NSMQ2025 Trier Contests: Past Questions and Answers (fundamental, Speed Race, and True/False): SET 04.

PREAMBLE: Find the least and the greatest value of the given quadratic function on the given interval.

1. () = ² − 6 + 10 on the interval 0 ≤ ≤ 4

ANS: L=1 and G=10

2. () = ² + 2 − 5 on the interval −3 ≤ ≤ 1

ANS: L=-6 and G=-2

3. () = ² − 10 + 21 on the interval 4 ≤ ≤ 8

ANS: L=-4 and G=5

PREAMBLE: There are several types of antennae in insects, depending on the insect order. Provide the kind of antennae with the given description

4. Antennae with uniform width, e.g., possessed by cockroaches and grasshoppers

ANS: Filiform

5. Antennae like strings of beads, e.g., possessed by termites

ANS: Moniliform

6. An antenna that increases in diameter distally, e.g., possessed by butterflies

ANS: Clubbed

PREAMBLE: A copper wire of length L and cross-sectional area is heated from ₁ to ₂. If the coefficient of linear thermal expansion for copper is 1.60 × 10^-5 ℃ and the Young’s modulus is , calculate the reaction force if the wire is constrained from expanding, given the values of , , ₁, ₂, and .

7. L = 4.00m, A = 5.60mm², ₁ = 25.0℃, ₂ = 75.0℃ and = 120GPa

ANS: 538N

8. L = 3.00m, A = 9.20mm², θ₁ = 30.0℃, θ₂ = 40.0℃ and = 108GPa

ANS: 159N

9. L = 2.00m, A = 7.20mm², θ₁ = 20.0℃, θ₂ = 80.0℃ and = 110GPa

ANS: 760N

PREAMBLE: Find the rate of increase of the volume of a cylinder in terms of if the total surface area is increasing at the rate of 4² / when the height ℎ and radius are as given;

10. ℎ = 12 cm and = 10 cm

ANS: 15 cm³/s

11. ℎ = 24 cm and = 6 cm

ANS: 16 cm³/s

12. ℎ = 30 cm and = 10 cm

ANS: 24 cm³/s

PREAMBLE: Provide a contrast between the parasympathetic and sympathetic nervous systems with respect to the following

13. Heartbeat

Ans: The sympathetic nervous system accelerates the heartbeat, whereas the parasympathetic nervous system reduces the heartbeat

14. Urinary bladder

Ans: The sympathetic nervous system relaxes urinary bladder, whereas the parasympathetic nervous system contracts the urinary bladder

15. Salivary and digestive glands

Ans: The sympathetic nervous system inhibits the secretions from the salivary and digestive glands, whereas the parasympathetic nervous system stimulates their secretions.

16. A prescription for a corrective lens calls for +1.50 D. The lens maker grinds the lens from a “blank” with a refractive index of 1.56 and a preformed convex front surface of radius of curvature 40.0 cm. What should be the radius of curvature of the other surface?

Ans: 5.60 m

17. Both surfaces of a double convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens material?

Ans: −1.54

18. A Lucite planoconcave lens has a refractive index of 1.50. If the radius of curvature for the concave surface is −18.4 cm, what is the focal length of the lens?

Ans: 36.8 cm

PREAMBLE:  Xylem development occurs in four ways; provide the type of development with the given description.

19. Protoxylem lies towards the inside and metaxylem towards the periphery.

ANS: Endarch

20. The protoxylem is located towards the center and surrounded by metaxylem.

ANS: Mesarch

21. Protoxylem is found in the central core, and the metaxylem forms a cylinder around it.

ANS: Centrarch

SPEEDRACE

PREAMBLE: Determine the resultant force on a test charge placed midway between the other charges 1 and 2 whose distance of separation is , given the values of , ₁, _2, and .

22. = 14.00 μC, ₁ = 12.00 μC,   ₂  = 20.00 μC,     and = 2.000 m

ANS: 1.008 N

23. = 16.00 nC, ₂  = 12.00 nC,     ₁  = 6.000 nC,     and = 1.000 mm

ANS: 3.456 N

24. = 24.00 μC, q₁  = 12.00 μC,     q₂  = 8.000 μC,     and = 2.000 m

ANS: 0.8640 N

PREAMBLE: State the effect of each of the following solutions on litmus paper.

