Test di Medicina 2021 Worked Solution

Full explanation

According to the given statement, for a recruit to be eligible, they must meet all of these criteria: Citizenship: Swiss citizen from birth.

Religion: Catholic.

Gender: Male.

Age: Between 19 and 30 years old.

Military: Must have completed Swiss Army training.

The statement that is certainly FALSE is A. Since the prompt asks which statement regarding the enlistments is false, and Enea could not have been legally recruited under these rules, stating that he "was enlisted" is a factual impossibility.

Full explanation

Let's set up the 7 Venn regions: only-A (a), only-B (b), only-C (c), A∩B only (d), A∩C only (e), B∩C only (f), A∩B∩C (g).

Given: g = 1, c = 1, a = b + 1 |A| = a + d + e + g = 4 → a + d + e = 3 |B| = b + d + f + g = 4 → b + d + f = 3 |C| = c + e + f + g = 4 → e + f = 2 Subtracting the first two equations: (a−b) + (e−f) = 0.

Since a−b = 1, that forces e − f = −1.

But we also need e + f = 2.

Two numbers can't simultaneously sum to 2 (even) and differ by 1 (odd) and both be integers — check parity: (e+f) + (e−f) = 2e must be even, but 2 + (−1) = 1, which is odd.

Contradiction.

So there is genuinely no valid configuration — the answer is

E) 0.

Full explanation

The proportion is based on the relationship between a measuring instrument and the physical quantity it measures: A hygrometer is used to measure humidity.

An anemometer is used to measure the speed or pressure of wind.

Therefore, the correct term to complete the proportion is

D) X = anemometer.

Full explanation

Based on the problem, the number of boxes n must satisfy: Condition 1: n/2 has a remainder of 1 ⟹ n is odd.

Condition 2: n/3 has a remainder of 0 ⟹ n is a multiple of 3.

Condition 3: n/5 has a remainder of 4 ⟹ n ends in 4 or 9.

Constraint: 4 < n < 45.

From Condition 1 and 3: n must end in 9.

List the number of candidates ending in 9 and must be a multiple of 3: 9 and 39.

Therefore, there are 2 possible solutions (9 and 39) for the number of Alice's shoe boxes.

Full explanation

The problem states that each box is a cube, completely full, and the marbles are arranged in layers where they touch the sides of the box.

This describes a Simple Cubic Packing (or "grid" arrangement).

Think about what happens when you double the number of marbles along one side of the box: Let's assume; V=4/3 Π r³ The Volume of one marble: If you fit twice as many marbles along an edge, each marble's diameter is halved.

Because volume is a cubic function ( V is proportional to r³ ), each marble now has only 1/8th of the original volume.

The Count of marbles: If you have twice as many marbles along each of the three dimensions (length, width, height), you now have 2×2×2=8 times as many marbles.

When you find the new volume; the equation would be V=4/3 π r³ ×1/8 × 8=4/3 π r³ (The total volume of material stays exactly the same as long as the marbles are in identical cubes) It doesn't matter if you have 1 giant marble that perfectly fits the box or 1,000,000 tiny marbles; as long as they are arranged in this grid pattern, they will always fill the same percentage of the box.

Therefore, the correct answer is D.

Full explanation

To solve this problem, we need to understand the relationship between the radii of tangent circles and the triangle formed by their centers.

When two circles with radii r₁ and r₂ are tangent to each other externally, the distance between their centers is exactly r₁+r₂.

If we have three circles with radii a, b, and c, the lengths of the sides of the triangle formed by their centers will be: Side 1 = a + b, Side 2 = b + c, Side 3 = a + c.

The problem states that these three sides must form a right triangle.

According to the Pythagorean theorem (A²+B²=C²), the sum of the squares of the two shorter sides must be equal to the square of the longest side (the hypotenuse).

Assuming c is the largest radius, the longest side will be b+c.

Let's assume c>b>a, so the two shorter sides are (a+b) and (a+c), and the equation to check becomes: (a+b)²+(a+c)²=(b+c)².

Now check each option by computing the triangle's three sides from its radii, then testing whether the two shorter sides squared and summed equal the longest side squared:

A) 2,3,10 -> sides = 5, 12, 13.

Check: 5²+12²=25+144=169, and 13²=169.

They match -- this forms a right triangle.

B) 3,4,5 -> sides = 7, 8, 9.

Check: 7²+8²=49+64=113, but 9²=81. 113≠81 -- not a right triangle.

C) 5,12,13 -> sides = 17, 18, 25.

Check: 17²+18²=289+324=613, but 25²=625. 613≠625 -- not a right triangle.

D) 7,24,25 -> sides = 31, 32, 49.

Check: 31²+32²=961+1024=1985, but 49²=2401. 1985≠2401 -- not a right triangle.

E) 8,15,17 -> sides = 23, 25, 32.

Check: 23²+25²=529+625=1154, but 32²=1024. 1154≠1024 -- not a right triangle.

