IMAT 2013 Answers & Worked Solution

Full explanation

Passage summary : People moving away for work and education boosted opportunities and the economy, but left many elderly without nearby family, increasing care demands and economic costs. So, this is similar to showing two sides of a coin.

Analysis of the given options

Option A : This option accurately captures the essence of the passage — weighing the positive outcomes of workforce mobility against its negative consequences for the elderly and the economy.

Option B : The passage doesn’t mention what elderly people expect.

Option C : The passage doesn’t make a recommendation about what people should do. It describes a trend and its consequences but stops short of advising people to stay near home.

Option D : The passage highlights a problem, not a policy solution.

Option E : Again, the passage notes a social consequence but doesn’t prescribe personal priorities or suggest that people ought to choose family care over career opportunities.

Full explanation

Passage summary : Plans to make drug safety research public might scare companies from launching new drugs due to fear of competitors copying vital details.

Conclusion: Drug companies won’t introduce new important drugs because of fear of imitators if information is made public.

Analysis of the given options

Option A : Irrelevant — doesn’t address fear of imitation or the argument’s reasoning.

Option B : Strengthens the argument by supporting the idea that disclosure would be risky.

Option C : Irrelevant to companies’ fear of competitors copying their products.

Option D : Not relevant to imitation fears or whether companies would stop introducing drugs.

Option E : This directly weakens the fear of imitation. If patent laws protect new drugs, competitors can’t legally copy them even with access to information — so companies wouldn’t need to withhold new drugs from the market.

Full explanation

Many historic UK buildings are decaying because strict renovation laws make repairs too expensive or impractical. If the law allowed cheaper, modern techniques, people would be more willing to maintain them. It’s better to lose some original character than lose the whole building.

Main Conclusion:

A change in the law is needed if we hope to preserve more ‘At Risk’ buildings.

Analysis of the given options;

Option A : A supporting idea, but not the main conclusion.

Option B : Actually part of the problem, not the argument’s conclusion.

Option C : This sums up the passage’s main point — that legal reform is essential for saving these buildings.

Option D : A premise supporting the conclusion, not the conclusion itself.

Option E : Not mentioned or relevant to the argument.

Full explanation

Passage summary : While many think foreign travel is beneficial for confidence and independence, it isn’t the only way. It can also harm local cultures and the environment. Local projects may seem less glamorous but can be just as rewarding.

Main Conclusion: Projects within our own society can be as rewarding as foreign travel.

Analysis of the given options

Option A : Not stated or implied

Option B : A supporting idea, not the main conclusion.

Option C : This is the key point the passage builds towards — challenging the assumption that only foreign travel is valuable and promoting local projects as equally worthwhile.

Option D : Contradicts the main argument which questions this assumption.

Option E : Mentioned as a concern but not the main point.

Full explanation

Passage summary : Interviews with adult learners found those who felt most successful were highly motivated. Early success and favourable conditions might influence motivation, and both success and motivation might be linked to natural aptitude. Yet, the researchers conclude it’s impossible to learn anything without motivation.

Now — we’re asked which one is NOT a flaw in the argument.

Analysis of the given options

Option A : Flaw — feelings of success don’t always reflect real achievement.

Option B : Flaw — self-reported motivation might not match actual motivation.

Option C : Flaw — it fails to check for counterexamples, yet concludes motivation is essential.

Option D : Flaw — the research only ever looked at adult learners, yet the conclusion (“It’s impossible to learn anything without motivation”) is stated as a universal claim about all learning, not just learning by adults. Generalising from an adult-only sample to a claim about learning in general is unwarranted.

Option E : This is NOT a flaw — because the passage does not make this assumption.

Full explanation

The Inca civilization was centred in what is now modern-day Peru, with its capital at Cusco. At its height, the Inca Empire extended into parts of modern-day Ecuador, Bolivia, Chile, and Argentina — but Peru was its heartland.

Full explanation

A placebo is a substance or treatment with no active therapeutic effect, often used in clinical trials as a control to test the effectiveness of new medications or treatments. It relies on the placebo effect, where patients may perceive improvements simply because they believe they are being treated.

Full explanation

Passage summary : A nationwide survey says most people wouldn’t give up their car. A local survey in a traffic-heavy area says 76% would prefer public transport if it were more reliable. The argument then claims the nationwide survey was wrong based on this local result and calls for restrictions on car use and improvements in public transport.

Analysis of the given options

Option A : Not essential to the flaw in reasoning.

Option B : Not required — the main issue is with representativeness of data.