25. Na₂SO₄

ANS: No effect on blue and red litmus paper

26. K₂CO₃

ANS: Turns red litmus paper blue

27. NaNO₃

ANS: No effect on blue and red litmus paper

28. Find the number of proper subsets of the set = {1, 2, 3, 4, 5}

ANS: 31

29. A rhombus with a side of length 25. If the length of one diagonal is 48 . Find the length of the other diagonal.

ANS: 14

30. Given the vectors = 8 − 11 and = −4 − 6. Find the length of the vector −

ANS: 13

31. What name is given to the study of energy flow and the cycling of chemicals among the various biotic and abiotic components in an ecosystem

ANS: Ecosystem ecology

32. 4% of the population is born with severe sickle cell anaemia. What percentage of the population would be resistant to the Plasmodium parasite?

ANS: 32%

33. What name is given to the excretory organ of Arachnids?

ANS: Coxal gland

34. Find the sum of the atoms in the molecular formula of the hydrocarbon with 85.7% carbon and 14.3% hydrogen by mass, given that its molecular mass is 112 gmol^-1.

ANS: 24

35. Aluminium hydroxide dissociates as Al(OH)₃ ⇋ Al³⁺ +    If _sp    = 2.70 × 10^-11, calculate the pH of the saturated solution.

ANS: 11.5

36. A lab technician needs to prepare 500 ml of a 2% m/v NaCl solution from 100 ml of a 10% m/v stock solution. How much water should be added?

ANS: 400 ml

37. An object starts from rest and moves with uniform acceleration. Find the ratio of the distance travelled in the 5^th second to the distance in the 3rd second.

ANS: 9 ∶ 5

38. A five-pulley block and tackle system has an efficiency of 80.0%. Find the effort required to raise a load of 100 N.

ANS: 25.0 N

39. A torque of 120 Nm turns a coil of cross-sectional area 1.0 m carrying a current of 15 A placed in a radial magnetic field of flux density 0.50 T. What is the number of turns of the coil?

ANS: 16 turns

TRUE/FALSE

1. The determinant of a diagonal matrix is equal to the product of its diagonal entries.

ANS: true

2. The determinant of a matrix remains unchanged when any two rows are swapped.

ANS: false

3. The determinant of a sum of two matrices is the sum of their determinants.

ANS: false

4. If two vectors are parallel, then one is the scalar multiple of the other.

ANS: True.

5. If two vectors and are parallel, then ⋅ = ||||.

ANS: False

6. If two vectors and are parallel and in opposite directions, then ⋅ = −||||.

ANS: True

7. A carrier of a trait does not express the allele for that trait.

ANS: True

8. A test cross can be used to show all possible outcomes of genetic crosses.

ANS: True

9. In Mendel’s experiment, the F1 was always homozygous for the studied trait.

ANS: False

10. Collenchyma cells are specialized.

ANS: True

11. The cell wall of sclerenchyma cells is made up of cellulose and pectin.

ANS: False

12. Collenchyma cells are tightly packed with no air spaces.

ANS: False

Preamble: The probability (per unit time interval) that a photon will be detected in any small volume centered on a given point in a light wave is proportional to the

13. Amplitude of the wave’s electric field vector at that point.

ANS: False

14. The square root of the amplitude of the wave’s electric field vector at that point.

ANS: False

15. Square of the amplitude of the wave’s electric field vector at that point.

ANS: True

Preamble: While boiling an egg in boiling water on a gas burner,

16. Turning up the flame cooks the egg faster.

Ans: False

17. It will take longer to cook the egg on a hill than at sea level.

Ans: True

18. It will take a mountaineer a shorter time to cook the egg in a pressure cooker.

Ans: True

19. The addition of alkaline KMnO₄ to substances containing alkynes results in a colourless solution.

ANS: False

20. Ammoniacal silver (I) trioxonitrate (V) can be used to test for the presence of alkenes in substances.

ANS: False

21. The iodoform test can be used to test for the presence of methyl ketones in substances.

ANS: True

22. The flame coloration of magnesium salt is golden yellow.

ANS: False

23. The flame coloration of lithium salt is scarlet red.

ANS: True

24. The flame coloration of copper salt is blue-green.

ANS: True

SOURCE: GALMEEK.COM

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