A common trap in this question is to see triples like (3, 4, 5) or (5, 12, 13) and assume they are the answer because they are famous Pythagorean triples.

However, those are the radii, not the sides of the triangle.

When the radii are 2, 3, and 10, the sides of the triangle become 5, 12, and 13, which do form a perfect right triangle.

Therefore, the correct answer is

A) 2,3,10.

Full explanation

Teacher Alice provided two specific conditional statements: Differentiable ⟹ Continuous (Differentiability implies continuity) Continuous ⟹ Integrable (Continuity implies integrability) When you link these two together, you get a "chain" of logic: Differentiable ⟹ Continuous ⟹ Integrable Since differentiability implies continuity, and continuity implies integrability, a function that is differentiable is integrable, which makes option B true.

Full explanation

Given that Enea bought 10 birds in total and spent €81.

Prices Partridges - €12 Pigeons - €9 Quails - €6 Enea bought at least 2 of each type of bird.

In that case, it would cost; 2 (€12) + 2 (€9) + 2 (€6) = 54€ (for 6 birds) From the total money spent, 27€ (81 – 54) remains, and we need to arrange 4 birds that cost exactly 27€. 3 quails and 1 pigeon satisfy this number.

( 3(€6) + €9€ = 27€).

Therefore, the total number of partridges bought is 2 (option C).

Full explanation

To find the percentage increase, we first need to look at the price of a single pastry before and after the change.

Old price: €9 for 12 pieces | price per pastry = 9/12 = €0.75 per pastry New price: €9 for 10 pieces | price per pastry = 9/10 = €0.90 per pastry Price difference = 0.90 – 0.75 = €0.15 Percentage increase = (price increase/original price)× 100=0.15/0.75 × 100=20% The price of a single pastry increased by 20%.

The correct answer is C.

Full explanation

Assume a,b,c,d are 2,3,4,5 in order.

Original product = 2 x 3 x 4 x 5 = 120 Now, let’s test adding 1 to the smallest vs the largest: Add 1 to the smallest (2): 3 x 3 x 4 x 5 = 180 Add 1 to the largest (5): 2 x 3 x 4 x 6 = 144 144 is much smaller than 180.

To keep the result as small as possible, always add 1 to the largest number.

The correct answer is B.

Full explanation

In Italy, the Racial Laws (Leggi Razziali) were a set of decrees initiated by Benito Mussolini's Fascist regime between 1938 and 1943.

These laws were primarily directed against Italian Jews and mirrored the Nuremberg Laws of Nazi Germany.

The correct answer is

A) 1938.

Full explanation

The city of Fiume is known today as Rijeka.

It is a major port city located on the northern Adriatic coast of Croatia.

The correct answer is

C) Croatia.

A little bit of history: After WWI, Italy did not receive all the territories promised to it by the Treaty of Versailles.

This sentiment was called vittoria mutilata.

Gabriele D’Annunzio, a famous poet and nationalist, led a group of irregular soldiers (the Granatieri) to seize Fiume, declaring it an independent state called the Italian Regency of Carnaro.

Full explanation

The correct answer is

B) Consignment note (or in Italian, Fattura).

In the Italian language, the word fattura fits both definitions perfectly: Commercial Context: A fattura is an invoice or a "document issued with commercial references." It tracks a sale, the parties involved, and the tax (IVA) applied.

Esoteric Context: A fattura is also a spell or an "act of witchcraft" (often a "hex").

This comes from the Latin factura, meaning "a making" or "a creation," implying a curse that has been "made" or "crafted" against someone.

Full explanation

-teca is a suffix derived from the Greek word thēkē, which means "repository," "container," or "collection." Among the given options, Fonoteca means a collection of sound recordings.

Emeroteca means a collection of newspapers and periodicals.

Pinacoteca means an art gallery or a museum specifically for paintings.

Biblioteca means a collection of books (a library).

Zapoteca does not refer to a collection of items.

It refers to an indigenous pre-Columbian civilization.

Therefore, this is the odd one out of the given options.

Full explanation

First performed in 1969, Mistero Buffo is considered the masterpiece of Dario Fo, who won the Nobel Prize in Literature in 1997.

The correct answer is

B) Dario Fo.

Full explanation

The Day of Legality (Giornata della Legalità) is observed every year on May 23rd to honor the victims of the Mafia and, specifically, to commemorate the anniversary of the Capaci massacre (May 23, 1992).

The correct answer is

B) May 23.

Full explanation

In 1913, Henry Ford revolutionized industrial production by introducing the first moving assembly line for the mass production of an entire automobile at his Highland Park plant.

The correct answer is

A) Ford.

Other options

B) Aston Martin: Founded later (1913) and focused on luxury, hand-built sports cars.

C) Buick: While Buick was a pioneer (and a founding pillar of General Motors), it did not innovate the moving assembly line.

D) Peugeot: One of the oldest car companies in the world (founded as a coffee mill manufacturer), but it adopted assembly line techniques later, following Ford's lead.

