NSMQ2025 Trier Contests: Past Questions and Answers (fundamental, Speed Race, and True/False): SET 06.

FUNDAMENTAL

PREAMBLE: Find the equation of the circle

1. In the first quadrant touching both axes and the line y = 10

Ans: ( − )²   + ( − )   =

2. In the third quadrant touching both axes and the line y = -2

Ans: ( + )² + ( + )   =

3. In the second quadrant touching both axes and the line X = -6

Ans: ( + )²   + ( − )   =

4. A particle moves with a velocity of = (5.0 ̂ − 3.0̂ + 6.0̂)/ under the influence of a constant force = (10 ̂ + 10̂ + 20̂) , what is the instantaneous power applied to the particle?

Ans:   140 W or 140J/s

5. An engine exerts a force = (20 ̂ − 3̂ + 5̂) and moves with a velocity = (6.0 ̂ + 20̂ − 3.0)̂/, what is the power of the engine

Ans:   45 W

6. What is the work done by a force = ( ̂ − 2̂ + 3̂) acting on a particle in displacing it from the point ₁ = ( ̂ + ̂ + ) to the point ₂ = ( ̂ − ̂ + 2)

Ans:   7 J

7. A 25.0 cm³ solution of a monoprotic acid HA requires 20.0 cm³ of 0.1 mol/dm³ NaOH for neutralization. Calculate the concentration of the acid and deduce whether it is strong or weak if its pH is found to be 2.0.

Ans:    0.08 mol/dm³ , the acid is weak

8. A 30.0 cm³ sample of a monoprotic acid requires 25.0 cm³ of 0.120 mol·dm⁻³ NaOH for complete neutralization. If the pH of the acid solution is 3.0, calculate the concentration of the acid and state whether it is strong or weak.

Answer: Concentration = 0.10 mol·dm⁻³. The acid is weak (≈1% ionized).

9. A 15.0 cm³ sample of a monoprotic acid solution is titrated with 18.0 cm³ of 0.150 mol·dm⁻³ KOH until complete neutralization. If the measured pH of the original acid solution is 2.0, determine the concentration of the acid and whether it is a strong or weak acid.

Answer: Concentration = 0.18 mol·dm⁻³. The acid is weak (≈8.8%)

PREAMBLE: From a point P outside the circle, a line is drawn to intersect the circle at A and B and a tangent is drawn from P to meet the circle at T. find the length of

10. PT given that |PA|= 12cm and |AB|= 15cm

Ans:     |PT|= 18cm

11. |AB| given that |PT|=20cm and |PA|= 16cm

Ans:     9cm

12. |PT| given that |PB|= 40cm and |AB|= 30cm

Answer:     20cm

13. A 0.5 m long wire carries a current of 5A in a uniform magnetic field of 0.2 T. The force on the wire is 0.5N. What is the angle between the wire and the magnetic field.

Ans; 90֯

14. A proton moves at 5 × 10⁶ m/s perpendicular to a 0.02 T magnetic field. Calculate the radius of its circular path.

Ans: 2.61m

15. A rectangular loop of wire 0.2 m × 0.1 m carrying 2A is placed in a 0.4 T magnetic field, with the plane of the loop perpendicular to the field. Calculate the torque on the loop.

Ans; 0

Preamble: State the most stable product formed when the given alkene reacts with bromine in tetrachloromethane

16. 3-methyl-2-butene

Ans: 2,3-dibromo-2-methylbutane

17. 2-butene

Ans: 2,3-dibromobutane

18. 2,3-dimethyl-2-butene

Ans: 2,3-dibromo-2,3-dimethylbutane

19. Preamble: State one of the defining characteristic of molluscs

Ans:

• Dorsal visceral mass
• Glandular mantle.
• Ventral muscular foot

SPEEDRACE

20. A particle of mass 0.010kg travels with velocity given by (4.0 ̂ + 16̂)/ . After sometime, its velocity becomes (8.0  ̂ + 20̂)/. What is the work done on the particle during this interval of time

Ans:    0.96 J

21. Force constant of a weightless spring is 16 N/m. A body of mass 1.0kg suspended from it is pulled down through 5.0cm from its mean position and then released. What is the maximum kinetic energy of the body?

Ans: ∙ × ^-2 or 0.020 J

22. A light ray passes through a triangular glass prism with an angle of deviation of 30^o and an angle of the prism of 60^o. What is the refractive index of the material used to make the prism?

Ans:   0.5

23. A current of 2.0 A is passed through molten Al₂O₃ for 1.0 hour. Calculate the mass of aluminium deposited. (Al = 27, F = 96500 C/mol)

Ans: 0.67 g

24. When aluminium metal is added to an excess of sodium hydroxide solution, a colourless gas is evolved and a colourless solution is formed. Write balanced ionic equation for the reaction that occurs

Ans:   2Al_(s) + 2OH⁻_(aq) + 6H₂O_(l) → 2[Al (OH)₄] ⁻_(aq) + 3H₂_(g)

25. How is food prevented from entering the airway during swallowing?

Ans: the epiglottis moves down to close the trachea and the uvula (soft palate) moves up to close the entry to the nasal cavity.

26. What are the class of antibiotics on the basis of the effect on bacteria?

Ans: Bacteriostatic and bactericidal drugs.

27. Which two main factors varies with depth in water?

Ans: light intensity and pressure in water.

TRUE/FALSE

PREAMBLE: If A, B and C are three square matrices of the same order, then

28. A² – B² = (A – B)(A + B)

Answer: False

29. (AB)C = A(BC)

Answer: True

30. (AB)² = A²B²

Answer: False

31. In the Bohr model of the hydrogen atom, the angular momentum of the electron is quantized in multiples of ℎ = 2 where h is Planck’s constant.

Ans; FALSE

32. The binding energy per nucleon is always lower for heavier nuclei than for lighter ones, explaining why fusion releases energy.

Ans; TRUE

33. In quantum mechanics, the Pauli exclusion principle applies only to electrons and not to other fermions like neutrons.

Ans; FALSE

34. Aluminium oxide reacts with both dilute hydrochloric acid and sodium hydroxide to form salts.

Answer: True

35. Zinc hydroxide dissolves in excess ammonia solution to form a complex ion.

Answer: True

36. Lead (II) oxide does not react with excess sodium hydroxide because it is not amphoteric.

Answer: False.

The following phases of the moon are associated with spring tide

37. Early moon?

Answer: True

38. Three-quarter?

Answer: False

39. Full moon?

Answer: True

40. A parabola has exactly one inflection point

Answer: False

41. The graph of cubic polynomial has exactly one inflection point

Answer: True

42. The graph of linear polynomial has exactly one inflection point

Answer: False

43. In an AC circuit with a purely inductive load, the current leads the voltage by a phase angle of 90°.

Ans: FALSE

44. The impedance of a series R-L-C circuit at resonance is equal to the resistance of the circuit.

Ans: TRUE

45. In an AC circuit, the root mean square voltage is always equal to the peak voltage divided by √2.

Ans: FALSE

46. In aqueous solution, [Cu(H₂O)₆]²⁺ is blue because of d–d electronic transitions within the Cu²⁺ ion.

Answer: True

47. When concentrated ammonia is added to [Cu(H₂O)₆]²⁺, the deep blue complex [Cu(NH₃)₄(H₂O)₂]²⁺ is formed.

Answer: True

48. [Fe(H₂O)₆]³⁺ is colourless because all its 3d orbitals are completely filled.

Answer: False

Preamble: the following veins lack valves

49. Jugular vein.

Answer: False

50. Pulmonary vein

Answer. True

51. Umbilical vein

Answer: True

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