or Y. For a carrier mother and unaffected father, each son independently has a 1-in-2 chance of being affected and each daughter is unaffected but has a 1-in-2 chance of being a carrier — combining the 1-in-2 chance of the child being male with the 1-in-2 chance that son is affected gives an overall 1-in-4 (25%) chance that any given child is an affected boy.

30 Pedigree chart

Q30. There is an inherited condition in cats that leads to them having six toes rather than five toes on each paw….

There is an inherited condition in cats that leads to them having six toes rather than five toes on each paw. The allele that causes six toes is dominant. The pedigree diagram shows the inheritance of this condition in a family of cats.

Three of the cats have been labelled.

Which of the following statements about this inheritance is/are correct?

1. Cat P could be homozygous for the condition.

2. Over two generations, 12 cats were produced in the cross-breeding.

3. Breeding cat Q with cat R could produce 3 offspring, each with a different genotype.

A1 and 3 only
B3 only
C2 only
D1 only
E1 and 2 only

Correct answer: B 3 only

Full explanation

The pedigree diagram shows the inheritance of a dominant condition in a family of cats. Black dots represent cats with six toes (dominant condition).

Analysis of the given statements

1. Cat P could be homozygous for the condition.

This statement is impossible because if cat P is homozygous (2 six toes genes), all of the offsprings will have the condition because 1 gene each is contributed by each parent.

2. Over two generations, 12 cats were produced in the cross-breeding.

The pedigree shows 3 generations of cat family and on the second generation, 6 cats are produced and on the third generation, 4 cats are produced. Thus, the total is 10, not 12 for two offspring generations.

3. Breeding cat Q with cat R could produce 3 offspring, each with a different genotype.

Since cat P is heterozygous, parents of cat Q and R are also heterozygous and the cat Q and R will also be heterozygous. Thus, if genes of cat Q and cat R are crossed, it is true that there can be 3 offsprings, each with a different genotype (homozygous six toes, heterozygous and homozygous five toes)

Thus, the correct option is option B) 3 only

Summary to learn

Reading a pedigree for a dominant trait means working out each individual’s genotype from who does and doesn’t show the trait: an affected individual with an unaffected parent must be heterozygous (since a homozygous-dominant parent could only ever produce affected offspring), while unaffected individuals are always homozygous recessive. Crossing two heterozygotes for a dominant trait produces the classic 1:2:1 genotype ratio (homozygous dominant : heterozygous : homozygous recessive) among their offspring.

31 Cell membrane

Q31. The diagrams each show a section of the cell surface membrane to illustrate the fluid mosaic model. Which…

The diagrams each show a section of the cell surface membrane to illustrate the fluid mosaic model. Which diagram is most accurate?

Key: black shape represents cholesterol; grey shape represents protein.

Correct answer: E Option E

Full explanation

The cell membrane is primarily composed of a phospholipid bilayer, where hydrophilic (polar) heads face outward, interacting with the extracellular and intracellular environments, while hydrophobic (nonpolar) tails face inward, forming a barrier to most water-soluble substances.

The membrane is also embedded with proteins (integral and peripheral, function in transport, signalling and structural support), cholesterol molecules (help maintain membrane fluidity and stability), and carbohydrates, which attach to lipids (forming glycolipids) or proteins (forming glycoproteins) on the extracellular surface only, playing key roles in cell recognition and signalling.

Option A is false: it shows cholesterol spanning the entire phospholipid bilayer like a transmembrane protein. Cholesterol is actually embedded within just one leaflet of the bilayer.

Option B is false: it shows the carbohydrate complexes on the intracellular side, when they are actually found only on the extracellular surface.

Option C is false: it shows the phospholipids the wrong way round — hydrophilic heads should face outward toward the aqueous environment, with hydrophobic tails facing inward, away from water.

Option D is false, for the same reason as option C: the phospholipid orientation is reversed.

Option E correctly shows the fluid mosaic model of the cell membrane.

Hence, the correct answer is (E).

Summary to learn

The fluid mosaic model describes the cell membrane as a phospholipid bilayer with hydrophilic (polar) heads facing outward into the surrounding water on both sides, and hydrophobic (nonpolar) tails facing inward, away from water. Cholesterol sits embedded within just one leaflet of the bilayer (not spanning the whole membrane like a protein would), and carbohydrates attach to lipids or proteins exclusively on the extracellular face, where they function in cell recognition and signalling.

32 Physiology : circulatory system

Q32. Which of the following changes occur during contraction of the atria in a healthy human heart?

Which of the following changes occur during contraction of the atria in a healthy human heart?

Arow 1
Brow 5
Crow 2
Drow 3
Erow 4

Correct answer: B row 5

Full explanation

During the contraction of the atria, a phase called atrial systole, the muscles of the atrial walls contract. This contraction pushes blood from the atria into the ventricles. As the atria contract:

The volume of the atria decreases, because the atrial walls are squeezing inward.

Atrial pressure increases due to the reduced volume and the force of contraction.

The atrioventricular (AV) valves — the tricuspid valve on the right side and the mitral (bicuspid) valve on the left side — are open at this stage. This allows the blood to flow smoothly from the atria into the ventricles.

At this point, the semilunar valves (leading to the pulmonary artery and aorta) remain closed, ensuring blood only moves into the ventricles.

Atrial contraction completes the filling of the ventricles with blood before the ventricles themselves contract (ventricular systole).

Matching this to the table: volume in the atria decreases, pressure in the atria increases, and the atrioventricular valves are open — exactly row 5. Hence, the correct answer is (B).

Summary to learn

During atrial systole (contraction of the atria), the atrial walls squeeze inward, so atrial volume decreases while atrial pressure rises. At this point the atrioventricular valves (tricuspid and mitral) are open, letting the rising atrial pressure push blood through into the relaxed ventricles below, while the semilunar valves leading out of the heart remain closed.

33 Physiology : excretory system

Q33. The diagram shows a glomerulus and part of a nephron in the kidney of a healthy human.Which of the following…

The diagram shows a glomerulus and part of a nephron in the kidney of a healthy human.

Which of the following cause(s) water to move from the glomerulus into the tubule?

1. An increase in pressure caused by the left ventricle of the heart

2. The effect of blood proteins on the direction of osmosis

3. An increase in pressure of the liquid in the tubule

A1 only
B1 and 2 only
C2 and 3 only
D2 only
E3 only

Correct answer: A 1 only

Full explanation

The movement of water from the glomerulus into the tubules is influenced by three pressures:

Glomerular Hydrostatic Pressure

This is the blood pressure inside the glomerular capillaries.

It favors filtration by pushing water and solutes out of the capillaries into Bowmanʼs capsule.

Source: Mainly the contraction of the left ventricle of the heart.

55 mmHg (value in humans).

1. Capsular Hydrostatic pressure

Pressure exerted by the fluid already present in Bowmanʼs capsule and tubules.

Opposes filtration by pushing back against the incoming fluid from the glomerulus.

15 mmHg (value in humans).

2. Oncotic pressure

Caused by plasma proteins (like albumin) that remain in the capillaries.

This opposes filtration by pulling water back into the capillaries.