E) Cadillac: Known for pioneering the interchangeability of parts in 1908 (which won them the Dewar Trophy), a necessary precursor to the assembly line, but not the assembly line itself.

Full explanation

The correct answer is

B) Stream of consciousness.

This term (in Italian, flusso di coscienza) refers to a narrative technique that attempts to replicate the continuous, often chaotic, and non-linear flow of thoughts, feelings, and memories passing through a character's mind.

Full explanation

In the context of the Italian political system (and most parliamentary democracies), a legislature (legislatura) does not refer to the laws themselves, but to the lifespan of the Parliament.

Therefore, the correct answer is

D) The period during which a given legislative body is in office and carries out its electoral mandate.

Other options

A) Prime Minister: The Prime Minister (Presidente del Consiglio) does not have a fixed term; they stay in power as long as they have the "confidence" of Parliament.

B) Set of laws: This is usually referred to as the Legal System (ordinamento giuridico) or Legislation.

C) President of the Republic: The President's term is called a mandate and lasts 7 years, not 5.

E) Commercial/Labor law: These are specific branches of law (Diritto commerciale and Diritto del lavoro).

Full explanation

In grammar, the passive voice (forma passiva) occurs when the subject of the sentence does not perform the action, but rather receives it.

Among the given options, the correct answer is option A. Breakdown of Option A: Subject: "The deeds of Aeneas" (Le gesta di Enea) – This is the recipient of the action.

Verb: "Were sung" (Furono cantate) – Formed by the auxiliary "to be" + past participle.

Agent: "By Virgil" (da Virgilio) – The person actually performing the action.

Full explanation

Three statements to evaluate: A1: Hydrogen is the only element with different names for its isotopes — TRUE (protium, deuterium, tritium — genuinely unique to hydrogen).

A2: An atom's mass in kg is between 10^-31 and 10^-29 — FALSE. That range is actually the electron's mass (~9.1×10^-31 kg).

A real atom (even hydrogen) has a mass around 1.67×10^-27 kg — off by two to four orders of magnitude.

A3: Except for hydrogen, all atoms have equal numbers of electrons and neutrons — FALSE. Equal electrons/protons is true (neutral atoms), but neutrons vary independently (isotopes), and heavier elements have far more neutrons than protons — e.g., uranium has 92 protons but 146 neutrons.

Hence, only statement A1 is correct.

Full explanation

The correct answer is

A) The Prince (Il Principe).

Written in 1513 and dedicated to Lorenzo de' Medici, The Prince is a cornerstone of modern political science.

Other options

B) Of the Prince and Fine Letters (Del Principe e delle Lettere): Written by Vittorio Alfieri.

It is a critique of the relationship between writers and absolute rulers.

C) On Crimes and Punishments (Dei delitti e delle pene): The famous Enlightenment masterpiece by Cesare Beccaria, which argued against torture and the death penalty.

D) On the Duties of Men (Dei doveri degli uomini): Written by Silvio Pellico (famous for Le mie prigioni).

E) Dialogue on Nobility (Dialogo della nobiltà): Associated with Giuseppe Parini.

Full explanation

To solve this, we use Chargaff's Rules.

Total Nucleotides: 6000 Base Pairing Rules: In a double-stranded DNA molecule: The amount of Guanine (G) is always equal to Cytosine (C).

The amount of Adenine (A) is always equal to Thymine (T).

Therefore, G+C+A+T=100% of the nucleotides.

If G = 20%, then C must also be 20%.

The remaining percentage (60%) must be shared equally between Adenine and Thymine.

If 60% is divided by 2, we get the percentage of Adenine.

Percentage of Adenine = 30% Number of Adenine from the total = 30% of 6000 = 0.30 x 6000 = 1800 The correct answer is

D) 1800

Full explanation

During prophase I, the nuclear membrane breaks down and chromosomes pair up, becoming homologous pairs.

Crossing over occur at the point of contact of 2 homologs.

Among the given images, image no.3 satisfies the requirement.

The homologs are in contact.

Image no.1 represents Anaphase I since the homologs have separated and are being pulled toward opposite poles of the cell.

Image no.2 and 4 represent Anaphase II since the sister chromatids have separated and are being pulled toward opposite poles of the cell.

Image no.5 represents Metaphase with the chromosomes organized at the imaginary metaphase plate.

Therefore, the correct option is option

A) IMAGE 3

Full explanation

Karyokinesis is not present in the division of a prokaryotic cell.

Karyokinesis refers specifically to the division of a nucleus.

Since prokaryotes (like bacteria) are aneucleated—meaning they lack a membrane-bound nucleus—karyokinesis cannot occur.

Prokaryotes divide via binary fission, a simpler process that does not involve the complex stages of mitosis (prophase, metaphase, etc.) associated with nuclear division.

Other options Cytokinesis: This is the physical division of the cytoplasm and cell membrane to create two separate cells, which occurs at the end of binary fission.

Growth of the cell: The cell must increase in size and volume before it can successfully divide.

