IMAT 2021 Worked Solution

The principle behind the committee’s decision can be identified from the following sentence mentioned in the paragraph:

“The committee overseeing transplant decisions argued that the system it used had to be administered solely in accordance with the rationale behind its waiting writ list.” In other words, it says that the committee decision is based on the waiting list which is organized according to the order of urgency.

Option A Explanation:

A) Decisions on transplants cannot be influenced by emotions.
The committee does not say anything about emotions. It only states about the waiting list and the order of urgency. Thus, this statement is false.

Option B Explanation:

B) Decisions on transplants should include social considerations.
The committee does not say anything about social considerations. It only states about the waiting list and the order of urgency. Thus, this statement is false.

Option C Explanation:

C) Decisions on transplants should focus on the medical need of the potential recipient.
This option correctly states the principle behind the committee’s decision.

Option D Explanation:

D) The donor’s wishes should not be considered.
The committee does not say anything about the donor’s wishes. It only states about the waiting list and the order of urgency. Thus, this statement is false.

Option E Explanation:

E) Donations between family members are not allowed.
The committee does not say anything about the donations between family members. It only states about the waiting list and the order of urgency. Thus, this statement is false.

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

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

Option A Explanation:

A) It ignores the possibility that people with higher self-esteem might be more inclined to take part in outdoor activities.
This correctly describes the flaw in the argument.

Option B Explanation:

B) It ignores the likelihood that many people with varying levels of self-confidence would benefit from the advice of a mental health professional.
While professional mental health support is important, the argument’s flaw is not about disregarding therapy but rather about making a faulty causal assumption.

Option C Explanation:

C) It ignores the fact that not everyone with low self-esteem has the desire to go for a run or a walk outside.
The argument’s flaw is not about individual preferences but about the incorrect assumption regarding causality.

Option D Explanation:

D) It assumes that people who manage to appear 'perfect' in the different parts of their lives will not suffer from problems with self-confidence.
The argument does not claim that appearing “perfect” eliminates self-confidence issues.

Option E Explanation:

E) It assumes that high levels of self-confidence or self-esteem are all that are needed for a person to enjoy good mental health.
The argument does not assume that self-confidence is the only factor for mental well-being—it simply promotes outdoor activities as a solution.

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

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

Option A Explanation:
A) Young people feel rejection, disappointment and failure more because they lack wider experience.
This is a supporting premise, not the conclusion. It explains why rejection is harder for young people.

Option B Explanation:
B) Young performers are robbed of their childhood by the demands of performing.
This is also a supporting point—it describes the negative impact of performing, but it doesn’t state what should be done about it.

Option C Explanation:
C) Young people can be suddenly thrust into the limelight.
This is a background fact rather than the conclusion.

Option D Explanation:
D) Young performers need further protection by law.
This best expresses the main conclusion of the above argument.

Option E Explanation:
E) Young people have been protected from exploitation by the entertainment industry for many years.
This is an introductory statement setting the context, not the main claim being argued.

● X = Attending a particular school.
● Y = Being offered a place at the local universities.

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

This reasoning can be restated as:

● If X, then Y.
● Since you do not have X, you are not guaranteed Y.

Option A Explanation:

A) In our country, everyone who becomes a teacher must have a university degree. Since you do not have a degree, you are not qualified to become a teacher.
If you think of having a university degree as X, becoming a teacher is Y. In this case, X cannot guaranteed Y. It is stated as just one of the necessary qualifications. Thus, this statement does not parallel the stated reasoning.

Option B Explanation:

B) Everyone who has a free bus pass is entitled to travel on buses after 9:30 am without payment. Since it is after 9:30 am and you have a free bus pass, you do not have to pay for this bus journey.
If you have a free bus pass (X), then you can travel without payment (Y).
Since you have a bus pass (X), you do not have to pay (Y).
This doesn’t fit the original statement reasoning.

Option C Explanation:

C) The only way to stand for election to Parliament is to be nominated by voters in a geographical constituency. Since you have not been nominated, you cannot stand for election.
If being nominated is X, then standing an election is Y.
The second statement says that since no X, there is no Y.
This reasoning is similar, but the focus is on exclusion based on a necessary condition, not on a guarantee like option A.

Option D Explanation:

D) Everyone who becomes a student at our college has achieved a high score in their high school examinations. You have a high score, and therefore you are sure to be accepted as a student at our college.
If you have a high score (X), you are accepted as a student (Y).
Since you have a high score (X), you are accepted (Y).
This doesn’t fit the original statement reasoning.

