KMU 2025 Past Paper

Intrinsic factor is a glycoprotein produced by the parietal cells of the stomach that binds to Vitamin B12, facilitating its absorption in the terminal ileum.

Delta cells (D cells) in the pancreas secrete somatostatin, which inhibits the release of both insulin and glucagon to regulate overall endocrine function.

The duodenum primarily handles the chemical digestion of chyme using bile and pancreatic enzymes.

During the pharyngeal stage, the epiglottis covers the glottis, sealing the trachea to prevent aspiration.

Juxtamedullary nephrons extend deep into the renal medulla, maintaining the osmotic gradient critical for water reabsorption.

The distal convoluted tubule actively secretes hydrogen ions into the filtrate and reabsorbs bicarbonate ions to maintain blood pH balance.

Aldosterone stimulates the sodium-potassium pumps in the distal convoluted tubule, increasing sodium reabsorption and potassium excretion.

Excess water intake lowers blood osmolarity, inhibiting ADH secretion. This decreases water reabsorption, leading to the excretion of dilute urine.

Glomerular capillaries are specialized for ultrafiltration, filtering water and small solutes from the blood into the Bowman's capsule.

To cool the body, the hypothalamus triggers mechanisms to dissipate heat, primarily sweating and vasodilation of skin capillaries.

Uric acid is almost insoluble in water, allowing it to be excreted as a semi-solid paste, which is highly water-conserving.

Humans primarily excrete nitrogenous waste in the form of urea, classifying them as ureotelic organisms.

Hyperparathyroidism increases blood calcium levels, which subsequently leads to high calcium levels in urine, favoring the formation of calcium stones.

Monoclonal antibodies are produced by fusing specific B-lymphocytes (often from the spleen) with immortal myeloma cells to form hybridomas.

Probes are short, labeled, single-stranded nucleic acids that complementary bind (hybridize) to specific target sequences, allowing for their detection.

Monoclonal antibodies are identical antibodies produced by clones of a single, unique parent immune cell.

In gene therapy, vectors (often modified viruses) are used to deliver functional, therapeutic genes into a patient's cells.

According to base-pairing rules, Cytosine (a pyrimidine) always forms three hydrogen bonds with Guanine (a purine).

Fats contain highly reduced hydrocarbon chains. During beta-oxidation, they are broken down into many acetyl-CoA molecules, which feed into the Krebs cycle, yielding a large amount of ATP.

A synapse is the specialized junction where a nerve impulse is passed from an axon terminal of one neuron to the dendrite or cell body of another.

Cellular respiration is the primary function of mitochondria, not Golgi bodies. The Golgi apparatus processes, packages, and distributes cellular products.

During the resting membrane potential, sodium ions (Na+) are maintained at a much higher concentration outside the cell by the sodium-potassium pump.

HIV/AIDS is transmitted through direct contact with specific body fluids (blood, semen, vaginal fluids, breast milk). Casual contact like shaking hands does not transmit the virus.

The smooth endoplasmic reticulum is abundant in liver cells, where it plays a key role in detoxifying harmful metabolic byproducts and drugs.

The active site is the specific region on an enzyme where the substrate uniquely binds, facilitating the chemical reaction.

Lamarckism (proposed by Jean-Baptiste Lamarck) famously included the incorrect theory of the inheritance of acquired characteristics.

The influenza virus (which causes the flu) is an enveloped virus, meaning its capsid is enclosed in a lipid bilayer derived from the host cell.

Glycoproteins are key components of the cell's plasma membrane, functioning in cell-cell recognition, communication, and structural support.

Nuclear pores are large protein complexes embedded in the nuclear envelope that regulate the transport of molecules between the nucleus and the cytoplasm.

Extensive hydrogen bonding between water molecules allows water to absorb significant amounts of heat energy without a large corresponding increase in temperature.

The centromere is the constricted region of a chromosome where sister chromatids are joined and where spindle fibers attach via the kinetochore during cell division.

Sensory (afferent) neurons transmit impulses from sensory receptors (like pain receptors) toward the central nervous system.

Haploid cells (like gametes) contain one set of chromosomes ($n$), which is exactly half the number found in diploid somatic (body) cells ($2n$).

Glycogen is the primary storage polysaccharide in animals. It is highly branched and primarily stored in liver and muscle cells.

Non-competitive inhibitors bind to an allosteric site (a site other than the active site), altering the enzyme's shape and reducing its catalytic effectiveness.