DNA duplication: Prokaryotes must replicate their single circular chromosome so each daughter cell receives a copy.

Full explanation

Key facts about the cell cycle: G1 phase: DNA has not yet been replicated.

S phase: DNA replication occurs, doubling the DNA content.

G2 phase: Replication is complete, but the cell has not yet divided, so it still contains twice the DNA it had in G1.

After mitosis/cytokinesis, each daughter cell returns to the same DNA content in the G1 phase.

Since a haploid cell has half the genome of a diploid cell in G1 phase, if it is compared with G2 (with its duplicated genome), the DNA content of a haploid cell would be 4 times less than that of G2 phase.

Therefore, the correct answer is option B.

Full explanation

In the graph, the X-axis plots the photon flux (light intensity), and the Y-axis plots the oxygen production (a measure of photosynthetic rate) As light intensity increases, oxygen production rises until a plateau is reached.

At low light → photosynthesis is limited by light At the plateau → light saturation point has been reached; increasing light further does not increase photosynthesis because another factor (usually CO₂ or enzyme activity) becomes limiting.

Point Y: where net O₂ production = 0, meaning the rate of photosynthesis = respiration.

Below Y → more respiration than photosynthesis (negative O₂ production).

At Y → compensation point.

Point W: where photosynthesis reaches maximum (light saturation point) Analysis of each option

A) Photosynthesis is always limited by photon flux.

False — only at low light intensities.

Beyond point W, other factors limit photosynthesis.

B) When the photon flux is between Y and W, photosynthesis does not occur.

False — photosynthesis does occur and increases with light in this range.

C) At point Y, all the oxygen produced by photosynthesis is used for respiration.

True — by definition, this is the compensation point (net O₂ = 0).

D) If the photon flux is greater than W, photosynthesis stops.

False — it plateaus (remains constant), it doesn’t stop.

E) Photosynthesis is limited by CO₂ when the photon flux is between Y and W. False — between Y and W, the limiting factor is still light, not CO₂.

Full explanation

Analysis of each option

A) Krebs cycle: Yes, it produces ATP (or GTP) directly via substrate-level phosphorylation, and also generates NADH and FADH₂ that later yield ATP via the electron transport chain.

B) Lactic fermentation of glucose: Yes, it yields ATP — not during fermentation itself, but through glycolysis, which precedes fermentation (net gain of 2 ATP per glucose).

C) Calvin cycle: No, the Calvin cycle consumes ATP and NADPH to fix CO₂ into sugars during photosynthesis.

D) Glycolysis: Yes, it directly produces ATP via substrate-level phosphorylation.

E) Electron transport chain: Yes, it generates ATP via oxidative phosphorylation.

Full explanation

Glycolipid synthesis Lipids (including phospholipids and ceramide precursors) are synthesized mainly in the smooth endoplasmic reticulum (SER).

Carbohydrate chains are then added to some lipids in the Golgi apparatus, forming glycolipids.

So, lipid synthesis occurs in the SER, and glycosylation (attachment of sugars) occurs in the Golgi.

(option C)

Full explanation

First, we need to determine Francesca’s genotype The color blindness gene is X-linked recessive.

Francesca’s father is color-blind, so his genotype is X^cY (X^c = color‑blind allele).

Francesca received his X^c chromosome (since she got his only X).

Francesca is not color-blind, so her other X (from her mother) must be normal (X).

Francesca’s genotype = X^cX (carrier).

Paolo is not color-blind, so his genotype = XY. To predict offspring genotypes, we will use punnett square.

Possible gametes: Francesca → X or X^c Paolo → X or Y

Result Males: 50% color‑blind (X^cY), 50% normal (XY) Females: 0% color‑blind (all have at least one normal X), though 50% are carriers.

Therefore, correct answer:

B) Male 50% – Female 0%.

Full explanation

The epidermis (the outermost layer of the skin) is composed of stratified squamous epithelium — more specifically, keratinized stratified squamous epithelium that protects against abrasion, dehydration, and infection.

Therefore, the correct answer is option

D) Stratified squamous epithelium.

Full explanation

Human vertebral column structure: Cervical: 7 vertebrae Thoracic: 12 vertebrae Lumbar: 5 vertebrae Sacral: 5 fused vertebrae (forming the sacrum) Coccygeal: 3–5 fused vertebrae (coccyx) Curvatures (in adult spine) Cervical lordosis (inward curve) Thoracic kyphosis (outward curve) Lumbar lordosis (inward curve) Sacral kyphosis (outward curve) So, overall: two lordoses (cervical, lumbar) and two kyphoses (thoracic, sacral).

Therefore, among the given options, only option C is true.

Full explanation

Let’s review what gastric glands secrete: Parietal (oxyntic) cells: secrete hydrochloric acid (HCl) and intrinsic factor (for vitamin B₁₂ absorption).

Chief (zymogenic) cells: secrete pepsinogen, which becomes pepsin, a proteolytic enzyme.

Mucous cells: produce mucus to protect the stomach lining.