Option E Explanation:

E) Everyone over the age of 60 is entitled to a bus pass, which gives them free travel on buses after 9:30 am. Since you are younger than 60, you are not entitled to free bus travel.
If you are over 60 (X), you are entitled to a bus pass (Y).
Since you are not over 60 (not X), you are not entitled to a bus pass (not Y).
This reasoning is the same structure as the original argument: a specific condition (X) leads to a guarantee (Y), and lacking the condition (not X) leads to being excluded from the guarantee (not Y).

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

Option A Explanation:
A) The main reason why we throw food away is that we do not value it much.
This is the best assumption. The argument suggests that the more we value something, the less we waste it (alcohol is thrown away the least, while bread, which is seemingly less valued, is wasted the most).

Option B Explanation:
B) We should be more moderate when it comes to buying bread.
This is a suggestion, not an assumption of the argument.

Option C Explanation:
C) The more expensive a food or drink is, the less likely it is that it will be wasted.
This might be true in some cases, but the argument does not explicitly focus on the cost of food or drink, only the value placed on them.

Option D Explanation:
D) Bread goes stale faster so is more likely to be thrown away.
While this could explain some of the waste, the argument does not mention the freshness or shelf life of bread as the cause for its higher waste rate.

Option E Explanation:
E) Bread is a low-quality food.
This is not necessarily true, and the argument does not make a claim about the quality of bread. The focus is on how much we value different foods, not their quality.

According to the survey,

• 10% of the cats preferred Moggiemeat.
• 20% of the cats preferred Fuss-a-Puss.
• 40% of the cats preferred Yummy Paws.
• 6 cats did not care which food they ate.
• 27 cats would not touch any of these foods.

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

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

Since 30% corresponds to 33 cats,

total number of cats × (30 ÷ 100) = 33
total number of cats = 33 ÷ (30 ÷ 100) = 110 cats

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

Option A Explanation:
A) Montana
The letters “M, O, T and A” are symmetric, but “N” is not, so this would not work.

Option B Explanation:
B) Idaho
The letters “I, A, H and O” are symmetric, but “D,” is not. This would not work.

Option C Explanation:
C) Hawaii
All the letters “H,” “A,” “W,” “I” are symmetric. Thus, this is the only state whose name can be read the same from both front and back.

Option D Explanation:
D) Oklahoma
The letters “O, A, H and M” are symmetric, but “K and L” are not. This would not work.

Option E Explanation:
E) Alabama
The letters “A, and M” are symmetric, but “L and B” are not. This would not work.

Option A Explanation:
A) Maria Montessori – pedagogy
Developed the Montessori method of education.

Option B Explanation:
B) Max Planck – physics
Founder of quantum theory.

Option C Explanation:
C) John Maynard Keynes – economics
Developed Keynesian economics.

Option D Explanation:
D) Hans Jonas – medicine
Hans Jonas was a philosopher, not a medical scholar. He is best known for his work in ethics, philosophy of biology, and technology.

Option E Explanation:
E) B. F. Skinner – psychology
Known for behaviorism and operant conditioning.

Option A Explanation:
A) The Bolshoi Theatre – Saint Petersburg
The Bolshoi Theatre is in Moscow, not Saint Petersburg.

Option B Explanation:
B) Metropolitan Opera House – New York
Correct. The Metropolitan Opera House (commonly called the Met) is located in New York City and is one of the world’s most famous opera houses.

Option C Explanation:
C) San Carlo – Venice
San Carlo (Teatro di San Carlo) is in Naples, not Venice.

Option D Explanation:
D) The Palais Garnier Opera House – Brussels
The Palais Garnier is in Paris, not Brussels.

Option E Explanation:
E) La Fenice – Florence
La Fenice is in Venice, not Florence.

The correct answer is:
C) Egyptian hieroglyphs

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

1. Ancient Greek
2. Demotic script (a later Egyptian script)
3. Egyptian hieroglyphs

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

Option A Explanation:

A) European Commission

Incorrect. Members are appointed by national governments.

Option B Explanation:

B) Court of Justice of the European Union

Incorrect. Judges are appointed by member states.

Option C Explanation:

C) Council of the European Union

Incorrect. Composed of government ministers from member states.