Option C : This is the best statement of flaw. The passage uses a localised survey from an area with heavy traffic problems to dismiss a nationwide survey — which is flawed reasoning, because the preferences in one specific area (with worse traffic) might not reflect those of the entire country.

Option D : That minority doesn’t invalidate the core issue — which is using unrepresentative data.

Option E : A practical concern, but not a flaw in the reasoning about survey representativeness.

Full explanation

Hannibal Barca, the famous Carthaginian general, famously crossed the Alps with his army — including war elephants — during the Second Punic War to launch a surprise attack on Rome from the north. It’s one of the most remarkable military feats in ancient history.

Full explanation

The World Health Organization (WHO) has its headquarters in Geneva, Switzerland.

Full explanation

Number of cars that can be held in the top 7 levels (levels 2-8)

– 8 rows per level

– 2 rows x 15 cars = 30 cars

– 6 rows x 10 cars = 60

– Total per level = 30 + 60 = 90

– Total for 7 levels = 7 x 90 = 630

Number of cars that can be held in level 1

– 2 rows x 15 cars = 30

– 4 rows x 10 cars = 40

– Total = 30 + 40 = 70

But – 4 spaces are reserved for staff parking.

Public parking spaces = 70 – 4 = 66

Total Public Parking Spaces = 630 + 66 = 696

90% of total capacity = 0.9 x 696 = 626.4 (Max – 626)

Full explanation

REGULAR JAR

– 250g costs €4.50

– Price per kg = (4.5)/(250) × 1000 = 18 €/kg

LARGE JAR

– 400g costs €6.30

– Price per kg = (6.30)/(400) × 1000 = 15.75 €/kg

Difference in Price per kg = 18.00 – 15.75 = 2.25 €/kg

Full explanation

The watch is a twenty four hour digital watch.

Analysis of the given options

Option A : 5.51 am If the watch is picked upside down, it would appear as 15:50 which is 3.50pm. So, this option is false.

Option B : 5.51 pm 5.51pm will be shown as 17.51 and 7 doesn’t work when flipped. So, this option is false.

Option C : 1.01am If the watch is picked upside down, it would appear as 10.10. So, this option is false.

Option D : 3.21pm 3.21pm will be shown as 15.21 . It would appear as 12.51 on upside down. So, this option is false.

Option E : 3.51pm 3.51pm will be shown as 15.51. It would appear as the same numbers 15.51 on upside down. So, this is the time when the display would appear the same whichever way I picked it up.

Full explanation

Facts

– 1000 people entitled to vote

– One-person-one-vote system

– To win in the first ballot, a candidate needs more than 50% of votes cast → more than 500 votes

– This candidate got 350 votes

– A second ballot took place (which means no one got more than 500 votes in the first)

So, What positions are possible for this candidate after the first round?

If a second ballot happened :

– This candidate with 350 votes could have:

– Had the most votes (if no one else had more than 350)

– Been second (if someone had more than 350 but less than 500)

– Or third (if two candidates had more than 350 each)

– Now — is it possible two candidates had more than 350 votes each?

Total votes = 1000 If this candidate had 350, for two others to have more than 350 : 350 (candidate) + 351 (candidate A ) + 351 (candidate B) = 1052 which is over 1000 — impossible. Maximum number of people who can have more than 350 is one. Meaning this candidate could only be first or second after the first round.

Full explanation

Key: look for a time that remained the best for the longest period before a new faster time appears.

From the table :

1904 — 21.6 Broken is 1932 — 21.2 Gap : 1932 – 1904 = 28 years

The 21.6 seconds from 1904 stood unbroken until 1932 — 28 years.

Full explanation

Summary : Some astronomers think that small deviations in the orbits of Uranus and Neptune suggest the existence of an undiscovered Planet X. But the argument claims these deviations aren’t reliable evidence for Planet X because the calculations of their orbits rely on old, probably inaccurate data — so the deviations might just be due to errors in prediction, not the pull of another planet.

Analysis of the given options Option A : This goes too far — the passage doesn’t conclude that Planet X cannot exist, only that the deviations aren’t reliable evidence for it.

Option B : The argument actually challenges this assumption by offering an alternative explanation (inaccurate data).

Option C : Correct. This perfectly captures the main conclusion — the deviations are inconclusive evidence for Planet X due to possibly faulty data.

Option D : This is a supporting reason within the argument, not the main conclusion. It explains why the deviations aren’t reliable evidence, but it isn’t the final takeaway.