30 mmHg (value in humans).

Analysis of the given conditions :

1. An increase in pressure caused by the left ventricle of the heart : This condition can increase the hydrostatic pressure in the glomerulus, pushing water to move from the glomerulus to the tubules (filtration)

2. The effect of blood proteins on the direction of osmosis : Proteins are the major contributor of the oncotic pressure, and this pressure pulls water back into the glomerular capillaries, opposing filtration.

3. An increase in pressure of the liquid in the tubule : This condition opposes filtration by reducing the pressure gradient between the glomerulus and Bowmanʼs capsule.

Thus, only the statement 1 (Option A) correctly describes a condition that causes water to move from the glomerulus into the tubules.

Summary to learn

Fluid movement from the glomerulus into the kidney tubules (glomerular filtration) is governed by three opposing pressures: glomerular hydrostatic pressure (blood pressure inside the glomerular capillaries, generated mainly by the heart’s left ventricle) pushes fluid out and favours filtration, while capsular hydrostatic pressure (fluid already in Bowman’s capsule pushing back) and oncotic pressure (created by plasma proteins that pull water back into the capillaries) both oppose it. Anything that raises glomerular hydrostatic pressure increases filtration; anything that raises the two opposing pressures reduces it.

34 Physiology : endocrine system

Q34. Drug Q reduces the release of vasopressin (ADH) into the bloodstream of a healthy human.Which organ releases…

Drug Q reduces the release of vasopressin (ADH) into the bloodstream of a healthy human.

Which organ releases ADH into the blood, and what is the effect of drug Q on the concentration of urea in the urine?

[Assume that the production of urea remains constant.]

ARow 2
BRow 5
CRow 3
DRow 4
ERow 1

Correct answer: D Row 4

Full explanation

Antidiuretic hormone (ADH) is synthesized in the hypothalamus and stored in the posterior pituitary, where it is released in response to low blood pressure or dehydration.

ADH acts on the collecting tubules of the kidneys, increasing water reabsorption by inserting more aquaporin channels into the tubule membranes.

This reduces water excretion (increase water reabsorption), making the urine more concentrated.

Any stimulus or drug that inhibits ADH release has the opposite effect, leading to reduced water reabsorption and more dilute urine.

Since Drug Q reduces ADH release, it will:

Decrease water reabsorption in the collecting tubules. Increase water excretion, producing dilute urine.

Lower the concentration of urea in the urine due to increased water content.

The only row that correctly identifies the organ that releases ADH and its effect is row 4 (Option D).

Summary to learn

Antidiuretic hormone (ADH, or vasopressin) is made in the hypothalamus but released into the blood from the posterior pituitary gland, where it acts on the kidneys’ collecting tubules to increase water reabsorption by inserting more aquaporin channels. Less ADH means less water reabsorbed, so more dilute urine is produced — and since the amount of urea being excreted stays the same while it’s now dissolved in a larger volume of water, its concentration in the urine falls.

35 Physiology : nervous system

Q35. In the nervous system, which of the following pairs work in opposition to each other to control their target…

In the nervous system, which of the following pairs work in opposition to each other to control their target organs?

ASympathetic and parasympathetic nervous systems
BBrain and spinal cord
CSensory and motor pathways
DReflex and voluntary pathways
ECentral and peripheral nervous systems

Correct answer: A Sympathetic and parasympathetic nervous systems

Full explanation

Nervous system overview

Nervous system is generally divided into 2 main parts;

Central nervous system (process information and coordinates response) Brain and spinal cord

Peripheral nervous system

Enteric nervous system (controls the GI tract)

Somatic nervous system (controls voluntary movements and transmits sensory information)

Autonomic nervous system (regulate involuntary function) Sympathetic nervous system (Fight or flight response)

Parasympathetic nervous system (Rest and digest response)

Nerve pathways are generally divided into 2 parts; Sensory (Afferent) pathways

Motor (Efferent) pathways

Option A Explanation:

The sympathetic and parasympathetic nervous systems are subdivisions of the autonomic nervous system (ANS) and work antagonistically to regulate involuntary functions. They have opposing effects on target organs, e.g;

activating the sympathetic pathway increases the heart rate while activating the parasympathetic pathway decreases the heart rate. Thus, this option is true.

Option B Explanation:

The brain and spinal cord are parts of the CNS and work together, not in opposition. Thus, this option is false

Option C Explanation:

Sensory pathways transmit signals to the CNS, while motor pathways carry commands from the CNS to effectors, but they do not directly oppose each other. Thus, this option is false.

Option D Explanation:

Reflex pathways control automatic, rapid responses, while voluntary pathways control conscious movements, but they do not act in direct opposition. Thus, this option is false.

Option E Explanation:

The CNS and PNS work together, not against each other. Thus, this option is false.

Summary to learn

The autonomic nervous system, which regulates involuntary functions, is itself split into two divisions that consistently work in opposition to each other on the same target organs: the sympathetic division (the ‘fight or flight’ response, e.g. speeding up the heart) and the parasympathetic division (the ‘rest and digest’ response, e.g. slowing the heart down). Other paired structures in the nervous system, such as the brain and spinal cord, or sensory and motor pathways, work together rather than against one another.

Chemistry

General, inorganic, organic & biochemistry · 15 questions

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36 Acid-Base

Q36. Which of the following acids is/are weak?1. H₂CO₃ (aq)2. HCOOH (aq)3. HNO₃ (aq)

Which of the following acids is/are weak?

1. H₂CO₃ (aq)

2. HCOOH (aq)

3. HNO₃ (aq)

A2 and 3 only
B3 only
C2 only
D1 only
E1 and 2 only

Correct answer: E 1 and 2 only

Full explanation

Common weak acids are H₂CO₃, HNO₂, H₂SO₃, H₃PO₄ and organic acids

such as HCOOH, CH₃COOH.

Common strong acids are substances that completely dissociate into their ions in aqueous solutions, releasing a high concentration of hydrogen ions (H⁺). The most important strong acids include hydrochloric acid (HCl), hydrobromic acid (HBr), hydroiodic acid (HI), nitric acid (HNO₃), sulfuric acid (H₂SO₄)—for its first proton—and perchloric acid (HClO₄). Because they ionize fully, strong acids have no equilibrium between the undissociated and dissociated forms in water, unlike weak acids which only partially dissociate.

Thus, from the given acids, the weak acids are 1) H₂CO₃ and 2) HCOOH (Option E)

Summary to learn

Strong acids (such as HCl, HBr, HI, HNO₃, H₂SO₄ for its first proton, and HClO₄) dissociate essentially completely in water, releasing all of their available H⁺ ions with no meaningful equilibrium between the dissociated and undissociated forms. Weak acids (such as H₂CO₃ and HCOOH) only partially dissociate, existing at equilibrium as a mixture of the intact acid and its dissociated ions — it’s this partial, equilibrium-based dissociation, not simply a low concentration, that defines a weak acid.

37 Atomic structure

Q37. Which of the following particles has the same number of neutrons as the⁷⁹₃₅Br⁻ ion?

Which of the following particles has the same number of neutrons as the

⁷⁹₃₅Br⁻ ion?