Option D Explanation:

D) European Parliament

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

Option E Explanation:

E) European Economic and Social Committee

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

Francis Ford Coppola directed The Godfather trilogy, which includes:

1. The Godfather (1972)
2. The Godfather Part II (1974)
3. The Godfather Part III (1990)

The trilogy is based on Mario Puzo’s novel The Godfather and is considered one of the greatest film series in cinematic history.

Option A Explanation:

A) Niels Bohr – electron microscope

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

Option B Explanation:

B) Wilhelm Conrad Röntgen – x-ray

Wilhelm Conrad Röntgen discovered X-rays in 1895.

Option C Explanation:

C) Dmitri Mendeleev – periodic table of elements

Dmitri Mendeleev formulated the periodic table of elements in 1869.

Option D Explanation:

D) Evangelista Torricelli – mercury barometer

Evangelista Torricelli invented the mercury barometer in 1643.

Option E Explanation:

E) Hans Wilhelm Geiger – particle detector

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

Option A Explanation:

A) OECD

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

Option B Explanation:

B) World Bank

Incorrect. Provides financial and technical assistance for development projects.

Option C Explanation:

C) World Economic Forum

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

Option D Explanation:

D) WTO

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

Option E Explanation:

E) IMF

Incorrect. IMF represents International Monetary Fund.
Focuses on financial stability and monetary cooperation, not trade regulations.

Option A Explanation:

A) Vladimir Nabokov – Lolita

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

Option B Explanation:

B) Leo Tolstoy – Anna Karenina

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

Option C Explanation:

C) Mikhail Bulgakov – Uncle Vanya

Uncle Vanya (1899) was written by Anton Chekhov, not Bulgakov.
Bulgakov is best known for The Master and Margarita (published posthumously in 1966).

Option D Explanation:

D) Boris Pasternak – Doctor Zhivago

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

Option E Explanation:

E) Fyodor Dostoyevsky – The Brothers Karamazov

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

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

Option A Explanation:

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

Incorrect. Bicameralism refers to legislatures, not institutional figures.

Option B Explanation:

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

Incorrect. This describes a government system, not bicameralism.

Option C Explanation:

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

Incorrect. Bicameralism is about legislatures, not courts.

Option D Explanation:

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

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

Option E Explanation:

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

Incorrect. This relates to judicial independence, not bicameralism.

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

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

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

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

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

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

Option A Explanation:
A) It maintains the fluidity of the cell membrane.
Cholesterol is a component of animal cell membrane. It maintains the fluidity of membrane by reducing membrane fluidity at moderate temperatures by reducing phospholipid movement, but at low temperatures it acts by hindering solidification by disrupting the regular packing of phospholipids. Thus, this statement is correct.

Option B Explanation:
B) It is used to make all hormones.
Cholesterol is used to make only the vertebrate sex hormones. Other hormones are made mostly from polypeptides. Thus, this statement is false.

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

Option D Explanation:
D) It is a good source of energy because of the number of hydrogen atoms.
Cholesterol serves as a component of cell membranes and precursor of steroid hormones. It does not have a role as energy storage molecules. Thus, this option is false.

Option E Explanation:
E) It transports fatty acids around the body.
Cholesterol does not have a role as fatty acid transporter. It is lipoprotein that transports fatty acids around the body. Thus, this option is false.

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

Option A Explanation:
A) NAD⁺ + H₂ ⇌ NADH + H⁺
In this reaction, electron is transferred from H₂ to NAD⁺, resulting in NADH and H⁺. Thus, this reaction is a redox reaction and it occurs commonly in the cellular respiration process, NAD⁺ serving as electron carrier throughout the pathway.
This option is true.

Option B Explanation:
B) Depolarisation of a neuron
Depolarisation of a neuron is a result of ion concentration changes. This is not a redox reaction. Thus, this option is false.

Option C Explanation:
C) Glucose + glucose ⇌ maltose + water
This is a condensation reaction which does not contain electron transfer. Thus, this is not a redox reaction. This option is false.

Option D Explanation:
D) Polymerisation of amino acid
Polymerisation reactions does not contain electron transfer. Thus, this is not a redox reaction. This option is false.

Option E Explanation:
E) A cytosine and guanine pairing
Cytosine and guanine pairing involves hydrogen bonding and electron transfer is not involved in this bonding process. Thus, this is not a redox reaction. This option is false.

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

Analysis of the given statements about SRY gene

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

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

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

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

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

Meiosis is composed of 2 stages of cell division.