Option E : This is implied by the reasoning but again isn’t the main conclusion. It’s a consequence of using old data, not the core point the argument is trying to make.

Full explanation

Short summary : A recent analysis found that people named John are more likely to go to university than those named Wayne. The conclusion drawn is that naming your child John increases the chance they’ll go to university.

Analysis of the given options

Option A : This is tempting because it moves from a comparison of two names to a naming decision, but the bigger issue isn’t about generalizing — it’s about mistaking correlation for causation.

Option B : The argument doesn’t claim one needs to be called John to go to university, just that it would supposedly help — so this isn’t the flaw.

Option C : Not quite — there is evidence (the analysis of records). The issue lies in how the evidence is interpreted, not its absence.

Option D : Correct. The argument spots a correlation (more Johns at university than Waynes) and wrongly infers a causal link — that naming your child John would cause them to be more likely to go to university, without considering other social, economic, or cultural factors behind the numbers.

Option E : Irrelevant — the flaw isn’t about other names being ignored; it’s about the mistaken reasoning between correlation and causation.

Full explanation

Summary : The passage discusses poor literacy among science undergraduates, blames habits like texting and emailing for this, and stresses the importance of good writing skills for employment. It concludes that students need to understand that good writing matters.

Analysis of the given options Option A : Not the main conclusion. This might be implied as part of the background issue, but the passage focuses more on what needs to be done now, not assigning blame.

Option B : Correct. This is exactly what the passage is arguing towards — that undergraduates need to understand the value of strong writing skills because it affects their employment prospects.

Option C : This is part of the evidence/problem statement, not the conclusion.

Option D : True, and mentioned as support, but it’s not the main takeaway. It’s one reason why literacy matters.

Option E : Irrelevant — the passage criticises their time spent on SMS and email, not attention in lessons.

Full explanation

The claim: 24 washes using 1 full scoop per wash

You use : ¾ scoop per wash

So — how many washes can you get?

Number of washes you get = (total scoops in packet )/(scoops you use per wash) = (24)/(0.75) = 32

Full explanation

Short summary : The passage argues that two-year degrees aren’t realistic for engineering because students already struggle to reach older standards by the end of the second year of a three-year course. It implies that shortening the degree would make things worse.

Analysis of the given options

Option A : Correct. This is an assumption because if two-year degrees compressed the same total teaching hours into fewer years, the argument would weaken.

Option B : Not necessary for the argument. The passage notes students are behind earlier standards, but doesn’t assume exactly why.

Option C : Irrelevant. The issue is whether students’ current preparedness allows for a shorter degree, not whether the subject content importance has changed.

Option D : No. The argument is about preparation level and course length feasibility, not motivation.

Option E : Irrelevant to the feasibility argument — whether they’re popular or not doesn’t affect whether they’re realistic.

Full explanation

Short summary : The passage talks about how many road deaths involving commercial vehicles are due to drivers falling asleep, including police officers. It explains that while evidence like late braking can suggest tiredness, it’s not as conclusive as evidence for drink driving, making prosecutions harder.

Analysis of the given options

Option A : Not stated. The passage doesn’t compare the size of the problems — it only compares the ease of getting conclusive evidence.

Option B : Assumed maybe, but not stated in the passage. It mentions they are affected but doesn’t explicitly say why.

Option C : Not mentioned — no recommendation or policy proposal is made.

Option D : Correct. This is the logical conclusion — the passage highlights the difficulty of proving sleep-related accidents conclusively compared to drink driving.

Option E : Not stated — fairness isn’t discussed.

Full explanation

The electric battery was designed by Alessandro Volta, not Galileo.

Galileo did discover the movement of a pendulum produces a regular time measurement. He significantly improved the telescope and used it for astronomical discoveries. He is credited with developing an early thermoscope, a precursor to the modern thermometer. He also contributed to the development of the compound microscope.

Full explanation

Original price of pasta = €1.60

First discount (€0.20 off) = 1.60 – 0.20 = €1.40

Second discount (10% off total bill) = €1.40 – 10% of €1.40 = €1.40 – €0.14 = €1.26

Full explanation

Summary : A study says genes contribute about half to happiness. People find that unsettling. But this idea matches common sense. So, Even if you believe in a soul instead of genes, you’re still born with a set nature.

Analysis of the given options

Option A : True, but too narrow — it’s a supporting point, not the conclusion.

Option B : Best supported conclusion — matches the author’s point that, whether genes or a soul, you’re born with part of who you are.

Option C : Over-simplified and falsely limits it to a binary — not supported.