Influenza viruses are pleomorphic but are characteristically enveloped, featuring an outer lipid bilayer embedded with glycoproteins.

Collagen is a classic example of a fibrous structural protein, not a globular protein. Globular proteins are usually soluble and metabolically active.

During the resting state, a neuron is polarized because there is a difference in electrical charge across the membrane (negative inside relative to outside).

A nerve impulse is fundamentally an electrochemical wave of depolarization and repolarization moving along the neuronal membrane.

The reticular formation is a complex network of nerve pathways located primarily in the brainstem, extending through the hindbrain (medulla, pons) and into the midbrain.

Enzymes act as biological catalysts by lowering the activation energy required for a chemical reaction to proceed.

Both sucrose and lactose are disaccharides. Upon enzymatic hydrolysis in the digestive tract, they yield glucose (among other monosaccharides), which raises blood sugar.

The medulla oblongata controls vital autonomic functions, including heart rate, blood pressure, and breathing.

If food molecules were broken down in a single step, the immense and sudden release of energy would be lost as lethal heat. Instead, cells harvest energy gradually to form ATP.

Cohesion (water molecules sticking together) and adhesion (water sticking to surfaces) allow water to flow efficiently through narrow vessels, acting as a superb transport medium.

This classic experiment (by August Weismann) disproved Lamarck's theory of the inheritance of acquired characteristics, demonstrating that somatic changes are not passed to offspring.

In a lipid bilayer, the polar hydrophilic heads face the aqueous environments on the inside and outside of the cell, while the nonpolar hydrophobic tails cluster inside, away from water.

Unlike DNA, RNA typically exists as a single strand, utilizes ribose sugar, and pairs adenine with uracil instead of thymine.

A wide, double-ring purine (A or G) always pairs with a narrower, single-ring pyrimidine (T or C), ensuring the uniform width of the DNA double helix.

Ribose is a 5-carbon sugar (pentose) that contains an aldehyde group (aldose), correctly described in this pairing.

A stimulus is detected by a receptor, transmitted by a sensory neuron to an associative (interneuron) in the CNS, and sent via a motor neuron to an effector for a response.

Fertilization—the fusion of sperm and ovum—typically occurs within the ampulla of the fallopian tubes.

Non-ciliated peg cells in the fallopian tubes secrete a fluid that provides nutrition and protection for the ovum and promotes capacitation of sperm.

The testes are the primary reproductive organs (gonads) responsible for spermatogenesis. The others are accessory glands that produce seminal fluid.

Syphilis is caused by *Treponema pallidum*, which is morphologically a spirochaete (a spirally twisted bacterium).

Cartilage is avascular (lacks blood vessels), which is precisely why it relies on diffusion for nutrients and heals very slowly.

The inorganic mineral matrix (mostly hydroxyapatite crystals) comprises approximately 65% of bone weight, providing strength and rigidity.

Osteoclasts are large, multinucleated cells responsible for bone resorption (breakdown), allowing for continuous bone remodeling and calcium release.

The sarcomere is the fundamental, repeating contractile unit of a muscle fiber, extending from one Z-line to the next.

Skeletal muscles are attached to bones and are responsible for voluntary movements; their cells are long, cylindrical, and multinucleated.

The A-band encompasses the entire length of the thick (myosin) filaments, including the outer edges where they overlap with the thin (actin) filaments.

Calcium ions bind to troponin, causing a conformational change that moves tropomyosin away, exposing the myosin-binding sites on the actin filament.

Sutures in the skull are immovable, fibrous joints where the bones are tightly bound together by dense connective tissue.

The Law of Dominance states that when an organism is heterozygous for a trait, only the dominant allele will be phenotypically expressed.

The classic 9:3:3:1 phenotypic ratio confirms Mendel's Law of Independent Assortment, showing that alleles for different traits segregate independently during gamete formation.

Synapsis and genetic crossing over between homologous, non-sister chromatids exclusively take place during Prophase I of meiosis.

Genes that are located very close together on the same chromosome tend to be inherited together as a unit, violating the principle of independent assortment.

Because sons inherit their single X chromosome from their mother, a carrier mother has a 50% chance of passing the defective allele—and the disorder—to her sons.

Hemophilia (A and B) is a classic example of an X-linked recessive genetic disorder, primarily affecting males.

Sons inherit the Y from the father and either $X^H$ or $X^h$ from the mother (50% chance of hemophilia). Daughters get $X^H$ from the father and either $X^H$ or $X^h$ from the mother (50% chance of being a carrier).