However, amylases (enzymes that digest starch) are not produced in the stomach — they’re secreted by the salivary glands and pancreas.

Therefore, the correct answer is option E.

Full explanation

Analysis of the given options Coronary arteries originate from the pulmonary artery — incorrect.

They originate from the ascending aorta, just above the aortic valve.

The pulmonary artery carries arterial blood — incorrect.

It carries deoxygenated (venous) blood from the right ventricle to the lungs.

The pulmonary veins carry venous blood — incorrect.

They carry oxygenated (arterial) blood from the lungs to the left atrium.

The aorta carries arterial blood — correct.

It carries oxygenated blood from the left ventricle to the systemic circulation.

The venae cavae originate from the right ventricle — incorrect.

They empty into the right atrium, not the ventricle.

Full explanation

Analysis of the given options Is made up of osteocytes — Incorrect.

Osteocytes are bone cells found in the bone matrix, not in the marrow.

Bone marrow is the soft, semi-fluid tissue inside bones, filling the medullary cavities and the spaces within spongy bone.

It is made up of hematopoietic stem cells and fatty tissue.

Is made up of osteons — Incorrect.

Osteons are structural units of compact bone, not of bone marrow (which is a part of spongy bone) Is a lymphoid organ — Correct.

Bone marrow is classified as a primary lymphoid organ, where B lymphocytes mature, and hematopoiesis (blood cell formation) occurs.

Is found only in long bones — Incorrect.

Bone marrow is found in both long and flat bones.

Is found only in flat bones — Also incorrect for the same reason.

Full explanation

Analysis of each option Cranial nerves are only sensory — Incorrect.

Some cranial nerves are sensory (e.g., optic, olfactory), some are motor (e.g., oculomotor), and some are mixed (e.g., facial, trigeminal).

Spinal nerves are only motor — Incorrect.

Each spinal nerve contains both sensory and motor fibers.

Spinal nerves are sensory, while cranial nerves are motor — Incorrect.

Both groups include sensory and/or motor fibers depending on the specific nerve.

Spinal nerves originate from the meninges — Incorrect.

They originate from the spinal cord, not the meninges.

Spinal nerves have both motor and sensory components — Correct.

A spinal nerve forms by the union of a dorsal (sensory) root and a ventral (motor) root, so it carries mixed fibers.

Full explanation

The pancreas has two functional parts: Exocrine portion: produces digestive enzymes (like amylase, lipase, proteases) that are secreted into the duodenum.

Endocrine portion: consists of the islets of Langerhans, which secrete hormones directly into the blood.

Hormones from the endocrine pancreas: Insulin (from β cells) Glucagon (from α cells) Somatostatin (from δ cells) Pancreatic polypeptide (from PP cells) Now, let’s evaluate:

A) Prolactin → produced by the anterior pituitary.

B) Oxytocin → produced by the hypothalamus, released by the posterior pituitary.

C) Glucagon → produced by the α cells of the endocrine pancreas.

This is the correct answer.

D) Amylase → exocrine product (digestive enzyme).

E) Proteases → also exocrine enzymes.

Full explanation

Cystic fibrosis (CF) is autosomal recessive, meaning a person must have two recessive alleles (aa) to be affected.

Since both parents are healthy but have an affected child, they must be carriers (Aa × Aa).

Possible genotypes from Aa x Aa

Result: the probability that any new child will have cystic fibrosis (aa genotype) is 1/4 (25%).

Full explanation

In the polymerase chain reaction (PCR), each cycle has three main steps: Denaturation (~95 °C): DNA strands separate because the hydrogen bonds between base pairs break.

Annealing (~50–65 °C): Primers bind to their complementary DNA sequences.

Extension (~72 °C): Taq polymerase synthesizes new DNA strands from the primers.

At 95 °C, the purpose is the denaturation of the double‑stranded DNA.

Full explanation

A cloning vector is a DNA molecule used to carry foreign genetic material into a host cell, where it can be replicated or expressed.

Common types: plasmids, bacteriophages (phages), cosmids, and artificial chromosomes (e.g., BACs, YACs).

Now let’s check each option: Introns: Not cloning vectors.

Introns are non‑coding regions within genes, parts of eukaryotic DNA, not vehicles for gene transfer.

Plasmids: Cloning vectors (small circular DNA in bacteria).

Phages: Used as vectors (e.g. λ phage).

Artificial chromosomes: Used as large DNA vectors (BACs, YACs).

Cosmids: Hybrid vectors combining plasmid and phage features.

Full explanation

The cylinder has a fixed volume, and we assume the temperature stays constant (it's the same cylinder, same conditions of use).

Under these conditions, the Ideal Gas Law tells us that pressure is directly proportional to the number of moles: PV=nRT → P is proportional to n(since V,R,T are constant) This means: double the pressure → double the moles, and so on.