A⁷⁸₃₄Se
B⁸¹₃₅Br²⁺
C⁸¹₃₅Br⁻
D⁸²₃₆Kr
E¹⁰¹₄₄Ru⁺

Correct answer: A ⁷⁸₃₄Se

Full explanation

Number of neutrons = Mass number (A) – atomic number (Z)

⁷⁹₃₅Br⁻ represents a bromide ion (Br⁻) with:

Mass number (A) = 79 (superscript number) Atomic number (Z) = 35 (subscript number) Number of neutrons = 79-35 = 44

We have to find the particle that has the same number of neutrons as the

⁷⁹₃₅Br⁻ ion

Option A Explanation:

⁷⁸₃₄Se

Mass number (A) = 78 Atomic number (Z) = 34 Number of neutrons = 78-34 = 44

It has the same number of neutrons as the ⁷⁹₃₅Br⁻ ion.

Option B Explanation:

⁸¹₃₅Br²⁺

Mass number (A) = 81 Atomic number (Z) = 35 Number of neutrons = 81-35 = 46

Option C Explanation:

⁸¹₃₅Br⁻

Mass number (A) = 81 Atomic number (Z) = 35

Number of neutrons = 81-35 = 46

Option D Explanation:

⁸²₃₆Kr

Mass number (A) = 82 Atomic number (Z) = 36 Number of neutrons = 82-36 = 46

Option E Explanation:

¹⁰¹₄₄Ru⁺

mass number (A) = 101 atomic number (Z) = 44. Number of neutrons = 101-44 = 57

Summary to learn

In nuclide notation, the superscript is the mass number (protons + neutrons) and the subscript is the atomic number (protons), so the number of neutrons in any atom or ion is simply mass number minus atomic number — ionic charge affects the electron count but never the neutron count. Two completely different elements can still share the exact same number of neutrons (isotones), which is exactly what makes this kind of matching question possible: it’s testing neutron count specifically, not overall identity.

38 Basic concepts of chemistry

Q38. Equal volumes of liquids are mixed as the following pairs:1. Heptane and hexane2. Water and methanol3. …

Equal volumes of liquids are mixed as the following pairs:

1. Heptane and hexane

2. Water and methanol

3. Hexane and water

Which of the pairs form(s) a homogenous mixture?

A1 only
B1,2 and 3
C3 only
D1 and 2 only
E2 and 3 only

Correct answer: D 1 and 2 only

Full explanation

Mixture: a mixture consists of several different, chemically pure

substances. Mixtures do not have constant composition. The mixture can be homogenous, and heterogenous.

Homogenous mixture: Homogenous mixtures have the same composition throughout the sample. The compositions of such mixtures cannot be seen under a powerful microscope. They are called solutions. Examples are air, seawater, gasoline, etc.

Heterogenous mixture: heterogenous mixtures consist two or more phases, which have different compositions.

For a mixture to be homogeneous, its components must have similar water solubilities, allowing them to mix uniformly.

Analysis of the given mixtures

1. Heptane and hexane: Since both are hydrophobic molecules, they can mix well with each other forming a homogenous mixture.

2. Water and methanol: Both are hydrophilic molecules. They dissolve completely in each other forming a homogenous mixture.

3. Hexane and water: Hexane is hydrophobic while water is hydrophilic.

Due to their differing solubilities, they do not mix forming a heterogenous mixture.

Thus, only mixtures 1 and 2 are homogenous. (Option D)

Summary to learn

Whether two liquids mix into a single homogeneous solution or separate into distinct layers depends on how similar their polarities are — the ‘like dissolves like’ principle. Two nonpolar (hydrophobic) liquids, such as two similar alkanes, mix freely with each other, and two polar (hydrophilic) liquids, such as water and an alcohol, also mix freely with each other; but a nonpolar liquid and a polar liquid, such as an alkane and water, do not mix and instead form separate, heterogeneous layers.

39 Organic chemistry

Q39. Consider the following general equation that describes one way of synthesizing a particular type of BIOFUEL,…

Consider the following general equation that describes one way of synthesizing a particular type of BIOFUEL, represented by Y.

X represents a neutral (uncharged) organic molecule involved in the reaction.

Which of the following statements about the reaction are correct?

1. Addition of an enzyme is an essential condition

2. Y is an ester

3. X contains an alcohol group

Anone of them
B1 and 2 only
C2 and 3 only
D1 and 3 only
E1, 2 and 3

Correct answer: C 2 and 3 only

Full explanation

The reactant on the left consists of a triester of glycerol (triglyceride). The product includes three molecules of Y and one molecule of glycerol (HO- CH₂-CHOH-CH₂OH). This suggests that the reaction is transesterification, where triglycerides react with an alcohol (X) to produce esters (Y) and glycerol.

This type of reaction is commonly used in biodiesel production, where vegetable oils (triglycerides) react with methanol (or ethanol) in the presence of a catalyst.

In biodiesel production, transesterification is typically catalyzed by acid, base, or enzymes (lipases). While enzymes can be used, they are not

essential.

Thus, the correct statements are 2 and 3 only. (Option C)

Summary to learn

Transesterification is the reaction of a triglyceride (an ester of glycerol with three fatty acid chains) with an alcohol, which swaps the fatty acid chains onto the alcohol to produce three molecules of a new ester plus one molecule of glycerol released as a by-product. This reaction is the basis of biodiesel production, where plant oils react with methanol or ethanol; the reaction can be sped up by an acid, base, or enzyme (lipase) catalyst, but none of those catalysts is strictly essential for the reaction to occur.

40 Chemical bonding and structure

Q40. Which of the following substances in pure liquid form has/have hydrogen bonds between their molecules?1. …

Which of the following substances in pure liquid form has/have hydrogen bonds between their molecules?

1. H₂O

2. HF

3. CH₄

A1 and 2 only
B2 only
C2 and 3 only
D1 only
E3 only

Correct answer: A 1 and 2 only

Full explanation

Hydrogen bonding occurs when a hydrogen atom, covalently bonded to a highly electronegative atom such as nitrogen (N), oxygen (O), or fluorine

(F) — known as the hydrogen bond donor — interacts with a lone pair of electrons on another highly electronegative atom, which acts as the hydrogen bond acceptor. The donor provides the hydrogen atom with a partial positive charge (δ⁺), while the acceptor must have a lone pair of electrons to interact electrostatically with the hydrogen. For hydrogen bonding to occur, it is essential that hydrogen is directly bonded to N, O, or F, because their high electronegativity and small atomic size create the strong polarity necessary for hydrogen bond formation. This interaction significantly influences the physical properties of substances, such as increasing boiling points and solubility in polar solvents like water.

Among the given molecules:

1. H₂O (water) contains hydrogen bonded to oxygen, allowing hydrogen bonding between its molecules.

2. HF (hydrofluoric acid) contains hydrogen bonded to fluorine, which also enables hydrogen bonding.

3. CH₄ (methane) does not contain hydrogen bonded to F, O or N. Thus, hydrogen bonding cannot occur.

The correct option is option A) 1 and 2 only

Summary to learn

Hydrogen bonding is a particularly strong intermolecular force that requires a hydrogen atom to be covalently bonded directly to one of the three most electronegative, small atoms — nitrogen, oxygen, or fluorine — giving that hydrogen a strong partial positive charge that can then interact with a lone pair on an electronegative atom of a neighbouring molecule. Molecules like water (O−H) and hydrogen fluoride (F−H) can hydrogen-bond to each other for exactly this reason, while a molecule like methane, whose hydrogens are bonded only to carbon, cannot.