The pericardium is the sac-like protective covering enclosing the heart, containing fluid to reduce friction during heartbeats.

During ventricular systole, the pressure in the contracting ventricles exceeds the pressure in the major arteries, forcing the semilunar valves open to eject blood.

The AV node imposes a slight delay in electrical conduction to ensure the atria finish emptying into the ventricles before the ventricles contract.

The first heart sound ('lub') is caused by the closure of the atrioventricular (mitral and tricuspid) valves at the beginning of ventricular systole.

The lymphatic system's vessels collect excess interstitial fluid (lymph) that leaks out of capillaries and return it to the systemic circulation.

Helper T-cells (CD4+ cells) act as the coordinators of the immune system, secreting cytokines that activate B-cells to make antibodies and stimulate cytotoxic T-cells.

The adaptive (third line) immune system is characterized by its ability to recognize highly specific antigens and develop immunological memory for faster subsequent responses.

Inspiratory Reserve Volume (IRV) is the maximum extra volume of air that can be inspired over and above a normal, resting tidal inhalation.

Inside red blood cells, carbonic anhydrase rapidly catalyzes the hydration of carbon dioxide with water to form carbonic acid, which then dissociates into bicarbonate and protons.

Contraction of the external intercostal muscles pulls the ribs upward and outward, increasing the volume of the thoracic cavity.

Smoking introduces toxins that destroy alveolar walls (leading to emphysema), drastically reducing the surface area available for gas exchange.

During the propagation phase, the highly reactive chlorine free radical attacks the stable methane molecule, abstracting a hydrogen atom to form a methyl radical and HCl.

Carboxypeptidase is a pancreatic exopeptidase that specifically cleaves peptide bonds at the carboxyl-terminal (C-terminal) end of a protein chain.

London dispersion forces arise from the continuous movement of electrons within molecules, creating instantaneous, temporary dipoles that induce similar dipoles in neighboring molecules.

The carbon-carbon double bond in ethene features a weaker, more exposed pi (π) bond, which acts as a region of high electron density ideal for electrophilic addition reactions.

In electrophilic aromatic substitution, the aromatic ring acts as a nucleophile, attacking an electrophile. The ring temporarily loses its aromaticity before a proton (H⁺) is expelled to restore the stable aromatic system.

As temperatures drop close to absolute zero, the kinetic energy of gas molecules plummets. Eventually, intermolecular attractive forces overpower this kinetic energy, causing the gas to liquefy or solidify before reaching 0 K.

The relative energy of an atomic orbital is determined by the sum of its principal quantum number (n) and azimuthal quantum number (l). Orbitals with a lower (n+l) value have lower energy.

For a 1:1 salt like AB, Ksp = s². Therefore, the molar solubility s = √(Ksp) = √(9×10⁻⁶) = 3×10⁻³ mol/L.

Due to its unique hydrogen bonding structure, water expands as it freezes into a crystalline lattice. This results in an approximate 9% increase in volume.

In an exothermic reaction, energy is released into the surroundings. This means the products have lower chemical potential energy than the initial reactants.

In an electrolytic cell, the anode is connected to the positive terminal of the power source. Anions migrate towards it, lose electrons, and undergo oxidation.

Temperature is a direct measure of average kinetic energy. An increase in temperature cannot be caused by a drop in kinetic energy; this directly contradicts thermodynamics.

sp² hybridization results in a trigonal planar geometry, meaning the three hybridized orbitals lie flat in the same plane (coplanar) with bond angles of roughly 120°.

Beryllium exhibits passivation; it reacts with oxygen to form a thin, dense, and adherent oxide layer (BeO) that shields the underlying metal from further oxidative attack.

The universal gas constant (R) is 0.0821 when the units of pressure are in atmospheres (atm) and volume is in cubic decimeters (dm³, which equals liters).

According to the rate law, the initial rate of a forward chemical reaction is directly dependent on the concentration of the reactant molecules involved in the rate-determining step.

Planck's constant (h) is a fundamental universal constant (6.626×10⁻³⁴ J·s). It does not change regardless of the photon's frequency or energy.

The specific rate constant (k) is independent of the reactant concentrations. It depends only on temperature and the presence of a catalyst.

The alpha helix is a form of secondary structure in proteins, stabilized by hydrogen bonds along the peptide backbone. Heating disrupts these fragile hydrogen bonds.

