IMAT 2022 Answers & Worked Solution

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.

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.

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.

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).

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.

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

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.

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.

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%.

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).

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).

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.

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.

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).

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.

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.

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.

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.

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.

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).

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.

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.

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).

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

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.

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)

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

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.

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)

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)

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

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).

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).

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.

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).

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.

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)

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

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)

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)

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

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

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.

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.

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.

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.

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.

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.

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.

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).