41 Chemical bonding and structure

Q41. In which of the following does the central atom share all its outer shell electrons?1. BF₃2. NH₄⁺3. …

In which of the following does the central atom share all its outer shell electrons?

1. BF₃

2. NH₄⁺

3. CO₂

[Atomic numbers: H = 1; B = 5; C = 6; N = 7; 0 = 8; F = 9]

A1 and 2 only
B2 and 3 only
C1 and 3 only
D1, 2 and 3.
ENone of them

Correct answer: D 1,2 and 3

Full explanation

In BF₃, the central atom is boron (B), which has the electron configuration 1s²2s²2p¹, giving it three valence electrons. Boron shares all three of its

outer electrons with fluorine atoms, forming three single covalent bonds in the BF₃ molecule.

In NH₄⁺, the central atom is nitrogen (N), with the electron configuration 1s²2s²2p³, meaning it has five valence electrons. Nitrogen shares four electrons with four hydrogen atoms and uses its lone pair to form a

coordinate covalent bond with a proton (H⁺), resulting in the ammonium ion (NH₄⁺). Thus, nitrogen utilizes all of its outer shell electrons in bonding.

In CO₂, the central atom is carbon (C), which has the electron configuration 1s²2s²2p², providing four valence electrons. Carbon shares all four electrons by forming two double covalent bonds with two oxygen atoms, completing its octet.

Since the central atoms of all the given molecules share all of its outer shell electrons, the correct option is D) 1,2 and 3

Summary to learn

An atom’s valence electron count (from its electron configuration) tells you how many electrons it has available to share in covalent bonds. Boron in BF₃ (3 valence electrons) forms three single bonds and shares all three; nitrogen in NH₄⁺ (5 valence electrons) forms four bonds — three ordinary covalent bonds plus one coordinate (dative) bond using its lone pair — and so shares all five; carbon in CO₂ (4 valence electrons) forms two double bonds and shares all four. In each case, every one of the central atom’s outer-shell electrons ends up involved in a bond.

42 Oxidation-Reduction

Q42. In which of the following reactions does HCl act as a reducing agent?

In which of the following reactions does HCl act as a reducing agent?

AAl₂O₃ + 6HCl → 2AlCl₃ + 3H₂O
BZn + 2HCl → H₂ + ZnCl₂
CNH₃ + HCl → NH₄Cl
DMnO₂ + 4HCl → MnCl₂ + Cl₂ + 2H₂O
EMg(OH)₂ + 2HCl → MgCl₂ + 2H₂O

Correct answer: D MnO₂ + 4HCl → MnCl₂ + Cl₂ + 2H₂O

Full explanation

Option A Explanation:

Al₂O₃ + 6HCl → 2AlCl₃ + 3H₂O

In this reaction, no species undergoes oxidation or reduction. The oxidation state of each atom remains unchanged in both the reactants and the

products. Therefore, this is not a redox reaction, making this statement false.

Option B Explanation:

Zn + 2HCl → H₂ + ZnCl₂

In this reaction, H is reduced because its oxidation state decreases from +1 to 0. Zn is oxidized because its oxidation state increases from 0 to +2.

In a redox equation the substance that is reduced is the oxidizing agent, the substance that is oxidized is the reducing agent.

Thus, in this reaction, HCl is the oxidizing agent, not the reducing agent.

Option C Explanation:

NH₃ + HCl → NH₄Cl

In this reaction, no species undergoes oxidation or reduction. The oxidation state of each atom remains unchanged in both the reactants and the

products. Therefore, this is not a redox reaction.

Option D Explanation:

MnO₂ + 4HCl → MnCl₂ + Cl₂ + 2H₂O

In this reaction, Mn is reduced because its oxidation state decreases from

+4 to +2. Cl is oxidized because its oxidation state increases from -1 to 0 in Cl₂. Thus, in this reaction, HCl is the reducing agent.

Option E Explanation:

Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O

In this reaction, no species undergoes oxidation or reduction. The oxidation state of each atom remains unchanged in both the reactants and the

products. Therefore, this is not a redox reaction.

Summary to learn

In a redox reaction, the species that is itself oxidised (loses electrons, its oxidation state increases) is called the reducing agent, because it causes something else to be reduced; the species that is itself reduced (gains electrons, oxidation state decreases) is the oxidising agent. Tracking oxidation-state changes atom by atom across a reaction is how you tell a genuine redox reaction (where these numbers change) apart from a simple acid-base or precipitation reaction (where every atom’s oxidation state stays the same throughout).

43 Equilibrium

Q43. Hydrogen sulfide gas was shaken with a solution of sodium hydroxide in a closed system. An equilibrium was…

Hydrogen sulfide gas was shaken with a solution of sodium hydroxide in a closed system. An equilibrium was rapidly established.

H₂S (g) + 2OH⁻ (aq) ⇌ S^2⁻ (aq) + 2H₂O (l)

The experiment was repeated at the same temperature and pressure, but one additional substance was added to the equilibrium mixture.

Adding which of these substances, on its own, will increase the number of molecules of H₂S present at equilibrium?

1. Hydrochloric acid

2. Solid potassium hydroxide

3. Sodium sulfide

A2 and 3 only
B2 only
C1 only
D1 and 3 only
E1 and 2 only

Correct answer: D 1 and 3 only

Full explanation

To increase the number of H₂S molecules, we need to shift the reaction equilibrium to the left.

Analysis of the given substances

1. Hydrochloric acid: HCl dissociates in solution, increasing the concentration of H⁺ ions. The H⁺ ions can react with OH⁻, reducing its concentration. Since OH⁻ is a reactant, its removal shifts the equilibrium left, increasing H₂S. Thus, adding HCl increases H₂S at equilibrium.

2. Solid potassium hydroxide: KOH dissociates into K⁺ and OH⁻, increasing the OH⁻ concentration. Higher OH⁻ shifts the

equilibrium right, consuming H₂S. Thus, adding KOH decreases H₂S, so it does not help.

3. Sodium sulfide: Na₂S dissociates into Na⁺ and S²⁻ ions. Increasing S²⁻ shifts the equilibrium left, forming more H₂S. Thus, adding Na₂S increases H₂S at equilibrium.

Adding Hydrochloric acid (HCl) and Sodium sulfide (Na₂S) will increase the number of molecules of H₂S present at equilibrium.

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

Summary to learn

Le Chatelier’s principle: when a system at equilibrium is disturbed, it shifts in whichever direction partially counteracts the disturbance. Removing a species that sits on one side of the equilibrium (here, removing OH⁻ by reacting it with added H⁺, or removing H₂S indirectly by adding a substance that consumes a product) pulls the equilibrium toward replacing what was lost, while adding more of a species already present on one side pushes the equilibrium the other way, away from that side.