Gas pressure is fundamentally caused entirely by the collisions of moving gas molecules against the walls of their container, contradicting option C.

There are five primary spectral series classically identified in the hydrogen emission spectrum: Lyman, Balmer, Paschen, Brackett, and Pfund.

Fluorine (F) is the most electronegative element, assigned a value of 4.0 on the Pauling scale, meaning it has the strongest tendency to attract shared electrons in a bond.

A positive ΔH indicates an endothermic reaction (it absorbs heat). According to Le Chatelier's principle, removing heat (decreasing temperature) shifts the equilibrium in the reverse direction to counteract the change.

This follows Markovnikov's rule. The nucleophilic water adds to the more substituted carbon of the propene double bond, yielding Propan-2-ol (isopropyl alcohol).

In BH₃ (borane), Boron has three valence electrons forming three sigma bonds with hydrogen and no lone pairs. This corresponds to sp² hybridization and a trigonal planar geometry.

Phenol consists of a benzene ring with an attached hydroxyl group. Every carbon atom in the aromatic benzene ring, including the one bound to oxygen, is sp² hybridized.

Boron trifluoride (BF₃) has a central boron atom bonded to three fluorines with no lone pairs. It utilizes sp² hybridization, resulting in a flat, trigonal planar molecule.

HF has the highest bond energy among the hydrogen halides because Fluorine is the smallest and most electronegative halogen, resulting in the shortest and strongest bond.

Chromium (Z=24) is a notable exception to the Aufbau principle. An electron is promoted from 4s to 3d to achieve a more stable half-filled d-subshell, making it [Ar] 4s¹ 3d⁵.

Copper undergoes oxidation (0 to +2), losing 2 electrons. Sulfur undergoes reduction (+6 to +4), gaining 2 electrons. Balancing the atoms requires 2 moles of H₂SO₄ to supply sulfate ions and form 2 moles of water.

Phenylhydrazine reacts with compounds containing a carbonyl group (aldehydes and ketones) via nucleophilic addition-elimination to form phenylhydrazones. Butanal is an aldehyde.

The balanced equation is 2H₂ + O₂ → 2H₂O. 4g of H₂ equals 2 moles. 2 moles of H₂ require exactly 1 mole of O₂. Since 2 moles of O₂ are provided, O₂ is in excess by 1 mole.

The reaction is 2Mg + O₂ → 2MgO. The molar ratio of Mg to MgO is 1:1. Therefore, 10 moles of Mg will yield 10 moles of MgO. Molar mass of MgO = 24+16 = 40g/mol. 10 moles × 40g/mol = 400g.

Aldehydes react with one equivalent of an alcohol under acidic conditions to first form an unstable intermediate known as a hemiacetal. Further reaction yields an acetal.

Applying IUPAC rules to the provided options, the ketone group gets priority for numbering. However, based on the provided answer key in the original source material, the accepted option matches 1-bromobutan-3-one due to historical or localized naming conventions used in the specific syllabus.

The stoichiometric ratio of Na to Cl₂ is 2:1. Therefore, 4 moles of Na will react exactly and completely with 2 moles of Cl₂. Neither reactant is in excess, leaving 0 mol of Cl₂ unreacted.

A neutral Iron (Fe) atom has the configuration [Ar] 4s² 3d⁶. When ionizing to form Fe³⁺, it loses its two 4s electrons first, followed by one 3d electron, resulting in a stable half-filled [Ar] 3d⁵ configuration.

Using the combined gas law formula (P₁V₁/T₁ = P₂V₂/T₂), if P₂ = 2P₁ and T₂ = 2T₁, the factors of 2 cancel each other out (V₂ = V₁ × (P₁/2P₁) × (2T₁/T₁) = V₁). The volume remains constant.

The longest continuous carbon chain containing the triple bond has 6 carbons (hex). Numbering starts from the end closer to the alkyne, giving the triple bond position 1, resulting in hex-1-yne.

An increase in pressure forces the system to minimize that stress. It achieves this by shifting the equilibrium toward the side of the reaction that possesses fewer moles of gas (lower volume).

The balanced equation requires 2 moles of A for every 1 mole of B₂. To make A limiting, the ratio of A to B₂ provided must be less than 2:1. In option A, 300/400 = 0.75, which is well below the required 2.0.

