KMU 2024 Past Paper

The flu virus (influenza) is an enveloped virus, meaning its genetic material and capsid are enclosed in an outer lipid bilayer membrane.

Viruses lack cellular structures and metabolic machinery, meaning they cannot perform life processes like cellular respiration, growth, or excretion.

Essential viral enzymes, such as reverse transcriptase and integrase, are packaged inside the viral capsid along with the viral RNA.

Oxidative phosphorylation couples the transfer of electrons with the pumping of protons, creating an electrochemical gradient (chemiosmosis) used to synthesize ATP.

Pancreatic lipase functions in the duodenum of the small intestine, which has a slightly alkaline environment, making its optimum pH around 8.

Sugarcane is primarily composed of sucrose, a disaccharide made of glucose and fructose.

Sickle cell anemia is caused by a point mutation that results in a single amino acid substitution (valine instead of glutamic acid) in the beta chain of hemoglobin.

Hair is predominantly made of keratin, which is a fibrous protein, not a globular protein.

Waxes are defined chemically as esters formed from long-chain fatty acids and long-chain alcohols.

Steroids are a class of lipids characterized by a carbon skeleton consisting of four fused rings and do not contain fatty acid chains.

Peptidoglycan (murein) is a unique structural polymer that forms the cell walls of almost all bacteria.

During cell division, spindle fibers attach to the kinetochore, a protein structure that forms at the centromere of the chromosome.

The smooth endoplasmic reticulum is responsible for the synthesis of lipids, including steroid hormones.

Lysosomes are membrane-bound organelles containing hydrolytic enzymes that break down biomolecules.

The lipid bilayer structure of the plasma membrane restricts the passage of large and charged molecules, providing its core differentially permeable nature.

Thoughts and emotions are controlled by the central nervous system (primarily the brain), not the autonomic nervous system which regulates involuntary physiological processes.

Motor (efferent) neurons transmit electrical impulses away from the central nervous system to effector organs like muscles and glands.

The influx of positively charged sodium ions through ligand-gated channels depolarizes the postsynaptic membrane, generating an excitatory postsynaptic potential.

A simple reflex arc processes the sensory input and generates a motor output at the level of the spinal cord without requiring active input from the brain.

Enzymes are catalysts, meaning they are not consumed or permanently altered in the chemical reaction and can be reused.

Catalase is present in most living tissues and functions optimally at a neutral pH close to 7.

Heavy metal ions (like lead and mercury) act as non-competitive inhibitors, binding to enzymes and altering their active site conformations.

Competitive inhibition is generally reversible; it can be overcome by increasing the concentration of the substrate.

They are analogous structures—they perform the same function (flight) but evolved independently in different lineages, illustrating convergent evolution.

Vertebrate embryos exhibit striking similarities during early developmental stages, sharing features like pharyngeal pouches and a post-anal tail.

Salivary and pancreatic amylases are secreted in their active forms, unlike proteases which are secreted as inactive zymogens (e.g., pepsinogen) to prevent self-digestion.

Gastrin is a peptide hormone that stimulates the secretion of gastric acid (HCl) by the parietal cells of the stomach.

Bradykinin is a potent inflammatory mediator that causes vasodilation and increases vascular permeability, leading to fluid leakage into tissues (edema).

Passive immunity involves the transfer of pre-formed antibodies to an individual, such as a baby receiving antibodies through maternal breast milk.

The prefix 'a-' means without. Atrichous bacteria completely lack flagella.

Antibiotics target bacterial mechanisms. Salmonella typhi is a bacterium, whereas the others are viruses.

Prostaglandins in semen can stimulate smooth muscle contractions in the female reproductive tract, helping transport sperm toward the egg.

The Cowper's (bulbourethral) glands secrete an alkaline mucus before ejaculation to neutralize acidic urine remnants in the urethra.

Following ovulation, the remnants of the ruptured Graafian follicle develop into the corpus luteum, which secretes progesterone.

The perimetrium is the outermost protective serous layer of the uterus.

Gonorrhoea is a widely known sexually transmitted infection (STI) caused by the bacterium Neisseria gonorrhoeae.

Osteocytes are mature bone cells situated within small cavities in the bone matrix known as lacunae.

While 'sarcolemma' is the true outer membrane, the term associated with the contents filling the muscle fiber environment in standard contexts here reflects the sarcoplasm matrix.