Option D : Too extreme — the passage doesn’t say that.

Option E : Again, too strong — the author talks about predisposition, not permanence.

Full explanation

Facts

ALPHA air – takes off every 10 mins – takes 90 mins to arrive Milan

BETA air – takes off every 5 mins – takes 60 mins to arrive Milan

A BETA plane takes off from Rome 5 mins after the previous ALPHA plane departed. The question ask how many ALPHA planes the BETA flight have passed during the course.

To approach this question, let’s assume the particular BETA flight takes off at 00:35.

Previous ALPHA flight departure time would be 00:30. Let’s name the flight as Alpha 1 and the flights before it as 2,3,4,\… in order.

For BETA flight, take off time — 00:35, arrival time — 1:35

For ALPHA 1, take off time — 00:30, arrival time — 02:00 (later than beta, so beta have passed this flight along the course)

For ALPHA 2, take off time — 00:20 arrival time — 01:50 (later than beta, so beta have passed this flight along the course)

For ALPHA 3, take off time — 00:10 arrival time — 01:40 (later than beta, so beta have passed this flight along the course)

For ALPHA 4, take off time — 00:00 arrival time — 01:30 (sooner than beta, so beta didn’t pass this flight along the course)

Therefore, Captain Johnston will have passed 3 ALPHA planes as he lands in Milan.

Full explanation

Step 1 : Let the total distance be D miles.

Distance completed so far = 60% of D = 0.6D

Remaining = 40% of D = 0.4D

Step 2 : He walks 60% of the remaining distance next:

60% of 0.4D = 0.6 × 0.4D = 0.24D

Remaining after that = 0.4D − 0.24D = 0.16D

Step 3 : Set up the equation :

0.16D = 60

D = (60)/(0.16) = 375 miles

Full explanation

We’re finding the internal base dimensions, which means: We need to subtract the thickness of the steel from both sides (left + right, front + back).

Internal Width: External width = 48 cm Subtract 4 cm from each side (left + right): 48 − (2×4) = 40 cm

Internal Depth: External depth = 44 cm Subtract 4 cm from each side (front + back): 44 − (2×4) = 36 cm

Internal dimensions of the base of the safe = 40 cm × 36 cm

Full explanation

The hand is fixed pointing up, so we find where the big dots on the rotating faces are currently located.

Outer ring (Hours) — rotates clockwise:

– If we count from the big dot, the hours passed is 8 hours. (each smaller dot counts 1 hour)

Inner ring (Minutes) – rotates anticlockwise.

– If we count from the big dot, the minutes passed is 40 mins. (each smaller dot count 5 mins)

Therefore, the clock shows 8:40

Full explanation

Let’s check the unemployment rate first.

The US, Germany and UK saw a fallen unemployment rate while the rest saw a higher trend. (Can exclude Japan and France from this fact)

Among three countries, it can be seen that only the US experienced a rise in inflation rate.

Therefore, the statement ‘Unemployment has fallen but there has been a rise in the inflation rate’ is referring to the United States.

Full explanation

Summary : The world saw the earthquake damage immediately. Main problem: getting aid from the airport to distant areas. Roads were blocked, so helicopters were the only practical method. Yet, food wasn’t delivered effectively, and even a week later it still depended on trucks. Therefore, great nations should be ashamed — implying they could have done more (e.g., sent helicopters).

To conclude that great nations should be ashamed for not getting aid there faster, especially via helicopters, the author must assume: “Great nations had helicopters available that could reach Haiti within a week.”

Analysis of the given options

Option A : Relief agencies imported trucks but not helicopters — Too specific and not required for the conclusion.

Option B : Correct. This is the unstated premise that connects the criticism to the situation.

Option C : There was enough food in Haiti — The argument is about distribution, not food availability.

Option D : Images failed to prompt action — The argument implies action was attempted, but was insufficient.

Option E : Haitians cleared roads — Irrelevant; the argument says roads were still largely blocked.

Full explanation

Transcription is a process of copying a segment of DNA into RNA for the purpose of gene expression. Therefore, the product of transcription of a DNA should only be an RNA.

Among the given choices,

Insulin, monoclonal antibodies and primary structure of a protein are protein varieties which could only be resulted from translation of a mRNA, not from transcription.

A replicate DNA molecule could only be produced from DNA replication, not from the transcription process.

Therefore, the correct answer is option C. mRNA.