• Meiosis 1 is reductional division (homologous chromosomes separation)
• Meiosis 2 is equational division (sister chromatids separation)

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

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

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

1. Atrial and ventricular diastole: AV valves open and semilunar valves close.
2. Atrial systole and ventricular diastole: AV valves open and semilunar valves close.
3. Ventricular systole and atrial diastole: AV valves close and semilunar valves open.

Option A Explanation:
A) When the left atrium contracts, the aortic valve opens.
During atrial systole phase, AV valves open and semilunar valves (aortic valve) close.
Thus, this option is false.

Option B Explanation:
B) When the right atrium contracts, the left ventricle contracts.
During atrial systole phase, ventricles relax.
Thus, this option is false.

Option C Explanation:
C) When the right ventricle contracts, the right atrio-ventricular valve opens.
During ventricular systole, AV valves close and semilunar valves open.
Thus, this option is false.

Option D Explanation:
D) When the right atrio-ventricular valve closes, the left atrio-ventricular valve opens.
AV valves close and open simultaneously.
Thus, this option is false.

Option E Explanation:
E) When the left ventricle relaxes, the aortic valve closes.
During ventricular diastole, semilunar valves (aortic valve) close.
Thus, this option is correct.

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

As we move down the group:

• Melting point increases because the size of the molecules increases and London dispersion forces become stronger with increasing atomic size.
• Electronegativity decreases because as atomic size increases, the effective nuclear affinity on bonding electrons is reduced. Fluorine is the most electronegative element.
• First ionizing energy decreases because as the atomic radius increases, the outermost electrons are further from the nucleus and less energy is needed to remove the outermost electron.

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

Analysis of the given statements

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

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

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

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

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

X(g) + e⁻ → X⁻(g)

Option A Explanation:
A) Cl⁻(g) + e⁻ → Cl(g)
Incorrect. This is the reverse of electron affinity, representing electron loss.

Option B Explanation:
B) 2Cl⁻(g) - 2e⁻ → Cl₂(g)
Incorrect. This represents the formation of Cl₂ from Cl⁻ ions, not a single-atom process.

Option C Explanation:
C) Cl(g) + e⁻ → Cl⁻(g)
Correct. This follows the form: X(g) + e⁻ → X⁻(g)

Option D Explanation:
D) Cl₂(g) + 2e⁻ → Cl₂(g)
Incorrect. This doesn't show the formation of Cl⁻ from Cl atoms.

Option E Explanation:
E) Cl⁻(g) → Cl⁻(g) + e⁻
Incorrect. This represents electron loss, not gain.

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

Analysis of the given statements

1. The hydrogen ion concentration in Y is four times greater than the hydrogen ion concentration in X
X: HNO₃ fully dissociates as HNO₃ → H⁺ + NO₃⁻
[H⁺] of given Nitric acid solution = 0.050 mol L⁻¹ (same as the acid concentration)

Y: H₂SO₄ fully dissociates as H₂SO₄ → 2H⁺ + SO₄²⁻
[H⁺] of given Sulfuric acid solution = 2 × 0.050 mol L⁻¹ = 0.1 mol L⁻¹
Thus, the hydrogen ion concentration in Y is two times greater than the hydrogen ion concentration in X, not four times. This statement is incorrect.

2. Only the acid in Y will be completely dissociated into ions
Since both of the given solutions are strong acids, both will completely dissociate into ions.
Thus, this statement is incorrect.

3. Y has a pH value of less than 2 at 25°C
Solution Y has hydrogen concentration of 0.1 mol L⁻¹
pH = -log [H⁺] = -log [10⁻¹] = 1
Since pH = 1 is less than 2, this statement is correct.

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

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

Option A Explanation:
A) Propanal, CH₃CH₂CHO
• No strong hydrogen bonding because C=O(carbonyl)does not have an H directly attached to O.
• Only dipole-dipole and Van der Waals forces.

Option B Explanation:
B) Ethanoic acid, CH₃COOH
Forms strong hydrogen bonds due to –OH in the carboxyl group.

Option C Explanation:
C) Fluoromethane, CH₃F
• No strong hydrogen bonding because H is not directly bonded to F.
• Only dipole-dipole interactions due to polar C–F bonds.

Option D Explanation:
D) Trimethylamine, (CH₃)₃N
• No hydrogen bonding because there is no H attached to N.
• Only weak dipole-dipole interactions.