We can set up a simple ratio. n_(initial)/P_(initial)=n_(final)/P_(final) We know: n_initial = 100 mol P_initial = 4 × 10⁵ Pa P_final = 1 × 10⁵ Pa n_final = ? n_(final)=n_(initial)×P_(final)/P_(initial) n_(final)=100×1×10⁵/4×10⁵=100×1/4=25 mol So 25 mol of hydrogen remain in the cylinder after use.

This is the easy part students often forget — the question asks for moles used up, not moles remaining! n_(consumed)=n_(initial)-n_(final)=100-25=75 mol

Full explanation

Lithium-4, written as ⁴₃Li (mass number A = 4, atomic number Z = 3) In proton emission, the unstable nucleus literally ejects a proton (¹₁H) from itself.

This is different from beta decay — no particle is created from a neutron converting; a proton already in the nucleus is expelled directly.

If one proton is removed from ⁴₃Li, it will become ³₂He (a daughter nucleus with Z = 2 and A = 3), matching answer A.

Full explanation

To answer this, we need to check two conditions for each pair: Is the molecular geometry trigonal planar (according to VSEPR)?

Do the central atoms have the same number of valence electrons?

Trigonal planar geometry occurs when the central atom has: 3 bonding groups and 0 lone pairs.

According to the chart and the options, only option B satisfies the criteria.

Full explanation

A decomposition reaction has the general form AB → A + B (one compound breaking down into two or more simpler products), and it specifically must involve ammonium nitrate (NH₄NO₃) as the reactant.

Among the given options, only option D has ammonium nitrate as the reactant.

The equation is properly balanced: ammonium nitrate decomposing into NH₃, NO₂, NO, N₂ and H₂O. Therefore, this is the decomposition reaction of ammonium nitrate.

Full explanation

This problem looks complicated because of the two coupled reactions, but the key insight is recognizing that reaction (2) is "instantaneous" — meaning every I₃^- molecule produced by reaction (1) is immediately consumed by reaction (2), as long as S₂O₃^2- is still available.

This lets us combine the two reactions into one overall equation.

Calculate initial moles BrO₃^-: 0.100 L × 0.1 mol/L = 0.010 mol S₂O₃^2-: 0.006 mol (given) I^-: 0.09 mol (given) Combine reactions (1) and (2) into an overall equation and balance 9I^-+BrO₃^-+6H⁺+3I₃^-+6S₂O₃^(2-) →3I₃^-+Br^-+3H2O +9I^-+3S₄O₆^(2-) The 9 I^- and 3 I₃^- cancel from both sides BrO₃^-+6H⁺+6S₂O₃^(2-) →Br^-+3H2O +3S₄O₆^(2-) This combined equation tells us directly: 1 mol BrO₃^-reacts with 6 mol S₂O₃^(2-).

Use the given amount of S₂O₃^2- We're told all 0.006 mol of S₂O₃^2- has reacted.

Using the 1:6 ratio, we can deduce that 0.001 mol of  BrO₃^- is necessary.

Full explanation

Osmosis is the movement of solvent (water) across a semipermeable membrane, from a region of lower solute concentration (hypotonic) to a region of higher solute concentration (hypertonic) — the membrane lets water through but blocks (or restricts) the solute.

Here, solution A is hypertonic compared to B, meaning A has a higher solute concentration than B. So water will flow from B → A. It's important to understand that osmotic equilibrium is a dynamic equilibrium, not a static stop.

At equilibrium, water molecules are still constantly crossing the membrane in both directions — but the rate of water moving A→B equals the rate moving B→A, so there's no net flow anymore.

This is conceptually identical to chemical equilibrium: the reaction doesn't stop, but forward and reverse rates become equal.

Option A describes exactly the dynamic equilibrium concept above — water continues moving both ways, but equal numbers pass each direction, so net transport = 0.

Full explanation

CuCl is a sparingly soluble salt that establishes the following dissolution equilibrium in water: CuCl(s)⇌Cu⁺(aq)+Cl^-(aq) This equilibrium has a solubility product constant: K_(sp)=[Cu⁺][Cl^-] Since the solution is saturated, this equilibrium is already established, and K_sp is a fixed value at a given temperature (it doesn't change just because we add more ions to the solution).

What does adding CaCl₂ do?

CaCl₂ is a soluble, strong electrolyte that dissociates completely: CaCl₂→Ca⁽²⁺⁾+2Cl^- Adding 0.1 mol of CaCl₂ to 1 L of solution introduces 0.2 mol of additional Cl^- ions — and crucially, Cl^- is the same ion already present from the CuCl dissolution equilibrium.

This is exactly what's meant by the "common ion effect" — adding an ion that's already part of an existing equilibrium.

Apply Le Chatelier's Principle By suddenly increasing [Cl^-] significantly (from the CaCl₂), the equilibrium: CuCl(s)⇌Cu⁺(aq)+Cl^-(aq) is pushed to the left (toward the reactants) to counteract the increased Cl^- concentration and keep K_sp constant.

This means more solid CuCl will precipitate out, and less Cu⁺ remains dissolved in solution.