Full explanation

There are 2 main cavities in human body divided by the diaphragm

1. Thoracic cavity — above the diaphragm (mostly occupied by the lungs and bronchial tree, heart and main afferent and efferent vessels,and oesophagus)

2. Abdominal cavity — below the diaphragm (Occupied mainly by liver, Intestines, spleen and kidneys)

Among the given options, heart, pulmonary vein and artery and the alveoli (lungs) are located in the thoracic cavity, therefore, above the diaphragm and only liver is found below the diaphragm in the abdominal cavity.

Full explanation

Option A : Cell membrane Cell membranes are mostly made of lipids (specifically, phospholipid bilayers). However, membrane proteins (e.g. receptors, channels) are embedded throughout the membrane — and those are made of amino acids.

Option B : Amylose It is a polysaccharide — a long chain of glucose molecules. Therefore, no amino acids are involved.

Option C : Viruses Most viruses are made up of a protein coat (capsid), sometimes with protein enzymes inside. Proteins = made of amino acids.

Option D : Enzymes Enzymes are proteins that act as biological catalysts. They are amino acids in long folded chains.

Option E : Antibodies They are specialized proteins produced by B lymphocytes during an immune response. They are also made entirely of amino acids.

Full explanation

Option A : correct statement. This is their primary function! Ribosomes translate mRNA into proteins by linking amino acids in the correct order.

Option B : correct statement. Ribosomes exist freely in the cytoplasm or attached to the rough ER.

Option C : correct statement. Ribosomes attached to the RER give it the “rough” appearance. These ribosomes usually synthesize proteins that are secreted or membrane-bound.

Option D : correct statement. Ribosomes are made of ribosomal RNA (rRNA) and proteins. During translation, messenger RNA (mRNA) and tRNA also associate with them.

Option E : Incorrect. transcription is the process of making RNA from DNA, and it happens in the nucleus, carried out by RNA polymerase, not ribosomes. Ribosomes perform translation, not transcription.

Full explanation

When this molecule is broken into a phosphate, glycerol and two fatty acids, three bonds need to be broken. For the bonds to break, hydrolysis reaction must be carried out and 3 water molecules must be supplied, not released.

Therefore, the number of water molecules released is 0.

Full explanation

Complementary DNA: TGC-CGA-CCA-AGG

Given DNA strand : ACG-GCT-GGT-TCC

Transcripted mRNA : UGC-CGA-CCA-AGG

Number of H bonds in each triplet (1 A-T and 2 G-C) = (1 x 2) + (2 x 3) = 2 + 6 = 8

Analysis of the given statements

Statement 1 : Correct. The complementary DNA strand contains CGA triplet.

Statement 2 : Correct as calculated above.

Statement 3 : Incorrect. mRNA sequence contains only 1 uracil base.

Full explanation

Analysis of the given options

Option A : Sex-linked dominant condition This condition cannot explain the boy’s inheritance of the disease because if the gene inherited is a dominant one, the parent who gives the gene must have the condition too.

Option B : Sex-linked recessive condition This could be the case if the diseased X gene is inherited from the mother while mother does not have the condition because for a recessive gene to express in female, 2 diseased alleles are required.

Option C : Both parents are carriers If it is an autosomal recessive condition, parents do not have the condition by possessing abnormal allele each while it can produce an offspring with the condition if the offspring inherited that abnormal allele from both parents.

Option D : Autosomal recessive condition Same condition as option C.

Option E : Mutation Mutation is considered as one of the possible causes of every genetic disease.

Full explanation

Analysis of the given options

Option A : Antibodies are proteins produced by B cells and they bind to specific antigens on pathogens to neutralize or mark them for destruction. So, they are directly involved in fighting infections.

Option B : T cell is a type of lymphocyte that contributes to adaptive immune response. 2 main types can be divided. Helper T cells activate other immune cells and Cytotoxic T cells kill infected or abnormal cells. So, they are involved in defense.

Option C : Beta cells are cells in the pancreas that produce insulin to regulate blood sugar. It is not involved in defense. It is involved in metabolism.

Option D : B cells is another type of lymphocyte that produces antibodies and contributes to the adaptive immune response. So, it is involved in defense.

Option E : Phagocyte is a white blood cell that engulfs and digests pathogens and debris. It is a part of the innate immune system. So, it also has a role in defense.

Full explanation

Glycolysis — This process occurs in the cytoplasm. No CO₂ is released. Glucose (6C) → 2 Pyruvate (3C) + 2ATP + 2NADH.

Anaerobic respiration — Also called fermentation and takes place when oxygen is not available. In yeast, pyruvate is converted to ethanol and CO₂. In animals, pyruvate is converted to lactate (no CO₂).