44 Chemical bonding and structure

Q44. Barium sulfate is insoluble in water.Aqueous solutions of barium chloride and sodium sulfate are mixed. Which…

Barium sulfate is insoluble in water.

Aqueous solutions of barium chloride and sodium sulfate are mixed. Which of the following equations is the SIMPLEST ionic equation for the reaction that occurs ?

A2BaCl (aq) + Na₂SO₄(aq) → BaSO₄(s) + 2NaCl (aq)
BBa²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s)
CBa²⁺(aq) + 2Cl⁻(aq) + 2Na+(aq) + SO₄²⁻(aq) → BaSO₄(s) + 2Na⁺(aq) + 2Cl⁻(aq)
D2Ba⁺(aq) + SO₄²⁻(aq) → Ba₂SO₄(s)
EBaCl₂(aq) +Na₂SO₄(aq) → BaSO₄(s) + 2NaCl (aq)

Correct answer: B Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s)

Full explanation

First, we need to determine the chemical formulas of the molecules

involved.

Barium has 2 valence electrons and forms a Ba²⁺ ion. Sulfate ion (SO₄²⁻) has a charge of -2. Sodium has 1 valance electron and forms an Na⁺ ion. Chlorine has 7 valence electrons and form a Cl⁻ ion.

Barium sulfate – BaSO₄ Barium chloride – BaCl₂ Sodium sulfate – Na₂SO₄ Sodium chloride – NaCl

The full molecular equation of the given reaction would be : BaCl₂(aq) +Na₂SO₄(aq) → BaSO₄(s) + 2NaCl (aq)

The full ionic equation would be :

Ba²⁺(aq) + 2Cl⁻(aq) + 2Na+(aq) + SO₄²⁻(aq) → BaSO₄(s) + 2Na(aq) + 2Cl⁻(aq)

To get the simplest ionic equation, remove spectator ions (Na⁺ and Cl⁻, which appear on both sides) :

Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s)

Option A Explanation:

We can exclude this option because the molecular formula of barium chloride is wrong.

Option B Explanation:

This correctly states the simplest ionic equation.

Option C Explanation:

This is the full ionic equation.

Option D Explanation:

We can exclude this option because the molecular formula of barium sulfate is wrong.

Option E Explanation:

This is the full molecular equation.

Summary to learn

Writing the simplest (net) ionic equation for a precipitation reaction means first writing the full molecular equation, splitting every soluble ionic compound into its free ions to get the full ionic equation, and then cancelling the spectator ions — the ions that appear unchanged, in the same form, on both sides of the equation — leaving only the ions that actually combine to form the insoluble solid.

45 Basic concepts of chemistry

Q45. Which of the following separation techniques can be used to obtain liquid ethanal from an aqueous mixture of…

Which of the following separation techniques can be used to obtain liquid ethanal from an aqueous mixture of ethanol, ethanal and ethanoic acid

1. Filtration

2. Fractional distillation

3. Centrifugation

A3 only
B2 only
C1 and 2 only
D1 and 3 only
E1 only

Correct answer: B 2 only

Full explanation

Filtration is used to separate heterogeneous mixtures.

Fractional distillation is used to separate mixtures containing compounds with different boiling points.

Centrifugation is used to separate substances based on their density and weight differences.

Since the given mixture is a homogeneous aqueous solution and the

components have different boiling points—ethanal (21°C), ethanol (78°C), and ethanoic acid (118°C)—fractional distillation can be used to separate the components or isolate the desired ethanal.

Filtration (statement 1) only separates an insoluble solid from a liquid, and centrifugation (statement 3) only separates substances by density — neither applies to a homogeneous solution of three miscible liquids, so both are ruled out. Only fractional distillation (statement 2) can do the job. Hence, the correct answer is (B) 2 only.

Summary to learn

Different separation techniques exploit different physical properties: filtration separates an insoluble solid from a liquid (useless here, since all three substances are dissolved together in one solution); centrifugation separates substances by density (also no help for a true solution); fractional distillation separates the components of a homogeneous liquid mixture by their different boiling points. Since ethanal, ethanol and ethanoic acid each boil at a different temperature, fractional distillation is the technique that can isolate the ethanal.

46 Stoichiometry

Q46. A metal oxide, MO, reacts with sulfuric acid according to the following equation:MO + H₂SO₄ MSO₄ + H₂O2.8g of…

A metal oxide, MO, reacts with sulfuric acid according to the following equation:

MO + H₂SO₄ MSO₄ + H₂O

2.8g of the metal oxide requires 25 mL of 2.0 mol L⁻¹ sulfuric acid for complete reaction.

What is the relative atomic mass (Ar) of the metal?

(Ar value: O = 16)

A112
B96
C40
D56
E24

Correct answer: C 40

Full explanation

From the given information, we can first determine the moles of

H₂SO₄ used in the reaction. Since the balanced equation shows a 1:1 molar ratio between MO and H₂SO₄, we can then deduce the moles of MO that reacted.

Using the calculated moles of MO and the given mass of the metal oxide, we can determine its molar mass. Finally, by subtracting the mass of oxygen (16 g/mol) from the molar mass of MO, we can find the relative atomic mass (Ar) of the metal.

Given :

Volume of H₂SO₄ solution = 25 mL = 0.025 L Concentration of H₂SO₄ = 2.0 mol L⁻¹ mole of H₂SO₄ = volume x molar volume = 0.025ml ⋅ 2molL−1 =0.05moles

From the balanced equation, 1 mole of MO reacts with 1 mole of H₂SO₄.

Thus, moles of MO = moles of H₂SO₄ = 0.050 moles.

Molar mass of MO = mass / mole = 2.8g/0.05 mole = 56 g/mol

Thus, Relative atomic mass (Ar) of the metal (M)

= Molar mass of MO – Ar of Oxygen

= 56 – 16

= 40

The correct option is option C) 40.

Summary to learn

Solving a stoichiometry problem from a titration-style setup follows a fixed sequence: use the given volume and molarity of one reactant to find its moles (moles = concentration × volume), use the balanced equation’s mole ratio to find the moles of the other reactant, then use moles = mass ÷ molar mass (rearranged to molar mass = mass ÷ moles) to find that reactant’s molar mass, and finally subtract the known mass of any other element in its formula to isolate the unknown atomic mass.

47 Acid-Base

Q47. 0.365 g of hydrogen chloride is dissolved in sufficient water to make 10 litres of solution.What is the pH of…

0.365 g of hydrogen chloride is dissolved in sufficient water to make 10 litres of solution.

What is the pH of the HCl (aq) solution formed, at 25°C?

(A values: H = 1.0; Cl = 35.5)

A2.0
B4.0
C0.01
D3.0
E1.0

Correct answer: D 3.0

Full explanation

To solve this, we need to find the mole of HCl dissolved first.