Therefore, the correct option is option

B) The concentration of Cu+ decreases due to the common ion effect

Full explanation

Reading the diagram: A + B (reactants) start at a certain potential energy level The curve rises to a single peak (one "hump") representing the transition state The curve then descends to C + D (products), which sit at a lower energy level than A + B This tells us the reaction is exothermic overall (products are more stable/lower energy than reactants), and the energy profile passes through only one maximum.

Analysis of each option Option

A) The diagram represents a reaction whose mechanism involves a single stage in both directions Correct.

Since this diagram shows just one single peak, it means there is only one transition state and therefore the reaction proceeds in a single elementary step — and this is true whether you read the reaction forward (A+B → C+D) or backward (C+D → A+B).

A single-step mechanism is single-step regardless of which direction you're going.

Option

B) The activation energy is the same for both the forward and reverse reactions Incorrect.

Activation energy is measured as the height of the peak above the starting point.

Since C+D is at a lower energy than A+B, the reverse activation energy must be larger than the forward one Option

C) The transition state coincides with the stabilization of the activated complex Incorrect.

This is conceptually backwards.

The transition state/activated complex is, by definition, the LEAST stable, highest-energy point along the reaction pathway — it's a fleeting, high-energy arrangement, not a "stabilized" species.

Option

D) The forward reaction is catalyzed, while the reverse reaction is not Incorrect.

There's no information here about catalysis at all.

Option

E) The potential energy of reactants and products is the same Looking at the diagram, the C + D level is clearly drawn lower than the A + B level — they are explicitly at different heights, indicating the reaction releases energy overall.

Full explanation

Species 1 — Superoxide ion, O₂^- The sum of oxidation numbers must equal the total charge of the ion: 2x=-1 x=-1/2=-0.5 Species 2 — Molecular oxygen, O₂ This is the elemental form of oxygen.

Any element in its pure, uncombined elemental form always has an oxidation number of 0.

Species 3 — Hydrogen peroxide, H₂O₂ In H₂O₂, the structure is H–O–O–H. Using standard rules: Hydrogen = +1 (standard rule, 2 H atoms = +2 total) The molecule overall is neutral, so total charge = 0 2(+1)+2x=0 2+2x=0 x=-1

Full explanation

This question tests two distinct buffer concepts: pH (what determines it) and buffer capacity (what determines it) — and crucially, these are not the same thing.

Background — Henderson-Hasselbalch equation: pH=pK_a+log([A^-])/[HA] The key insight: pH depends only on the ratio of conjugate base to weak acid, not on their absolute concentrations.

Background — Buffer capacity: Buffer capacity is the buffer's ability to resist pH changes when small amounts of acid or base are added.

It depends directly on the absolute amount/concentration of the buffering species present — more concentrated buffers can "absorb" more added acid/base before the pH shifts significantly.

If you simply dilute the buffer (add water, no extra acid or base), both the weak acid and conjugate base get diluted by the same factor.

Since this ratio is unchanged, pH does not change upon dilution.

However, since both concentrations are now lower (everything diluted by 10%), there's less buffering material available to absorb incoming H⁺ or OH^- — so the buffer capacity decreases.

Therefore, option A is true.

Full explanation

What are structural isomers?

Molecules that share the same molecular formula but differ in how their atoms are connected/arranged (different bonding/structure).

The key test: same formula, different structure.

A) Butane and cyclobutane Butane: C₄H₁₀ (an open-chain alkane, C_nH_2n+2) Cyclobutane: C₄H₈ (a ring, C_nH_2n — rings have 2 fewer H than the open-chain equivalent because forming a ring requires losing 2 H atoms to close the loop) Different formulas (C₄H₁₀ vs C₄H₈) → not isomers

B) Acetone and propionaldehyde Acetone (propan-2-one): CH₃–CO–CH₃ → molecular formula C₃H₆O Propionaldehyde (propanal): CH₃–CH₂–CHO → molecular formula C₃H₆O Same molecular formula (C₃H₆O), but completely different functional groups.

They are isomers.

C) 2-chlorophenol and o-chlorophenol "2-chlorophenol" and "o-chlorophenol" are just two different names for the exact same molecule — not two different compounds at all.

D) Benzene and cyclohexane Benzene: C₆H₆ (aromatic ring with 3 double bonds) Cyclohexane: C₆H₁₂ (saturated ring, no double bonds) Different formulas (C₆H₆ vs C₆H₁₂) → not isomers.

E) Propane and propyne Propane: C₃H₈ (alkane, fully saturated) Propyne: C₃H₄ (alkyne, contains a triple bond) Different formulas (C₃H₈ vs C₃H₄) → not isomers.

Full explanation

Hund's rule states that when electrons fill a set of degenerate (same-energy) orbitals — like the three 2p orbitals — they must: Occupy each orbital singly first before any orbital gets a second electron (pairing) All unpaired electrons in those singly-occupied orbitals must have parallel spins (all pointing the same direction) Among the given configurations, only config 2 and 5 respect Hund’s rule.

Full explanation

Solution Let's solve this step by step.