Kreb cycle — occurs in the mitochondrial matrix. CO₂ is released at multiple steps : Isocitrate → α-ketoglutarate (CO₂ released) α-ketoglutarate → Succinyl-CoA (CO₂ released)

Full explanation

To find the percentage of thymine, let’s use Chargaff’s rules, which state:

In double-stranded DNA: %A = %T %G = %C Total = 100%

Given : %G = 32% → so %C = 32% So G + C = 32% + 32% = 64% The remaining 36% must be A + T, and since %A = %T, we divide it equally: A = T = 36% ÷ 2 = 18%

Full explanation

Mitosis stages in order Prophase — Chromosomes condense, spindle forms. Metaphase — Chromosomes align at the metaphase plate. Anaphase — Sister chromatids separate to opposite poles. Telophase — Chromatids arrive at poles, nuclear envelope reforms. (Then → Cytokinesis, division of the cytoplasm)

Therefore, telophase comes immediately after anaphase.

Full explanation

1. an advantageous mutation. Introduces a new allele that gives a survival or reproductive benefit. Example: A mutation for darker scales might help fish camouflage better → increased survival → more offspring with that trait.

2. increased reproductive success of individuals with that phenotype. Even without a new mutation, if individuals already possessing the phenotype reproduce more (due to mate selection, survival, etc.), their trait will become more common.

3. a change in the environment.

Can alter selective pressures, favoring one phenotype over others. Example: If water becomes murkier, fish with certain coloration might evade predators more effectively.

Full explanation

ATP (Adenosine Triphosphate) is produced in both: Photosynthesis (in the light-dependent reactions, inside chloroplasts) Cellular respiration (in glycolysis, Krebs cycle, and oxidative phosphorylation)

Glucose — made in photosynthesis but broken down in respiration

Reduced NADP(NADPH) — produced in photosynthesis, not in respiration.

Carbon dioxide — produced in respiration, used in photosynthesis

Oxygen — produced in photosynthesis. used in respiration.

Full explanation

A eukaryotic cell is defined by having a membrane-bound nucleus and other membrane-bound organelles (such as mitochondria, ER and Golgi) – features prokaryotic cells lack.

Mitochondria — membrane-bound organelles found only in eukaryotic cells, and present throughout the entire cell cycle regardless of what stage of division the cell is in. This makes them a reliable identifier here.

Ribosomes — found in both eukaryotes and prokaryotes, so they cannot be used to tell the two apart, at any stage of the cell cycle.

Nucleus — normally the key identifying feature of a eukaryotic cell, but the question specifies a cell in metaphase. By metaphase, the nuclear envelope has already broken down (this happens earlier, going into mitosis), so there is no intact nucleus present at that exact moment to serve as evidence – which is why statement 3 does not count here even though the nucleus is normally diagnostic.

Only mitochondria (statement 1) reliably identify this cell as eukaryotic at the stage described, so the correct answer is (A), 1 only.

Full explanation

The correct term for Gas → Solid is Deposition. Freezing is the change from liquid to solid.

Full explanation

Step 1 : CH₃CH=CH₂ → CH₃CHBrCH₃ Propene (alkene) reacts with HBr → bromoalkane. Type: Electrophilic addition across the C=C bond.

Step 2 : CH₃CHBrCH₃ → (CH₃)₂CHCN Bromoalkane reacts with KCN → nitrile. Br replaced with CN⁻ ion (Nucleophilic substitution).

Step 3 : (CH₃)₂CHCN → (CH₃)₂CHCH₂NH₂ Nitrile is reduced to primary amine. Reagents: H₂/Ni or LiAlH₄ (Reduction).

Full explanation

1. They have the same molecular formulae. Correct. Isomers by definition have the same molecular formula but differ in the arrangement of atoms. For example, C₂H₆O can be ethanol or dimethyl ether.

2. Their physical properties are very similar. Not necessarily true. Some isomers (especially structural isomers) can have very different physical properties due to changes in functional groups or molecular shape. For example, Ethanol (polar, hydrogen bonding) vs. dimethyl ether (less polar) have different boiling points.

3. They have different structural formulae. Correct. Isomers differ in how atoms are connected (structural isomers) or arranged in space (stereoisomers), so their structural formulae are different.