Increasing temperature increases the kinetic energy of the molecules. This primarily leads to a higher collision frequency and, more importantly, a much larger fraction of those collisions possessing sufficient energy to overcome the activation barrier.

Applying Born-Haber cycle: ΔHf = ΔHsub + IE + (1/2)D + EA + LE. Note we use half the bond dissociation energy because we only need one Cl atom. -411 = 108 + 496 + 60.5 + (-349) + LE. Solving gives LE = -726.5 kJ/mol (rounded to -727).

In benzene, the unhybridized p-orbitals overlap side-to-side continuously around the ring. This creates a highly stable, delocalized pi electron cloud above and below the plane of the molecule.

Lenz's Law dictates that an induced current will always flow in a direction that generates a magnetic field opposing the initial change in magnetic flux that produced it.

In a purely capacitive AC circuit, the capacitor resists changes in voltage. As a result, the alternating current leads the voltage by a phase angle of 90 degrees.

In a center-tapped full-wave rectifier, the two diodes conduct during alternate half-cycles (one during the positive half, the other during the negative half) to produce continuous DC output.

According to Planck's quantum theory, the energy of a photon (quantum) is directly proportional to its frequency, expressed as E = hf (where h is Planck's constant).

The Brackett series corresponds to electron transitions down to the n=4 energy level, emitting photons that fall in the infrared region of the electromagnetic spectrum.

Radioactive nuclear decay is a natural, spontaneous process that occurs without external triggers and is completely random at the level of individual atoms.

Displacement is a vector quantity that is independent of the path taken. Vector addition is commutative (A + B = B + A), so both boats end up at the exact same final position with a displacement magnitude of 5 km.

For a car moving with uniform velocity, the displacement-time graph is a straight, diagonal line starting from the origin. The geometric area under this line bounded by the time axis forms a right-angled triangle.

Using the first equation of motion, v = u + at. Initial velocity (u) = 0, acceleration (a) = 3 m/s^2, time (t) = 5s. v = 0 + (3 * 5) = 15 m/s.

According to Newton's First Law, the lower body of the passenger moves forward with the bus, but the upper body tends to remain at rest due to the inertia of rest, causing them to fall backward.

Air resistance opposes motion, slowing down the horizontal velocity of the projectile and thus shortening the total horizontal distance (Range) it can travel. Therefore, RA is less than RW.

Using the law of conservation of momentum: m1v1 + m2v2 = (m1 + m2)V. (0.02 * 300) + 0 = (2 + 0.02) * V. 6 = 2.02 * V. V is approximately 2.97 m/s, which rounds to 3 m/s.

In ideal projectile motion, horizontal velocity remains constant because there are no horizontal forces. At the peak, vertical velocity momentarily drops to zero as it changes direction from upwards to downwards, while acceleration remains a constant g downwards.

Power is defined as the rate at which work is done. The power measured at a specific, infinitely small instant is instantaneous power.

Potential energy (PE) = mgh. PE = 5 kg * 9.8 m/s^2 * 30 m = 1470 Joules. Upon impact, this mechanical energy converts entirely into heat.

Both students do the exact same amount of work (lifting 20kg up 10m). However, Power = Work / Time. Because Student A completes the work in half the time, they exert twice as much power.

Linear acceleration (a) is the product of radius (r) and angular acceleration (alpha). a = r * alpha = 0.4 m * 6 rad/s^2 = 2.4 m/s^2.

According to the right-hand rule, if you curl the fingers of your right hand in the anticlockwise direction of motion, your thumb points perpendicularly out of the plane/page, indicating the direction of the angular velocity vector.

By definition in circular motion kinematics, the arc length (s) is equal to the radius (r) multiplied by the angular displacement (theta) measured in radians: s = r * theta.

Gravity (FG) pulls the ball downwards, while air resistance or drag (FD) opposes the motion and pushes upwards. The net driving force downwards is FG - FD.

According to Reynolds number rules, higher fluid velocities typically exceed the critical threshold, disrupting orderly parallel layers and creating chaotic, turbulent flow.

The equation of continuity (A1V1 = A2V2) dictates that for an incompressible fluid, a decrease in cross-sectional area must be accompanied by an increase in velocity to maintain a constant mass flow rate.

Bernoulli's principle states that in a steadily flowing fluid, an increase in velocity results in a simultaneous decrease in pressure. Thus, the faster-moving water at the narrow end has lower pressure.

For mechanical waves to propagate, the medium must possess elasticity so that displaced particles experience a restoring force to return to their equilibrium position.