Step 1: Multiply both sides by e^x (positive for all real x): => 3e^(2x) − 2e^x − 5 > 0

Step 2: Substitute t = e^x, t > 0: => 3t² − 2t − 5 > 0

Step 3: Solve the quadratic.

Discriminant: => Δ = (−2)² − 4(3)(−5) = 4 + 60 = 64 => t = (2 ± √64) / 6 = (2 ± 8) / 6 => t₁ = 5/3, t₂ = −1

Step 4: Since t = e^x > 0, reject t₂ = −1.

Apply t₁ = 5/3: => e^x > 5/3 => x > ln ln(5/3) The solution set is {x ∈ R : x > ln (5/3)}.

So, the correct answer is option B.

Full explanation

Solution Let's solve this step by step.

Step 1: Apply the logarithm product rule (sum of logs = log of product): => log( 1/2 · 2/3 · 3/4 · ⋯ · 9/10 )

Step 2: Evaluate the telescoping product (each numerator cancels the next denominator): => 1/2 · 2/3 · ⋯ · 9/10 = 1/10

Step 3: Evaluate the logarithm: => log(1/10) = log(10^-1) = −1

So, the correct answer is option A

Full explanation

Solution Let's solve this step by step.

Step 1: Complete the square for both x and y: => (x² − 4x + 4) + (y² + 2y + 1) + k − 5 = 0

Step 2: Rewrite in standard circle form (x − a)² + (y − b)² = r²: => (x − 2)² + (y + 1)² = 5 − k

Step 3: For a real, non-degenerate circle, r² must be strictly positive: => r² = 5 − k > 0 => k < 5

So, the correct answer is option B.

Full explanation

Solution Let's solve this step by step.

Step 1: Multiply both sides by 2 (positive, so the inequality direction unchanged): => cos x + 4 sin x + 1 > 0

Step 2: Analyse the expression on the interval [0, π].

Since sin x ≥ 0, it follows that 4 sin x ≥ 0.

Therefore: => cos x + 4 sin x + 1 ≥ cos x + 1

Step 3: On [0, π], cos x ∈ [−1, 1], so cos x + 1 ≥ 0.

Hence: => cos x + 4 sin x + 1 ≥ 0 Equality can occur only when cos x + 1 = 0 and 4 sin x = 0.

This happens only at x = π.

Substituting x = π: => cos π + 4 sin π + 1 = −1 + 0 + 1 = 0 Thus, the inequality is not satisfied at x = π.

Step 4: For every x ∈ [0, π), the expression is strictly positive, so the solution set is 0 ≤ x < π.

Hence, none of the given options are the correct answer.

Therefore, this question was cancelled (annullata) by MUR in the 2021 Medical Admission Test.

Full explanation

Solution Let's solve this step by step.

Given: Planet mass: M Planet radius: R Empty spacecraft mass: m Escape velocity for empty spacecraft: v Loaded satellite total mass: 1.44m

Step 1: Recall the escape velocity formula: => v = √(2GM/R)

Step 2: Identify the variables in the formula.

The escape velocity depends on G (gravitational constant), M (planet mass), and R (planet radius).

It does NOT contain the spacecraft mass.

Step 3: Changing the spacecraft mass from m to 1.44m has no effect on the escape velocity: => v_esc = √(2GM/R) = v (unchanged)

So, the correct answer is option B.

Full explanation

Solution Let’s solve this step by step.

Step 1: Recall the fundamental property of a conductor.

In electrostatic equilibrium, the electric field inside the conducting material is zero everywhere: => E = 0  inside the conductor

Step 2: Calculate the electric force on charge q: => F = qE = q·0 = 0

Step 3: Apply Newton’s second law: => F=ma=0 => a=0 With zero net force the charge q experiences no acceleration and remains stationary.

So, the correct answer is option A.

Full explanation

Solution Let’s solve this step by step.

Given: Current in rod: i Magnetic field: B Length of rod: L

Step 1: Recall the formula for the magnetic force on a current-carrying conductor: => |F| = iLB sinθ where is the angle between B and the current direction.

Step 2: Find the angle that maximises |F|: => Fis maximum when sinθ=1 =>θ=90°

Step 3: Compute maximum force: |F|max = iLB · 1 = iLB This occurs when B is perpendicular to the current direction.

So, the correct answer is option B.

Full explanation

Solution Let's solve this step by step.

Given: True weight: W = mg = 600 N Scale reading (normal force): N = 630 N

Step 1: Compare N and mg: => N − mg = 630 − 600 = 30 N > 0 (net force is upward)

Step 2: Apply Newton's second law (taking upward as positive): => N − mg = ma => 30 = ma => a = 30/m > 0 (upward)

Step 3: With g = 10 m·s^-2 and m = 60 kg: => a = 30/60 = 0.5 m·s^-2 (upward) Since a > 0, the elevator is accelerating upward.

The scale reads more than true weight precisely because the upward acceleration adds to the apparent weight.

So, the correct answer is option B.