Molar mass of HCl = 35.5 + 1 = 36.5 g/mol

Mole of HCl = mass / molar mass = 0.365 g / 36.5 g mol⁻¹ = 0.01 moles

Then, we can find the molarity of HCl solution:

Molarity = mole of solute / volume of solution = 0.01 mole / 10 L = 1 × 10⁻³ mol/L (M)

If we know the molarity, we can calculate the pH of solution. Since HCl is a strong acid, it fully dissociates:

Thus, [H⁺] = 0.001 M.

pH = −log[H⁺] = −log[1 × 10⁻³] = 3

The correct option is option D) 3.0.

Summary to learn

Finding the pH of a strong acid solution is a short chain of conversions: convert the given mass of acid to moles using its molar mass, divide by the solution’s volume to get molarity, and then — because a strong acid dissociates essentially completely — that molarity equals the hydrogen ion concentration [H⁺] directly, from which pH = −log₁₀[H⁺].

48 Chemical bonding and structure

Q48. Phosphorus is in Group V of the Periodic Table. What is the shape and the bond angle for the PH₄⁺ ion?

Phosphorus is in Group V of the Periodic Table. What is the shape and the bond angle for the PH₄⁺ ion?

ARow 1
BRow 3
CRow 5
DRow 2
ERow 4

Correct answer: A Row 1

Full explanation

In the PH₄⁺ ion, phosphorus (P) has 5 valence electrons. It forms four

covalent bonds with hydrogen atoms by sharing four electrons and loses its remaining electron to form a cation, resulting in no lone pairs around the central atom. With four bonding regions and no lone pairs, the electron domain geometry is tetrahedral, leading to a tetrahedral molecular shape. According to VSEPR theory, a tetrahedral molecule has bond angles of 109.5°. Therefore, the shape of PH₄⁺ is tetrahedral with bond angles of

109.5°, corresponding to Row 1.

Summary to learn

VSEPR theory predicts molecular shape from the number of electron-dense regions (bonding pairs and lone pairs) around the central atom, since these regions repel each other and spread out as far apart as possible. In PH₄⁺, phosphorus forms four bonds to hydrogen and has no lone pair left over (having used its fifth valence electron to form the extra bond that gives the ion its positive charge), so with four bonding regions and zero lone pairs the ion adopts a tetrahedral shape with bond angles of 109.5°.

49 Organic chemistry

Q49. Which of the following organic compounds are structural isomers of each other?1. Cyclohexene2. Methyl…

Which of the following organic compounds are structural isomers of each other?

1. Cyclohexene

2. Methyl cyclopentane

3. Hexane

4. Hex-1-ene

5. 3-methylpent-2-ene

A2 and 3 only
B2 and 4 only
C1 and 2 only
D1, 4 and 5 only
E2, 4 and 5 only

Correct answer: E 2, 4 and 5 only

Full explanation

Structural isomers share the same molecular formula but arrange their atoms differently, so the first job is working out each compound’s formula and ruling out anything that doesn’t match the others.

Cyclohexene is C₆H₁₀ — a six-carbon ring with one double bond, and that double bond costs it two hydrogens compared with a fully saturated ring. Hexane is C₆H₁₄, the straight-chain saturated alkane. Methylcyclopentane, hex-1-ene and 3-methylpent-2-ene are all C₆H₁₂: a saturated ring and an open-chain alkene both ‘use up’ exactly one degree of unsaturation — one ring or one double bond — so they end up costing the same two hydrogens and land on the same formula.

That immediately rules out cyclohexene (C₆H₁₀) and hexane (C₆H₁₄) — neither one’s formula matches anything else on the list. That leaves methylcyclopentane, hex-1-ene and 3-methylpent-2-ene, all sharing C₆H₁₂.

Sharing a formula is necessary but not enough on its own — the three compounds also need genuinely different atom connectivity, not just different names for the same skeleton. Methylcyclopentane is a saturated five-membered ring with a methyl branch (a cycloalkane); hex-1-ene is a straight six-carbon chain with a double bond at one end; 3-methylpent-2-ene is a branched five-carbon chain with a double bond in the middle. Three distinct skeletons, three distinct connectivities — so all three genuinely are structural isomers of one another.

That’s compounds 2, 4 and 5 — the correct answer is (E).

Summary to learn

Structural isomers share the same molecular formula but differ in how their atoms are connected. Formula comes first: a saturated ring or a straight-chain double bond each ‘cost’ the same two hydrogens relative to a fully saturated open chain (one degree of unsaturation each), so a cycloalkane, a straight-chain alkene and a branched alkene can all land on the same formula even though a straight-chain alkane (more hydrogens, no unsaturation) and a cyclic alkene (one ring plus one double bond, fewer hydrogens) do not. Sharing a formula is necessary but not sufficient for being isomers — the candidates also need genuinely different atom connectivity, not just different names for the same skeleton.

50 The periodic system of elements

Q50. Which of the following lists the given elements in order of DECREASING first ionisation energies?(Atomic…

Which of the following lists the given elements in order of DECREASING first ionisation energies?

(Atomic numbers: Li = 3; Be = 4; Na = 11)

ABe, Li, Na
BBe, Na, Li
CNa, Be, Li
DLi, Be, Na
ELi, Na, Be

Correct answer: A Be, Li, Na

Full explanation

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. It follows specific trends across the periodic table:

I.E increases left to right across a period I.E decreases top to bottom down a group

In this question, 3 elements are compared: Li, Be and Na. According to the trend,

Li has lower I.E than Be (across the period 2); and Na has lower I.E than Li (down the group 1).

Thus, the order of decreasing 1st ionization energy is Be>Li>Na, matching option (A).

Summary to learn

First ionisation energy (the energy needed to remove one electron from a gaseous atom) increases from left to right across a period, as increasing nuclear charge pulls the valence electrons in more tightly, and decreases down a group, as each added electron shell shields the nucleus and puts the outer electron further away. Comparing elements from different rows and groups at once means applying both trends together rather than just one.

Physics & Mathematics

Mechanics, electricity, thermodynamics, algebra & geometry · 10 questions

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51 Algebra

Q51. Evaluate 3√{[(9 × 10⁴)² − 10⁸ + 1.2 × 10¹¹] / [10⁻¹ − 9.8 × 10⁻²]}

Evaluate ³√{[(9 × 10⁴)² − 10⁸ + 1.2 × 10¹¹] / [10⁻¹ − 9.8 × 10⁻²]}

A400
B40 000
C8000
D10 000
E100 000

Correct answer: B 40 000

Full explanation

First simplify the numerator, writing every term as a multiple of 10⁸: (9 × 10⁴)² = 81 × 10⁸; 10⁸ = 1 × 10⁸; and 1.2 × 10¹¹ = 1200 × 10⁸.

Numerator = (81 − 1 + 1200) × 10⁸ = 1280 × 10⁸ = 1.28 × 10¹¹.

Now simplify the denominator: 10⁻¹ − 9.8 × 10⁻² = 0.1 − 0.098 = 0.002 = 2 × 10⁻³.

So the expression inside the cube root is (1.28 × 10¹¹)/(2 × 10⁻³) = 0.64 × 10¹⁴ = 64 × 10¹².

³√(64 × 10¹²) = ³√64 × 10¹²⁄³ = 4 × 10⁴ = 40 000.

Hence, the correct answer is (B).