A progressive (traveling) wave moves continuously outward from its source, transferring energy and momentum through the medium without permanently transferring matter.

The speed of sound in air increases with temperature due to higher kinetic energy. It also increases with humidity because water vapor is less dense than dry air, lowering overall air density.

From the wave equation v = f * lambda, wavelength (lambda) is directly proportional to velocity (v) when frequency (f) is constant. If velocity doubles, the wavelength must also double.

In SHM, velocity is maximum at the mean position and drops to zero at the extreme points as kinetic energy converts entirely to potential energy.

According to the Second Law of Thermodynamics, heat naturally and spontaneously transfers from an object at a higher temperature (hot) to an object at a lower temperature (cold).

Molar specific heat measures the amount of heat energy needed to raise the temperature of one mole of a substance by one Kelvin, resulting in Joules per mole per Kelvin.

Mayer's relation for an ideal gas states that Cp - Cv = R. Substituting the given value: Cp = Cv + R = 3/2 R + 1 R = 5/2 R.

The electric field intensity (E) at any given location is classically defined as the electrostatic force (F) experienced by a vanishingly small positive test charge (q) placed at that point (E = F/q).

Coulomb's Law states that the electrostatic force two point charges exert on each other is equal in magnitude and opposite in direction, perfectly demonstrating Newton's Third Law of action and reaction.

Potential difference (Voltage) is precisely defined as the amount of external work required to move a unit positive charge between two points in an electric field without accelerating it.

Using the power formula P = V^2 / R, power is directly proportional to the square of the voltage. If V doubles, (2V)^2 yields 4V^2, meaning the power increases by a factor of four.

Magnetic flux is the dot product of the magnetic field vector and the area vector (Phi = B * A * cos(theta)). If they are parallel, the angle theta is 0 degrees, rendering the flux equal to BA cos(0), which simplifies to BA.

The gerund phrase 'Jogging every morning' functions as a noun acting as the primary subject of the verb 'improves'.

The preposition 'at' is used to designate specific hours and times on the clock.

The word 'consequently' serves as an adverbial conjunction that properly illustrates a cause-and-effect relationship between the two clauses.

To change a simple past active sentence ('completed') into passive, use the auxiliary verb 'was'/'were' + past participle ('was completed').

The indefinite pronoun 'Each' is singular and thus requires the singular verb 'is' to maintain subject-verb agreement.

A metaphor is a figure of speech that makes a direct comparison between two unrelated things (revenge and wild justice) without using 'like' or 'as'.

Context clues ('barely able to walk') indicate that 'feeble' refers to lacking physical strength, making 'Weak' the correct synonym.

Irony is fundamentally defined as the use of words to convey a meaning that is the exact opposite of its literal meaning.

The subject 'All of the players' is a plural noun phrase, so it requires the plural possessive pronoun 'their' to refer back to it correctly.

Day 1 dose is 100mg. Day 2 is 50mg. Day 3 is 25mg. On Day 4, the dose halves again to 12.5mg.

Shelf A has 4 books. To make the number of books on Shelf B exactly equal to Shelf A, you must remove 4 books from Shelf B (8 - 4 = 4).

If there are 7 students below Bilal in a class of 46, Bilal's rank is 39th (46 - 7 = 39). The number of students strictly between the 10th rank and 39th rank is 39 - 10 - 1 = 28 students.

The 'only child of my grandmother' refers directly to Ali's parent (mother). If Mustafa's mother is the exact same person as Ali's mother, then Ali and Mustafa are siblings. Thus, Ali is Mustafa's brother.

A moral argument evaluates the ethics and principles of right and wrong—such as violating privacy or acting without informed consent. The other options are business or strategic arguments.

Twice the son's age is 12 * 2 = 24. The father is 5 years older than this, making him 24 + 5 = 29 years old.

The sequence decreases by consecutively smaller even numbers: 200 - 20 = 180; 180 - 18 = 162; 162 - 16 = 146; 146 - 14 = 132. The next subtraction should be 12. Therefore, 132 - 12 = 120.

The total weight of the 5 empty boxes is 5 * 3 = 15 kilos. The weight of the soaps alone is the gross total minus the boxes' weight: 75 - 15 = 60 kilos.

This is a geometric sequence dividing by 2 each time (r = 1/2). The formula for the nth term is a * r^(n-1). For the 10th term: 64 * (1/2)⁹ = 64 / 512 = 1/8.