Option E Explanation:
E) Hydrogen sulfide, H₂S
• No significant hydrogen bonding because H is not attached to N, F, or O.
• Only weak dipole-dipole and Van der Waals forces.

Given :

• Mass of KNO₃ = 3.2 g
• Volume of solution = 100 mL = 0.100 L

Initial concentration =
mass / volume =
^3.2⁄_0.1 = 32 gL⁻¹

After dilution in the volumetric flask,
25 mL of the initial solution is taken and diluted to 250 mL.

Dilution formula : C₁V₁ = C₂V₂

where : C₁ = 32 gL⁻¹, V₁ = 25 mL, V₂ = 250 mL, C₂ = ?

(32 gL⁻¹) × (25 mL) = C₂ × (250 mL)

C₂ = 32 × 25⁄₂₅₀ = 3.2 gL⁻¹

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

The general formula of a molecule is given : HₘXₒOₙ

First, assign Oxidation Numbers to Known Elements.

• Hydrogen (H): Usually +1.
• Oxygen (O): Usually –2.
• X: Unknown (we need to determine it).

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

Oxidation state of H + Oxidation state of X + Oxidation state of O = 0
m × (+1) + (Oxidation state of X) + n × (–2) = 0
m + (Oxidation state of X) – 2n = 0
Oxidation state of X = 2n – m

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

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

First, determine the Moles of Iron and Oxygen

Mole of Fe = 1.68 / 56 = 0.03 mol
Mole of O = 0.64 / 16 = 0.04 mol

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

Mole of Fe : Mole of O = 0.03 : 0.04
⇒ 1 : 1.33

To get a whole number ratio, multiply both sides by 3.

1 × 3 : 1.33 × 3
⇒ 3 : 4

Thus, the empirical formula is Fe₃O₄.
The correct option is option B) Fe₃O₄

We have to solve the given inequality:

(1/2)(2x + 3) − (2/3)(x + 1) < 2x

⇒ x + 3/2 − 2x/3 − 2/3 < 2x

Take the like terms on one side:

⇒ x − 2x/3 − 2x < 2/3 − 3/2

⇒ (3x − 2x − 6x)/3 < (4 − 9)/6

⇒ −5x/3 < −5/6

Multiply both sides by 6:

−10x < −5

Now divide both sides by −10. As we are dividing by a negative number, the sign of the inequality will be reversed:

(−10x)/−10 > (−5)/−10

⇒ x > 1/2

The hammer thrower swings the hammer in a horizontal circle with a constant angular velocity (ω) of 10 rad/s and a radius (r) of 2.5 m. To determine the correct row in the table, we calculate the linear speed (v) and centripetal acceleration (a) as follows:

1. Linear Speed (v): v = r · ω

Substituting the given values: v = 2.5 m × 10 rad/s = 25 m/s

This matches the speed in Row 1 and Row 2.

2. Centripetal Acceleration (a):

a = v² / r

Substituting the given values: a = (25²) / 2.5 = 625 / 2.5 = 250 m/s²

The speed is 25 m/s and the acceleration is 250 m/s², corresponding to Row 1. No other row matches both values.

The unit of Kinetic Energy
(½ × mass × velocity²) is Joules.
So, the unit of Joules would be:
(kg·m²/s²)

To determine which expressions can be measured in joules (J),
we analyse the units of each option:

1. Option A: (mass)² × velocity
Units: kg² × m/s = kg²·(m/s)
⇒ Not equivalent to J (kg²·m/s ≠ kg·m²/s²)

2. Option B: momentum × velocity
Units: (kg × m/s) × m/s = kg·m²/s²
⇒ Equivalent to J (kg·m²/s²)

3. Option C: voltage / (current × time)
• Voltage (V) = Joule per Coulomb (J/C)
• Current (I) = Coulomb per second (C/s)
• Time (t) = seconds (s)

Units: (J/C)/[(C/s) x s] = J/C²
⇒ Not equivalent to J

4. Option D: (charge)² × resistance
• Charge (Q) has unit Coulombs (C).
• Resistance (R) has unit Ohms (Ω) = V⁄A = (J⁄C)⁄(C⁄s) = J·s⁄C²

Units: C² × V⁄A = C² × ((J/C)/(C/s)) = C²×J.s/C² = J.s
⇒ Not equivalent to J

5. Option E: specific heat capacity ⁄ mass × temperature change
• Specific heat capacity (c) has units J⁄(kg·K)
• Mass (m) has units kg
• Temperature change (ΔT) has units K