Summary to learn

When simplifying an expression made of numbers in scientific notation, it helps to rewrite every term as a multiple of the same power of ten first, so the coefficients can simply be added or subtracted directly. Taking a cube root of a number in scientific notation works by taking the cube root of the coefficient and dividing the exponent of ten by three — which only comes out to a whole-number exponent if the coefficient is first rewritten as a perfect cube times a power of ten that’s a multiple of 3.

52 Dynamics

Q52. A block sliding along a flat horizontal surface at an initial velocity of 2.0 m/s experiences a constant…

A block sliding along a flat horizontal surface at an initial velocity of 2.0 m/s experiences a constant resistive force of 4.0 N that brings it to rest in a distance of 2.0 m.
What is the mass of the block?

A2.0 kg
B0.50 kg
C4.0 kg
D0.25 kg
E8.0 kg

Correct answer: C 4.0 kg

Full explanation

Using v² = u² + 2as with u = 2 m/s, v = 0 m/s (comes to rest), s = 2 m: 0² = 2² + 2a(2), so 0 = 4 + 4a, giving a = −1 m/s² (the negative sign shows the acceleration opposes the motion).

The only horizontal force is the resistive force F = 4.0 N, so by F = ma, m = F/a = 4.0/1.0 = 4.0 kg.

Hence, the correct answer is (C).

Summary to learn

The SUVAT equation v² = u² + 2as connects initial velocity, final velocity, acceleration and distance without needing time, which is exactly the right tool whenever a problem gives distance-to-stop but not time-to-stop. Once the deceleration is found this way, Newton’s second law F = ma (rearranged to m = F/a) converts the known resistive force directly into the object’s mass.

53 Coordinate Geometry

Q53. Find the area enclosed by the three lines y = 0, y = 2x − 4, and y = 11 − x.

Find the area enclosed by the three lines y = 0, y = 2x − 4, and y = 11 − x.

A39
B3
C22½
D37½
E27

Correct answer: E 27

Full explanation

Find the three intersection points. y = 0 and y = 2x − 4 meet where 0 = 2x − 4, x = 2, giving (2, 0). y = 0 and y = 11 − x meet where 0 = 11 − x, x = 11, giving (11, 0). y = 2x − 4 and y = 11 − x meet where 2x − 4 = 11 − x, so 3x = 15, x = 5, y = 6, giving (5, 6).

The triangle’s vertices are (2, 0), (11, 0), (5, 6). Using the determinant/shoelace formula: Area = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| = ½|2(0 − 6) + 11(6 − 0) + 5(0 − 0)| = ½|−12 + 66 + 0| = ½(54) = 27.

Hence, the correct answer is (E).

Summary to learn

To find the area enclosed by three lines, first find the three pairwise intersection points (solving each pair of line equations simultaneously) to get the triangle’s vertices, then apply the shoelace (determinant) formula, Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|, which computes a polygon’s area directly from its vertex coordinates without needing to identify a base and height by eye.

54 Ideal Gas

Q54. A fixed mass of an ideal gas is compressed slowly so that its volume halves and its pressure doubles.Which of…

A fixed mass of an ideal gas is compressed slowly so that its volume halves and its pressure doubles.
Which of the following statements about the gas after this change is/are correct?
1. The final temperature of the gas is the same as before the change.
2. The final internal energy of the gas is the same as before the change.
3. The final mean kinetic energy of the particles of the gas is the same as before the change.

A1 and 3 only
B1 only
C2 and 3 only
D1, 2 and 3
Enone of them

Correct answer: D 1, 2 and 3

Full explanation

By the ideal gas law PV = nRT: initially P₁V₁ = nRT₁, finally P₂V₂ = nRT₂, with P₂ = 2P₁ and V₂ = V₁/2. Substituting: (2P₁)(V₁/2) = nRT₂, so P₁V₁ = nRT₂ = nRT₁, giving T₁ = T₂. Statement 1 is correct.

For an ideal gas the internal energy U depends only on temperature (U = ⅓f•nRT), so since T₁ = T₂, the internal energy is unchanged. Statement 2 is correct.

The mean kinetic energy of the gas particles is also proportional only to temperature (KE = 3/2 kT), so it too is unchanged. Statement 3 is correct.

All three statements are correct. Hence, the correct answer is (D).

Summary to learn

For a fixed amount of an ideal gas, the ideal gas law PV = nRT ties pressure, volume and temperature together, so if pressure doubles while volume halves, their product PV is unchanged and therefore temperature is unchanged too. Because both the internal energy of an ideal gas and the mean kinetic energy of its particles depend only on temperature (not on pressure or volume individually), any process that leaves temperature unchanged — however pressure and volume move around underneath it — leaves both of those quantities unchanged as well.

55 Algebra

Q55. Which of the following is a simplification of the expression below?2x² − 9x − 18x² − 6x−3x² + 8x − 3x² + 3x

Which of the following is a simplification of the expression below?

2x² − 9x − 18x² − 6x−3x² + 8x − 3x² + 3x

A4/x − 1
B2/x − 1
C2 − 1/x
D4/x − 2
E4 − x

Correct answer: A 4/x − 1

Full explanation

Work on the two fractions separately first, then combine them. Start with the first one, and factor top and bottom. The numerator 2x² − 9x − 18 splits as 2x² − 12x + 3x − 18 = 2x(x − 6) + 3(x − 6) = (2x + 3)(x − 6), and the denominator x² − 6x factors as x(x − 6):

2x² − 9x − 18x² − 6x=(2x + 3)(x − 6)x(x − 6)=2x + 3x

The (x − 6) factor is on both the top and the bottom, so it cancels (this is valid since x ≠ 6 here).

Do exactly the same to the second fraction. The numerator 3x² + 8x − 3 splits as 3x² + 9x − x − 3 = 3x(x + 3) − 1(x + 3) = (3x − 1)(x + 3), and the denominator x² + 3x factors as x(x + 3):

3x² + 8x − 3x² + 3x=(3x − 1)(x + 3)x(x + 3)=3x − 1x

Now that both fractions have simplified down to the same denominator, x, subtract the numerators:

2x + 3x−3x − 1x=(2x + 3) − (3x − 1)x=−x + 4x

Splitting −x + 4 over x into two separate terms gives 4/x − 1.

Hence, the correct answer is (A).

Summary to learn

Subtracting one algebraic fraction from another starts with factoring every numerator and denominator fully (for a quadratic like 2x² − 9x − 18, splitting the middle term so it groups into two matching factors), which often reveals a common factor between a numerator and its own denominator that cancels before the fractions are ever combined. Once both fractions share the same denominator, their numerators combine directly over it, and the resulting single fraction can then be split back into separate terms if that matches the answer format required.

56 Electricity

Q56. An 18 V battery and a 3.0 Ω resistor are connected in series with each other, and in series with a parallel…

An 18 V battery and a 3.0 Ω resistor are connected in series with each other, and in series with a parallel arrangement of a 3.0 Ω resistor and a 6.0 Ω resistor.
What is the current in the battery? [Assume that the battery has no internal resistance.]