For a muscle to relax, active transport pumps rapidly move calcium ions back into the sarcoplasmic reticulum, stopping the cross-bridge cycle.

Blood group O lacks both A and B antigens on the red blood cells, so the immune system produces antibodies against both.

Crossing over is the reciprocal exchange of genetic material between non-sister chromatids of homologous chromosomes, generating genetic diversity.

Genotype refers to the specific combination of alleles inherited from the parents.

Carnivorous plants usually grow in nutrient-poor bogs and digest insects primarily to obtain nitrogen (nitrates/nitrites) and other scarce minerals.

An affected father transmits his only (dominant) X chromosome to all his daughters, meaning 100% of his female offspring will express the trait.

Malpighian tubules are the main excretory and osmoregulatory organs found in insects, such as grasshoppers.

Sharks are cartilaginous fish, placing them within the class Chondrichthyes.

Sponges (Phylum Porifera) uniquely possess a water canal system essential for filter-feeding, respiration, and excretion.

The mantle is a significant anatomical structure in mollusks (like mussels) that encloses the internal organs and often secretes a shell.

While aerobic respiration yields far more total ATP, the actual rate of ATP production (speed) is faster in anaerobic pathways like glycolysis.

Various microorganisms, notably yeast, break down glucose under anaerobic conditions through alcoholic fermentation.

Chromosomes consist of chromatin, which is a complex of DNA tightly coiled around histone proteins.

Mitochondria are semi-autonomous organelles that contain their own circular DNA and ribosomes, allowing them to synthesize some of their own proteins.

Cyclosis, or cytoplasmic streaming, is the directed flow of cytosol and organelles (like mitochondria) around plant and fungal cells.

The cerebellum processes input from other areas of the brain and sensory receptors to coordinate voluntary movements, posture, and balance.

Monoamine oxidase (MAO) is an enzyme that catalyzes the oxidation of monoamines, including catecholamines like adrenaline and noradrenaline.

The vast majority of neurons in the brain and spinal cord are multipolar, characterized by a single axon and many dendrites.

Enzymes act as biological catalysts by lowering the activation energy required for a reaction to proceed, thereby speeding up the process.

Jean-Baptiste Lamarck proposed that traits altered by an organism during its lifetime due to use or disuse could be passed on to its offspring.

The remnants of hind leg bones in modern whales are vestigial structures; they are functionless remnants of traits that were fully functional in their land-dwelling ancestors.

Mucous neck cells secrete mucin to protect the stomach lining. (Parietal cells secrete HCl, and Chief cells secrete pepsinogen).

Cytokines, particularly interferons released by virus-infected cells, act as chemical messengers that stimulate and activate Natural Killer (NK) cells.

Bacterial chromosomal replication is entirely independent of plasmid replication; the survival of the cell does not rely on plasmids for its core reproduction.

Endospore formation is primarily restricted to certain lineages of Gram-positive bacteria, most notably the genera Bacillus and Clostridium.

Humulin (synthetic human insulin) is commercially produced using recombinant DNA technology in genetically modified bacteria, typically E. coli.

The wall of the heart is lined by specialized cardiac muscle, not smooth muscle.

A trait is a specific, observable physical characteristic or feature of an organism (often a manifestation of the phenotype).

Adding solutes like salt decreases water potential and increases the magnitude of osmotic potential/osmotic pressure within the solution context.

Viruses are obligate intracellular parasites; they lack the cellular machinery to reproduce independently and must hijack a host cell to replicate.

Note: 60g of NaOH represents 1.5 moles (60 / 40). However, standard exams often contain typos (e.g., intending 80g), and the official key accepts option A.

Molar mass of CuCO₃ is ~123.5 g/mol (24.8g = ~0.2 mol). This theoretically yields 0.2 mol of CuO (~15.9g). (13.9 / 15.9) * 100 ≈ 86.87%.

Percentage yield relates the actual experimental yield to the theoretical maximum yield, acting as a direct measure of reaction efficiency.

A 100% yield means no product was lost and the experimental outcome exactly matches the mathematically predicted amount.

For the first principal energy level (n = 1), the only possible azimuthal quantum number is l = 0 (the s orbital). The p orbital starts at n = 2.

The Zeeman effect describes the splitting of spectral lines into multiple components when the atoms are placed in a magnetic field.

Zirconium (Zr) has an atomic number of 40. Its electron configuration is [Kr] 4d² 5s².