Units: (J⁄kg·K) ⁄ kg × K = J⁄(kg·K)²
⇒ Not equivalent to J

The power (P) of the heater is defined as the rate at which it supplies energy:

P = Q / t

Here: Q is the thermal energy supplied (in joules)
          t is the time for which the heater operates (in seconds)

The thermal energy Q supplied to the metal block is calculated using the formula:

Q = mcΔT

Here: m = mass of the metal block
          c = Specific heat capacity of the metal
          ΔT = Temperature change

So, Q = 1.2 kg × 500
J/(kg·°C) × (90°C − 40°C) = 1.2 × 500 × 50 J

Q = 30000 J

As, time is 5 min, which equals to 5 × 60 = 300 seconds.

So, power would be:

P = Q / t = 30000 J / 300 s = 100 W

We are given that PQR it is a right-angled triangle R.
From the problem statement:

• PR = PS + SR = 1 + 2.5 = 3.5 cm
• RT = 5 cm
• ST ‖ PQ (This indicates similarity of triangles)

Since ST ‖ PQ, ΔSRT ~ ΔPQR by the AA similarity criterion.

Thus, the ratio of similarity is:

RS / PR = 2.5 / 3.5 = 5 / 7

Using the same ratio, we find RQ:

RT / RQ = RS / PR = 5 / 7

As, RT = 5,

5 / RQ = 5 / 7

So, RQ = 7 cm.

Now, using the Pythagorean theorem to find PQ:

PQ = √(PR² + RQ²)
PQ = √((3.5)² + (7)²)
PQ = √12.25 + 49 = √61.25 = √(5 × 3.5 × 3.5) = 3.5 × √5
PQ = (7√5) / 2

Since ST ‖ PQ, the ratio between corresponding sides of similar triangles applies:

ST = PQ × (5/7) = (7√5 / 2) × (5 / 7) = 5√5 / 2

Also, QT = RQ − RT = 7 − 5 = 2 cm

Now, the Perimeter of Trapezium PQTS is the sum of all four sides:

PQ + ST + QT + PS

Substituting values:

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

So, Perimeter = 3(1 + 2√5) cm

To find the value of cos ∠RPS, we’ll analyse the given right-angled triangles step-by-step.

Given tan ∠PRQ = 1/7. So,

PQ / QR = 1 / 7

Now let, PQ = 1x, QR = 7x

As the area of triangle PQR is 14 cm². So:

(1/2) × PQ × QR = 14 cm²
(1/2) × 1x × 7x = 14 cm²
(7x²)/2 = 14 cm²
x² = 28 / 7 = 4 cm² → x = 2 cm

Thus,

PQ = 2 cm,     QR = 14 cm

Now, finding PR using the Pythagorean theorem:

PR = √(PQ² + QR²) = √(2² + 14²) = √(200) = 10√2 cm

Now in triangle PRS: ∠PRS = 90°, PR = 10 cm and RS = 5 cm, we can find PS using the Pythagorean theorem:

PS = √(PR² + RS²) = √((10√2)² + 5²) = √(200 + 25) = √225 = 15 cm

So, now we can find the value of cos ∠RPS.

cos ∠RPS = Adjacent side / Hypotenuse = RP / SP = 10√2 / 15 = (2√2) / 3

A hydraulic jack operates based on Pascal’s Principle, which states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

Now, pressure is equal at the same height in a connected fluid. So statement 1 is false and statement 2 is correct.

So, pressure at point X which is immediately below the small piston will be equal to the pressure at point Y, immediately below the large piston.

P_X = P_Y

Now, pressure is force upon area. Let the area of the small piston be A₁ and the area of the large piston be A₂. So, A₂ > A₁.

P_X = P_Y ⇒ F₁ / A₁ = F₂ / A₂

If A₂ > A₁, then in order to have P_X = P_Y, F₂ > F₁.
So, F₂ is greater than F₁.

Hence, statement 3 is correct and statement 4 is false.

So, out of the four statements, Statement 2 and 3 only are correct.

We have to simplify the given expression:

(x + 2)² / (x² + x − 2)

Now, let’s first factorise the denominator:

x² + x − 2 = x² − x + 2x − 2
= x(x − 1) + 2(x − 1)
= (x + 2)(x − 1)

Now simplifying the expression:

(x + 2)² / (x² + x − 2) = (x + 2)(x + 2) / (x + 2)(x − 1) = (x + 2) / (x − 1)