A1.5 A
B3.0 A
C3.6 A
D5.1 A
E9.0 A

Correct answer: C 3.6 A

Full explanation

The parallel arrangement of the 3.0 Ω and 6.0 Ω resistors has combined resistance R = (R₁R₂)/(R₁ + R₂) = (3 × 6)/(3 + 6) = 18/9 = 2.0 Ω.

This 2.0 Ω combination is in series with the other 3.0 Ω resistor, so the total circuit resistance is 3.0 + 2.0 = 5.0 Ω.

By Ohm’s Law, I = V/R = 18 V / 5.0 Ω = 3.6 A.

Hence, the correct answer is (C).

Summary to learn

For resistors combined partly in series and partly in parallel, work from the innermost combination outward: find the parallel combination’s single equivalent resistance first, using 1/R = 1/R₁ + 1/R₂ (or the shortcut R₁R₂/(R₁+R₂) for exactly two resistors), then add that equivalent resistance to any resistors in series with it to get the total circuit resistance, and finally apply Ohm’s law I = V/R using the battery’s full voltage and that total resistance to find the current the battery supplies.

57 Statistics

Q57. The mean of five non-zero positive integers is 20. The median is 24.What is the maximum possible value for…

The mean of five non-zero positive integers is 20. The median is 24.
What is the maximum possible value for the largest number?

Correct answer: E 50

Full explanation

Since the mean of the five numbers is 20, their total sum is 5 × 20 = 100.

Arrange the numbers in ascending order a ≤ b ≤ c ≤ d ≤ e. The median (the middle, third number) is c = 24, so the numbers are a, b, 24, d, e with a + b + 24 + d + e = 100.

To maximise e, minimise a, b and d subject to the ordering constraints. The smallest possible non-zero positive integers for a and b are both 1 (since a ≤ b ≤ c, this is allowed). Since d ≥ c = 24, the smallest possible value for d is 24.

So 1 + 1 + 24 + 24 + e = 100, giving e = 100 − 50 = 50.

Hence, the correct answer is (E).

Summary to learn

In a ‘maximise the largest value’ statistics problem with a fixed mean (and so a fixed total) and a fixed median, the way to push the largest number as high as possible is to make every other number as small as the given constraints allow: the smallest values are pushed down to their absolute floor (here, the smallest positive integers), and any value required to be at least as large as the median is pushed down to exactly the median itself, freeing up as much of the fixed total as possible for the one number being maximised.

58 Magnetism

Q58. A long single coil of wire is connected directly to an ammeter which is used to indicate the direction of the…

A long single coil of wire is connected directly to an ammeter which is used to indicate the direction of the current in the wire. As the N-pole of a bar magnet is inserted into the left-hand end of the coil, the ammeter indicates a current in a certain direction.
Which other action, performed separately, produces a current in the same direction?

Ainserting the S-pole of the magnet into the right-hand end of the coil
Bwithdrawing the N-pole of the magnet from the left-hand end of the coil
Cinserting the S-pole of the magnet into the left-hand end of the coil
Dwithdrawing the S-pole of the magnet from the right-hand end of the coil
Einserting the N-pole of the magnet into the right-hand end of the coil

Correct answer: A inserting the S-pole of the magnet into the right-hand end of the coil

Full explanation

By Lenz’s Law, the induced current always flows in a direction that opposes the change in magnetic flux causing it. Inserting the N-pole into the left-hand end increases the flux through the coil in a particular direction, and the coil responds with a current in a certain (reference) direction.

Inserting the S-pole into the right-hand end also increases the magnetic flux through the coil in that same direction (a south pole entering from the right has the same effect on flux direction as a north pole entering from the left), so the coil responds with a current in the same direction. This makes option A correct.

Withdrawing the N-pole from the left-hand end decreases the flux in that direction, producing the opposite current (B incorrect). Inserting the S-pole into the left-hand end increases the flux in the opposite direction, also producing the opposite current (C incorrect). Withdrawing the S-pole from the right-hand end decreases the flux in the original direction, again producing the opposite current (D incorrect). Inserting the N-pole into the right-hand end increases the flux in the opposite direction, producing the opposite current (E incorrect).

Hence, the correct answer is (A).

Summary to learn

Electromagnetic induction follows Lenz’s law: an induced current always flows in the direction that opposes the change in magnetic flux causing it. Because a magnet’s two poles produce opposite flux effects, and because entering a coil from one end has the opposite flux effect to entering from the other end, several different physical actions (a given pole entering one end vs. the opposite pole entering the other end, for instance) can end up inducing current in exactly the same direction, while the reverse motion of the same magnet always induces current in the opposite direction.

59 Geometry

Q59. The diagram shows two concentric circles, both with centre O. The angle of the shaded sector is θ°. [diagram…

The diagram shows two concentric circles, both with centre O. The angle of the shaded sector is θ°. [diagram not to scale]
The radius of the larger circle is 50% greater than the radius of the smaller circle. The total area of the smaller circle is 36π cm². The area of the shaded sector is 27π/8 cm².
What is the value of θ?

A15
B8 11/16
C16 10/8
D22½
E30

Correct answer: A 15

Full explanation

Let the smaller circle’s radius be r. Since πr² = 36π, r² = 36, so r = 6 cm. The larger circle’s radius is 50% greater: 1.5 × 6 = 9 cm, so its area is π(9)² = 81π cm².

The shaded sector (of the larger circle) has area (θ/360) × 81π cm². Setting this equal to the given area: (81π/360) × θ = 27π/8.

θ = (27π/8) × (360/81π) = 360/(8 × 3) = 360/24 = 15.

Hence, the correct answer is (A).

Summary to learn

A circle’s area scales with the square of its radius (Area = πr²), so a radius increase of 50% multiplies the area by 1.5² = 2.25, not by 1.5. The area of a sector is simply a fraction of the full circle’s area, that fraction being the sector’s angle out of the full 360° — so once a sector’s area and its circle’s full area are both known, the angle follows directly from θ = (sector area / full area) × 360°.

60 Simple Harmonic Motion

Q60. The simple pendulum of a tall clock swings freely backwards and forwards so that it passes through the…

The simple pendulum of a tall clock swings freely backwards and forwards so that it passes through the vertical position at 1.0 second intervals.
Assuming that the motion of the pendulum is simple harmonic, what is the length of the pendulum? [Take the gravitational field strength to be 10 N/kg, and take π² to be 10.]

A1.7 m
B0.25 m
C1.0 m
D2.5 m
E3.3 m

Correct answer: C 1.0 m

Full explanation

The pendulum passes through the vertical position twice per full oscillation (once each way), so passing through it every 1.0 s means the period is T = 2.0 s.

The time period of a simple pendulum is T = 2π√(l/g). Substituting T = 2 s and g = 10 N/kg: 2 = 2π√(l/10), so 1 = π√(l/10).

Squaring both sides: 1 = π²(l/10). Using π² = 10: 1 = 10(l/10) = l, so l = 1.0 m.

Hence, the correct answer is (C).

Summary to learn

A simple pendulum’s period, T = 2π√(l/g), is the time for one complete swing there-and-back — so if a pendulum is only reported as passing through its central (vertical) position at fixed intervals, remember that it does so twice per full swing (once travelling each way), meaning the true period is twice that stated interval, not equal to it.

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