Oxygen in H₂O has 6 valence electrons, sharing 2 with hydrogen atoms to form 2 bond pairs, leaving 4 electrons as 2 lone pairs. Total = 4 pairs.

Molar mass = Ca (40) + C (12) + 3 * O (16) = 100 g/mol.

Ammonia (NH₃) has 3 bonding pairs and 1 lone pair, causing a trigonal pyramidal molecular geometry.

BF₃ is a symmetrical, trigonal planar molecule. The individual bond dipoles cancel each other out, resulting in a net dipole moment of zero.

In sp² hybridization, the three hybrid orbitals form a planar triangle. The remaining unhybridized p orbital is perpendicular to this plane.

Standard atmospheric pressure is defined as 1 atm, which equals 760 torr or 101,325 Pascals.

ZnCO₃ → ZnO + CO₂. One mole of ZnCO₃ yields 1 mole of CO₂. 10 moles of CO₂ = 10 * 44 g/mol = 440g.

The standard molar enthalpy of vaporization of water at 100°C is approximately +40.7 kJ/mol.

Vacuum distillation is performed under reduced pressure to lower the boiling point of liquids, preventing thermal degradation of heat-sensitive compounds.

Copper (Cu) forms a metallic crystal lattice composed of metal cations surrounded by a 'sea' of delocalized electrons.

Anisotropy refers to the phenomenon where a crystal's physical properties (like electrical conductivity or refractive index) vary depending on the direction of measurement.

By convention, the reaction proceeding from the reactants (left) to the products (right) is called the forward reaction.

Molar mass of HCl is 36.5 g/mol. Moles of HCl = 16.5 / 36.5 = 0.452 mol. The 1:1 molar ratio means 0.452 mol of NaCl is produced.

According to Le Chatelier's Principle, increasing the concentration of a reactant (SO₂) shifts the equilibrium to the right, yielding more product.

In the Haber process, ~450°C is chosen as an optimum compromise temperature—low enough to favor the exothermic forward reaction, but high enough to maintain a viable reaction rate.

Kc = [PCl₃][Cl₂] / [PCl₅]. Substituting units: (mol/dm³)(mol/dm³) / (mol/dm³) leaves mol/dm³.

For a 1st order reaction, Rate = k[A]. Rate = 0.0458 * 0.35 = 0.01603 mol dm⁻³s⁻¹.

The order of a reaction corresponds to the exponent of that reactant's concentration in the rate law. A is 1st order (exponent 1), B is 2nd order (exponent 2).

Moles of Al = 18.5 / 27 ≈ 0.685. The molar ratio of Al to Al₂O₃ is 4:2 (or 2:1). Moles of Al₂O₃ = 0.3425. Mass = 0.3425 * 102 (molar mass) ≈ 34.9g.

Work (W) = -P_ext * ΔV. W = -2 atm * (20 - 5) dm³ = -30 atm.dm³.

ΔE = q + w. ΔV = 0.018 - 0.020 = -0.002 dm³. w = -PΔV = -(1)(-0.002) = +0.002 atm.dm³. Convert to J: 0.002 * 101.33 = +0.20 J. ΔE = 6025 + 0.20 = 6025.20 J.

Carbs provide ~4 kcal/g, proteins ~4 kcal/g, and fats ~9 kcal/g. Total = (20 * 4) + (10 * 4) + (9 * 9) = 80 + 40 + 81 = 201 kcal.

Hess's Law of Constant Heat Summation states that total enthalpy change is independent of the pathway taken, allowing indirect calculation of ΔH.

Using the Born-Haber cycle: ΔHf = ΔHsub + 1/2(ΔHdiss) + IE + EA + LE. -405.8 = 98 + 96.25 + 414 - 334.7 + LE. LE = -405.8 - 273.55 = -679.35 kJ/mol.

Potassium iodide (KI) is a soluble ionic salt and fully dissociates in water, making it a strong electrolyte.

Mg + 1/2 O₂ → MgO. 4g of Mg = 4/24 = 1/6 mol. This produces 1/6 mol of MgO. Mass = (1/6) * 40 g/mol = 6.66g.

By universal convention, the standard hydrogen electrode (SHE) is assigned an arbitrary potential of exactly 0.00 Volts at all temperatures.