Full explanation

1. The length of carbon to carbon bonds increases in the order C≡C, C=C, C-C. Correct. More shared electrons → stronger attraction → atoms pulled closer. Correct order — Bond length: C≡C < C=C < C–C

2. The strength of the C=C bond is less than twice the strength of the C-C bond. Correct. C–C bond energy ≈ 350 kJ/mol, C=C bond energy ≈ 610 kJ/mol So, 610 < 2 × 350 (700 kJ/mol)

3. The carbon atoms are joined by six electrons in the C≡C bond.

Correct. Triple bond = 1 sigma (σ) bond + 2 pi (π) bonds Each bond = 2 electrons 3 bonds x 2 electrons = 6 electrons shared

Full explanation

Option A : GaCO₃ → Ga (Gallium) typically forms a 3⁺ ion → Ga³⁺. CO₃²⁻ is a carbonate ion. Charges 3⁺ and 2⁻ are not balanced, so this is an incorrect formula. The correct formula would be Ga₂(CO₃)₃.

Option B : CsNO₃ → Cs (Cesium) is Group 1, so Cs⁺. NO₃⁻ is a nitrate ion. Balanced 1:1 (correct formula).

Option C : BeSO₄ → Be²⁺, SO₄²⁻. Balanced 1:1 (correct formula).

Option D : SnS₂ → Sn can be Sn⁴⁺. Sn⁴⁺ + 2 × S²⁻ → total 4+ and 4−. Balanced 1:1 (correct formula).

Option E : Ba(HCO₃)₂ → Ba²⁺, HCO₃⁻ (bicarbonate). 2 × HCO₃⁻ balances Ba²⁺ (correct formula).

Full explanation

To find the oxidation numbers of nitrogen in the given compounds, let’s evaluate each one individually:

1. NOCl Oxygen: -2, Chlorine: -1 Let nitrogen be x. x + (-2) + (-1) = 0 → x = +3

2. KNO₂ Potassium: +1, Oxygen (2 atoms): -2 × 2 = -4 Let nitrogen be x. (+1) + x + (-4) = 0 → x = +3

3. NO₂ Oxygen: -2 × 2 = -4 Let nitrogen be x. x + (-4) = 0 → x = +4

4. NO₂Cl Oxygen (2): -4 Chlorine: -1 Let nitrogen be x. x + (-4) + (-1) = 0 → x = +5

5. Ca(NO₃)₂ Calcium: +2 Each nitrate (NO₃⁻): sum must be -1 Oxygen (3): -6 Let nitrogen be x. x + (-6) = -1 → x = +5

Full explanation

We will balance this equation element by element.

We already have: 4 KMnO₄ → 4 MnSO₄ ⇒ Mn is balanced. 4 K → b K₂SO₄ ⇒ b = 2 (since 2 K per K₂SO₄ → 2×2 = 4 K)

5 C₂H₅OH → 5 CH₃COOH ⇒ 10 C → 10 C ⇒ C is balanced.

Since b=2, there is a total 6S on the right side and therefore, a should be 6. (S is balanced)

To balance H : Ethanol (C₂H₅OH): 5 × 6 H = 30 H Acetic acid (CH₃COOH): 5 × 4 H = 20 H H₂SO : 6 x 2H = 12H Hydrogen balance : 12 + 30 = 20 + 2c ⇒ 2c = 42-20 ⇒ c = 11

Check O as confirmation : 45 on left side : 45 on right side

Full explanation

Given : Mass of ethane (C₂H₆) = 3.0 kg = 3000 g Relative atomic masses: C = 12, H = 1 Avogadro’s constant = 6.0×10²³ mol⁻¹

Step 1 : FInd the molar mass. Molar mass = 2(12) + 6(1) = 24 + 6 = 30 g/mol

Step 2 : Find the number of moles. Moles = (3000)/(30) = 100 mol

Step 3 : Each molecule of C₂H₆ has 6 H atoms Total number of H atoms: 6 atoms x 100mol x 6.0×10²³ mol⁻¹ = 3.6 × 10²⁶ atoms

Full explanation

Statements: (1) the kinetic energy of the mass is at a maximum halfway up; (2) the potential energy of the system is at a maximum at the top of the mass’s motion; (3) the potential energy of the system is at a maximum at the bottom of the mass’s motion.

In simple harmonic motion (SHM), energy oscillates between kinetic energy (KE) and potential energy (PE). At the mean (equilibrium) position, KE is maximum and PE is minimum; at the extremes (top or bottom), PE is maximum and KE is zero.

In vertical SHM, the system’s total potential energy — gravitational plus the spring’s elastic PE combined, since both change together as the mass moves — is the same at the top and bottom (the mass oscillates symmetrically about equilibrium), so PE is maximum at both extremes — statements 2 and 3 are both correct.

