NSMQ2025 Trier Contests: Past Questions and Answers (fundamental and True/False): SET 07.

PREAMBLE: The resistivity of a lead alloy is 2.5 x 10^-7 Ωm.

1. Find the resistance of an alloy strip of length 0.30 m and cross-sectional area of 0.42 cm²

Ans: 1.8 x 10^-3 Ω

2. If the resistance of a piece of the alloy of length 0.12 m is 9.5 x 10 ^-3 Ω, find the cross-sectional area of the alloy.

Ans: 3.2 x 10-6 m²

3. The lead alloy of cross-sectional area of 8.0 x 10^-6 m² was found to have a resistance of 1.5 x 10^-3 Ω. Find the length of the alloy

Ans: 0.048 m or 4.8 x 10^-2 m

PREAMBLE: A 345g object attached to the end of a spring oscillates with an amplitude of 5.00 cm. Find the angular frequency given the following frequencies. (do not accept answers in π)

4. 50 Hz

Ans: 15.7 rad/s

5. 20 Hz

Ans: 26.4 rad/s

6. .80 Hz

Ans: 11.3 rad/s

PREAMBLE: Differentiate the following trigonometric functions:

7. y = cos (5x – 2)

Ans: -5sin (5x – 2)

8. y = tan (4x + 1)

Ans: 4sec 2 (4x + 1)

9. y = sin (2x + 3)

Ans: 2cos (2x + 3)

PREAMBLE: In the extraction of iron, hematite (Fe₂O₃) is reduced by carbon monoxide in a blast furnace to produce iron metal and carbon dioxide. Take Fe = 56.0, O = 16.0, C = 12.0

10. What mass of iron could be obtained from 80.0 g of Fe₂O₃?

Ans: 56.0 g

11. What mass of CO₂ is produced from 320.0 g of Fe₂O₃?

Ans: 264 g

12. If 448 g of Fe is produced, what mass in kg of Fe₂O₃ was used?

Ans: 0.640 kg

PREAMBLE: A student has a mixture containing sand (SiO₂), iron filings, salt (NaCl), and water. The following separation techniques are available: Filtration, Distillation, Magnetic separation, Evaporation, and Crystallization. (Award partial scores where required)

13. Which technique should be used first in the separation of the mixture, and why?

Ans: Magnetic separation, because iron is magnetic and can be easily removed without chemicals or phase change.

14. After filtration, why would crystallization be preferred over simple evaporation to recover the salt?

Ans: It is preferred over simple evaporation because it produces pure, well-formed crystals and prevents decomposition or overheating of the salt.

15. Why would distillation not be the most efficient method to separate salt from the salt solution in this process?

Ans: It is energy-intensive and time-consuming compared to evaporation or crystallization for solid salt recovery. (The goal is to obtain solid salt, not pure water, so simpler methods are preferred.)

PREAMBLE:  Glycolysis is the metabolic pathway that converts glucose into pyruvate, generating ATP and NADH. It consists of 10 enzyme-catalyzed steps. Name any 1 of the enzymes and state the reaction that it catalyzes. (NB: enzyme name is 1 pt; reaction it catalyzes is 2 pts) (Award partial scores where appropriate)

16. Answers:

• Hexokinase: Glucose → Glucose-6-phosphate
• Phosphoglucose Isomerase: Glucose-6-phosphate → Fructose-6-phosphate
• Phosphofructokinase-1 (PFK-1): Fructose-6-phosphate → Fructose-1,6-bisphosphate
• Aldolase: Fructose-1,6-bisphosphate → Dihydroxyacetone phosphate (DHAP) + Glyceraldehyde-3-phosphate (G3P)
• Triose Phosphate Isomerase (TPI): DHAP ↔ Glyceraldehyde-3-phosphate (G3P)
• Glyceraldehyde-3-phosphate Dehydrogenase (GAPDH): G3P → 1,3- Bisphosphoglycerate
• Phosphoglycerate Kinase: 1,3-Bisphosphoglycerate → 3-Phosphoglycerate
• Phosphoglycerate Mutase: 3-Phosphoglycerate → 2-Phosphoglycerate
• Enolase: 2-Phosphoglycerate → Phosphoenolpyruvate (PEP)
• Pyruvate Kinase: Phosphoenolpyruvate → Pyruvate

PREAMBLE: Protists are a diverse group of eukaryotic microorganisms, and they primarily reproduce asexually, especially under favourable environmental conditions. State one of the types of asexual reproduction in protists:

17. Answers:

• Binary fission
• Budding
• Multiple fission
• Sporulation or spore formation

TRUE/FALSE

18. In spherical geometry on a globe, the sum of the interior angles of a triangle is always 180°.

Ans: False.              In non-Euclidean geometry, the sum exceeds 180°.

19. The measure of an exterior angle is always equal to the sum of the measures of the two opposite interior angles.

Ans: True

20. A triangle can have interior angles of 100°, 40°, and 50°.

Ans: False. The sum (190°) is greater than 180

21. Two different species can never occupy the same ecological niche.

Ans: True

22. A niche describes only the physical location where a species lives.

Ans: False. It describes both the habitat and the species’ “profession” or role

23. A generalist species has a broader niche than a specialist species

Ans: True

24. Saponification is the acid-hydrolysis of esters to produce carboxylic acids and alcohols.

Ans: False.  It is specifically based on hydrolysis to produce soap (carboxylate salts) and glycerol.

25. The process requires a strong base like sodium hydroxide (lye).

Ans: True

26. Potassium hydroxide will produce a harder, solid soap compared to sodium hydroxide.

Ans: False.   KOH produces a softer, liquid/paste soap (e.g., liquid castile soap).

27. A linear transformation must always map the origin of the domain to the origin of the codomain.

Ans: True

28. All linear transformations are representable by a matrix.

Ans: True

29. A linear transformation can rotate, stretch, or shear vectors, but it cannot translate them.

Ans: True

30. Unmyelinated axons conduct action potentials faster than myelinated axons of the same diameter.

Ans: False.  Myelination dramatically increases conduction velocity via saltatory conduction.

31. Action potentials in unmyelinated axons propagate continuously along the entire axon length.

Ans: True

32. All axons in the human peripheral nervous system are myelinated.

Ans: False. Many peripheral nerves, especially for pain and temperature, contain unmyelinated C-fibers.

33. A bond between two atoms of the same element is always nonpolar.

Ans: True

34. A molecule with only nonpolar bonds must be a nonpolar molecule.

Ans: False. Consider CO₂; it has polar bonds, but its linear geometry makes it a non-polar molecule.

35. Carbon-Carbon (C-C) bonds are a classic example of a non-polar covalent bond.

Ans: True

36. In a simple gear train, the gear with the most teeth always rotates the fastest.

Ans: False. The gear with the fewest teeth (the pinion) rotates the fastest.

37. A gear system can be used to trade off rotational speed for torque, keeping power constant.

Ans: True

38. The gear ratio is defined as the number of teeth on the output gear divided by the number of teeth on the input gear.

Ans: True

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