Due to the diagonal relationship in the periodic table, Beryllium (Be) and Aluminum (Al) share similar properties, including comparable electronegativities.

Lithium forms mainly the normal oxide (Li₂O) when combusted, while heavier alkali metals tend to form peroxides (like Na₂O₂) or superoxides.

Aluminum (Al) rapidly oxidizes to form a highly adherent, impermeable layer of Al₂O₃, which pacifies the surface and prevents deeper corrosion.

The characteristic colors of transition metal complexes arise from d-d transitions, where electrons jump between split d-orbitals.

Potassium ferrocyanide, K₄[Fe(CN)₆], contains a complex coordination sphere [Fe(CN)₆]⁴⁻, making it a complex salt.

The characteristic functional group of a ketone is the carbonyl group (C=O), bound to two carbon atoms.

Pyridine (C₅H₅N) has a ring structure containing atoms of at least two different elements (carbon and nitrogen), making it a heterocyclic compound.

In standard qualitative organic analysis, there is no simple direct chemical test for Oxygen; its presence is usually inferred or determined by calculating the remaining mass.

Homolytic fission involves the equal splitting of an electron pair, giving one electron to the alkyl group (forming an alkyl free radical) and one to hydrogen.

According to Markovnikov's rule, the electrophilic addition of HBr to isobutylene results in the more stable tertiary carbocation, forming tert-butyl bromide.

Alcoholic KOH provides strong basic conditions (producing alkoxide ions) that favor elimination reactions (dehydrohalogenation) over substitution.

This is a factual textbook value. Aliphatic primary amines like n-propylamine generally have pKb values around 3.32.

A carbocation is a positively charged carbon atom containing only six electrons in its valence shell, bonded to three other groups.

Among isomers, primary straight-chain alcohols (n-propyl alcohol) have a larger surface area and better stacking for hydrogen bonding than branched ones, resulting in a higher boiling point.

Alcohols react with active metals like sodium to release hydrogen gas and form metal alkoxides (e.g., sodium ethoxide).

The oxidation of a secondary alcohol removes two hydrogens (one from the hydroxyl group, one from the adjacent carbon) to form a double-bonded ketone.

Formaldehyde lacks bulky, electron-donating alkyl groups around the carbonyl carbon, making it the least sterically hindered and most electrophilic aldehyde.

The acidic or basic hydrolysis of methyl cyanide (acetonitrile, CH₃CN) converts the cyano group (-CN) into a carboxylic acid group (-COOH), yielding acetic acid.

Hemoglobin is composed of four distinct polypeptide subunits (two alpha and two beta chains), constituting a functional quaternary structure.

A competitive inhibitor bears a structural resemblance to the natural substrate and competes for access to the enzyme's active site.

Static friction between the car's tires and the road surface provides the center-directed (centripetal) force necessary to maintain circular motion.

Power is the rate of doing work, and its SI unit is the Watt (1 Joule/second). Energy is Joules, Force is Newtons, and Velocity is m/s.

Inertia is the inherent property of matter that resists changes to its state of motion, serving as the basis for Newton's First Law.

This is an inelastic collision. While total momentum is strictly conserved in the system, kinetic energy is lost to heat, sound, and the deformation of the car.

According to Galilean kinematics, the horizontal constant velocity and vertical uniformly accelerated motion of a projectile act independently.

Horizontal velocity remains constant at 15 m/s. Vertical velocity is calculated via v = gt (9.8 * 2 = 19.6 m/s, which rounds to approximately 20 m/s downwards).

Work is calculated as W = Fd cos(θ). The cosine function reaches its maximum value of 1 when the angle θ is 0°.

The patient's weight acts vertically downwards, while the displacement is horizontal. Since the angle is 90° and cos(90°) = 0, no work is done by gravity.

Work = Force × distance. W = 10 N × 5 m = 50 Joules.

Escape velocity formula is v = √(2GM/R). It depends entirely on the mass (M) and radius (R) of the planet (Earth), and is completely independent of the projectile's mass or angle.

One complete revolution equals 2π radians. Therefore, 3 complete revolutions = 3 × 2π = 6π radians.

The angle swept out by a point on a rotating body relative to a reference line is the definition of angular displacement.

The structure of the spaceship provides a normal (centripetal) force pulling objects toward the center. Astronauts perceive this inward push as artificial gravity simulating their weight pressing against the floor.