The kinetic energy is maximum at the equilibrium position, which is the midpoint (halfway point) of the motion — so statement 1 is also correct.

All three statements are correct, so the answer is (A).

Full explanation

Name the points on the beam: left end = A, right end = B, suspension (pivot) point = O. The suspension point is 1.0 m from A (so 2.0 m from B). The 300 N weight is 0.5 m from A → 0.5 m to the left of O. The beam’s own 100 N weight acts at its centre, 1.5 m from A → 0.5 m to the right of O. The 80 N weight is placed x metres from B, so its distance from O is (2.0 − x) m.

Taking torques about the suspension point O:

Clockwise torques: due to the 80 N weight: 80 × (2.0 − x) = 160 − 80x N·m; due to the beam’s own weight: 100 × 0.5 = 50 N·m.

Anticlockwise torque: due to the 300 N weight: 300 × 0.5 = 150 N·m.

For balance, clockwise torque = anticlockwise torque:

50 + 80(2.0 − x) = 150 ⇒ 50 + 160 − 80x = 150 ⇒ 210 − 150 = 80x ⇒ 60 = 80x ⇒ x = 60/80 = 0.75 m.

Hence, the correct answer is (A).

Full explanation

Statements: (1) use more turns of wire in the coil; (2) use thicker wire; (3) change the speed of rotation.

Induced EMF in a coil is given by E = N·B·A·ω·sin(θ), where N is the number of turns, B is the magnetic field strength, A is the coil area, and ω is the angular speed.

Increasing N (statement 1) increases the induced EMF. Increasing the speed of rotation, ω (statement 3), also increases the induced EMF.

Using thicker wire (statement 2) changes the coil’s resistance, not the induced voltage itself — so it does not change the EMF.

Only statements 1 and 3 are correct, so the answer is (E).

Full explanation

The standard equation of a circle with centre (a, b) and radius r is (x − a)² + (y − b)² = r².

With centre (−1.5, 0.5) and radius 3: (x + 1.5)² + (y − 0.5)² = 9.

Expanding: x² + 3x + 2.25 + y² − y + 0.25 = 9 ⇒ x² + y² + 3x − y − 6.5 = 0.

Multiplying through by 2 (to clear the decimal and match the answer choices’ form): 2x² + 2y² + 6x − 2y − 13 = 0.

Hence, the correct answer is (D).

Full explanation

Expressions: (1) mv²/2t; (2) V²/R; (3) mgh/t.

Expression 1, mv²/2t, is kinetic energy divided by time — energy per unit time is power.

Expression 2, V²/R, is the standard electrical-power formula P = V²/R, so it already has units of power.

Expression 3, mgh/t, is gravitational potential energy divided by time — again energy per unit time, i.e. power.

All three expressions have units of power, so the answer is (E).

Full explanation

Using ln A + ln B = ln(AB): ln(x²/4y) + ln(xy) + ln 8 = ln[(x²/4y) · xy · 8].

Simplify inside the log: (x²/4y) · xy · 8 = 8x³y/4y = 2x³.

So the expression becomes ln(2x³) = ln 2 + ln(x³) = ln 2 + 3ln x.

Hence, the correct answer is (D).

Full explanation

Solve the first inequality: 12 − x² > 8 ⇒ 4 > x² ⇒ −2 < x < 2.

Solve the second inequality: 2x + 3 ≥ 5 ⇒ 2x ≥ 2 ⇒ x ≥ 1.

Taking the intersection of −2 < x < 2 and x ≥ 1 gives 1 ≤ x < 2.

Hence, the correct answer is (C).

Full explanation

Unshaded area = area of the isosceles right triangle − area of the quarter circle.

Name the triangle ABC, right-angled at C, with AC = BC = x (the two equal sides) and AB the hypotenuse. Drop an altitude from C to AB, meeting it at D; CD is perpendicular to AB and equals the circle’s radius r.

The hypotenuse AB = √(x² + x²) = √2·x.

The triangle’s area using AC and BC as base/height: ½ · x · x = x²/2. Using AB and the altitude CD = r as base/height: ½ · √2·x · r = rx/√2.

These are the same area, so x²/2 = rx/√2 ⇒ r = (√2 · x²)/(2x) = x/√2 ⇒ x = √2·r.

So the triangle’s area = x²/2 = (2r²)/2 = r².

The quarter circle’s area = ¼ · πr².

Unshaded area = r² − πr²/4 = r²(1 − π/4).

Hence, the correct answer is (A).