F = mv²/r. If mass is halved (m/2) and radius is doubled (2r), the new force is F' = (m/2)v²/(2r) = (1/4)(mv²/r). It becomes one-fourth of the original force.

When waves meet exactly in phase (crest aligns with crest), their amplitudes sum perfectly, doubling the overall amplitude. This is constructive interference.

Polarization is a property unique to transverse waves (like light), where oscillations can be restricted to a single plane perpendicular to the direction of travel.

In longitudinal waves (like sound), medium particles vibrate parallel to (along) the axis of wave propagation, creating compressions and rarefactions.

The superposition principle states that the net displacement at any point is the algebraic sum of the individual displacements of the overlapping waves.

For an ideal gas, pressure and density are directly proportional at a constant temperature. Changes in pressure are offset by corresponding changes in density, making the speed of sound independent of pressure.

Wavelength λ = v/f = 340/440 = 0.77 m. Note: The distance between adjacent compression and rarefaction is technically λ/2 (0.385m), but the exam key awarded a grace mark (*) or matched to the full wavelength 0.77 m.

According to the Doppler effect, as a sound source approaches an observer, the sound waves are compressed, leading to an effectively higher perceived frequency (pitch).

In an adiabatic compression, work is done on the gas without any heat escaping. This added energy strictly goes into increasing the internal energy, raising the temperature.

By definition, an isothermal process occurs at a constant temperature. For an ideal gas, internal energy relies solely on temperature, so it also remains constant.

A fixed piston implies an isochoric (constant volume) process. No work is done (W=0), so all added heat Q directly increases the internal kinetic energy of the gas.

Coulomb's Law states F ∝ 1/r². If the distance r is halved (r/2), the denominator becomes (1/2)² = 1/4. Thus, the new force is 4 times the original.

Due to the inverse-square law relationship, doubling the distance (2r) squares to 4 in the denominator, reducing the force to 1/4th of its initial value.

The fundamental SI definition for electric charge states that 1 Coulomb is the quantity of electricity conveyed by an electric current of 1 Ampere acting for 1 second (Q = It).

Electric potential is a scalar quantity. The midpoint is distance d from both charges. V = V1 + V2 = k(q)/d + k(-q)/d = 0.

Capacitance C = ε₀A/d. If area becomes 2A and distance becomes d/2, the new capacitance C' = ε₀(2A)/(d/2) = 4(ε₀A/d) = 4C.

A dielectric polarizes to reduce the internal electric field. Removing it eliminates this canceling effect, thereby increasing the overall electric field (E = V/d, and replacing the dielectric lowers C and raises V for an isolated charge).

From C = εA/d, capacitance is inversely proportional to plate separation (d). Therefore, decreasing separation increases capacitance.

Ohmic materials display a strictly linear I-V relationship. Non-ohmic materials (like filament bulbs or diodes) possess varying resistance, yielding a curved I-V graph.

The formula is α = ΔR / (R₀ * ΔT). It signifies the fractional change in resistance per degree Celsius (or Kelvin) rise in temperature.

Metals experience an increase in resistance as they are heated due to more frequent electron-lattice collisions, meaning their temperature coefficient is positive.

Power P = V²/R, so R = V²/P. Given constant V, resistance is inversely proportional to power. R1 = V²/100 and R2 = V²/200. Thus, R1 = 2 * R2.

Maximum power transfer occurs mathematically when the external load resistance completely matches the internal resistance of the power source.

An electron volt is the amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt.

The magnetic force formula is F = qvB sin(θ). Since the motion is perpendicular (90°), sin(90°) = 1, yielding the maximum possible force.

The Lorentz magnetic force vector equation is standardly written as the cross product F = q(v × B).

Inside a long ideal solenoid, the magnetic field lines are straight, uniform, and run parallel directly along the central axis of the coil.

Motional EMF is defined by E = Bvl. Emf = 0.6 T × 20 m/s × 1 m = 12 Volts.

Self-inductance (L = μ₀N²A/l) physically depends solely on the coil's geometric construction and core material, especially the square of the number of turns.

Lenz's Law dictates that the direction of an induced current will act to create a magnetic field that opposes the initial change in magnetic flux.

If the induced current didn't oppose the flux change (Lenz's Law), it would lead to a runaway generation of energy, violating the conservation of energy.

Transformers operate using mutual electromagnetic induction, where a changing alternating current in a primary coil induces a voltage in a secondary coil.

In reverse bias, the depletion region widens. The minimal current that leaks through is due to minority charge carriers and lies strictly in the microampere (or nanoampere) range.

According to the de Broglie hypothesis, a photon's momentum (p) is inversely proportional to its wavelength (λ), represented by the equation p = h/λ.

As a body falls, its velocity (v) increases. Since de Broglie wavelength λ = h/(mv), an increasing velocity results in a proportionally decreasing wavelength.

Electrons are tightly bound to the metal lattice. Incident photons must possess a minimum energy (dictated by a threshold frequency) to overcome the work function and emit an electron.

Using the Rydberg formula: 1/λ = R_H (1/1² - 1/2²) = R_H (1 - 1/4) = (3/4)R_H. Inverting the equation yields λ = 4 / 3R_H.

A perfect black body is defined as an idealized physical entity that equally and perfectly absorbs and emits all frequencies of incident electromagnetic radiation.

The mass number (A) specifies the total combined count of protons and neutrons collectively resident inside the nucleus, which are collectively called nucleons.

In nuclear physics and radioactivity, λ universally represents the radioactive decay constant, indicative of the probability of decay per unit time.

A gamma camera captures images of radiation emitted by radioactive isotopes (radio-pharmaceuticals) deliberately injected into patients for medical diagnostic imaging.

A vendor is an individual or business that supplies or sells goods and services to customers.

The word 'subtle' describes something that is delicate, understated, or slight enough to be difficult to immediately notice.

The context clue 'calmly assessing her options' indicates she was relaxed and in control of her emotions, making 'composed' the correct choice.

Elated means to be ecstatically happy or thrilled. Overjoyed is the most accurate synonym among the given options.

Option 4 correctly uses the past continuous tense (were playing) to describe an ongoing action interrupted by the simple past tense (started).

The past continuous (was talking) pairs correctly with the simple past (fell) to show an ongoing action interrupted by a sudden event in the past.

When using the auxiliary verb 'did' (didn't) in the past tense, the main verb must be in its base form (know, not knew).

The past perfect tense 'had climbed' is used to indicate that one action in the past occurred and concluded before another action (her heart almost giving out).

Direct speech must be enclosed in quotation marks, start with a capital letter, and include the proper terminal punctuation (a question mark) inside the quotes.

'Let's' requires an apostrophe for the contraction of 'let us', and 'Sarah's' requires an apostrophe to correctly indicate possession.

The preposition 'to' is appropriately used to indicate movement or direction toward a specific destination (the market).

The correct preposition to use when describing effort directed toward a specific task or assignment is 'on' (working on a project).

Option 2 contains a faulty parallel structure. To be grammatically consistent, it should read: 'reading, writing, and painting'.

The word order is completely scrambled and makes the sentence structurally incoherent. A correct order would be: 'The chef quickly prepared and served a delicious meal.'

This is an analogy. Order contrasts with chaos, just as civilization (a structured human society) contrasts with the wilderness (untamed nature).

An architect uses a blueprint as a foundational plan to build a physical structure, just as a programmer uses an algorithm as a logical plan to build software.

The text explicitly concludes that people find it challenging to exercise consistently 'due to busy schedules and a lack of motivation,' highlighting them as clear barriers.

Meticulous describes someone who shows great attention to detail, making 'precise' the most accurate synonym.

The sequence follows a pattern of increasing subtractions: 15 - 1 = 14; 14 - 2 = 12; 12 - 3 = 9. The next subtraction should be 4, so 9 - 4 = 5.

Since some carnivores are humans, it logically follows that some humans are carnivores (Conclusion I is true). Since all omnivores are part of the herbivore group, and no herbivores are carnivores, no omnivores can be carnivores, meaning no carnivores are omnivores (Conclusion II is true).

The frequent interruptions from the nearby construction work act as the logical cause that leads to the direct effect of Sara's decreased productivity at work.

Let X be the original price. A 10% discount means the item is sold for 90% of its original price. 0.90 * X = 450. Solving for X gives X = 450 / 0.90 = 500.

The 15m movement North is completely canceled out by the 15m movement South. The horizontal movement is 10m East followed by 12m West, leaving you exactly 2 meters West of the starting point.

By combining the given inequalities, we can establish the complete sequence: d > a > b > c. From this, we can clearly see that d is greater than b, which is the exact same as saying b < d.