NSMQ 2025 Trier Questions and Answers; Fundamental Concepts (Set 1)

Find the value of x if the first three terms of an exponential sequence are

1. x + 2, x, x – 3

Ans:  x = -6

2. x + 2, x, x – 1

Ans: x = 2

3. x + 2, x, x – 4

Ans: x = -4

4. x – 3, x, x + 6

Ans:  x = 6

• Major Areas to Cover and Basic Principles in Answering True/False, Multiple Choice, And Fill-In-The-Blank Questions.

• NSMQ 2025 TRIER QUESTIONS AND ANSWERS; (RIDDLES ONLY).

• Test Practical on Prawn/Crayfish, Crab, and Woodlouse.

• NSMQ 2024 BIOLOGY PAST QUESTIONS AND ANSWERS.

Preamble: Find the coordinate of the vertex of the given curve

5. y = (x – 3)(x + 3)

Ans: (0, -9)

6. y = (x – 4)(x + 2)

Ans: (1, -9)

7. y = (x – 2)(x – 4)

Ans: (3, -1)

8. y = (x – 1)(x +3)

Ans: (-1, -4)

9. The pH of a buffer system composed of 0.500 moldm^-3 of a weak acid and 0.0500 moldm^-3 of its salt is 5.0. Determine the Ka of the acid

Ans: Ka . × ⁻

10. Calculate the pH of a buffer system formed from 0.0036 moldm^-3 of a weak acid with Ka 1.0 × 10^-5 and 0.36 mol dm^-3 of its salt.

Ans: 7.0

11. Calculate the pH of a buffer system composed of 0.020 mol dm of a weak base of Kb 1.0 × 10^-4 and 0.20 moldm^-3 of its salt.

Ans: 9.0

12. The pH of a buffer system formed from a weak acid and its salt is 6.0. Determine the ratio of the concentration of the acid to the salt if the Ka of the acid is 1.0 × 10^-4

Ans: 100: 1

Preamble: A particle executes SHM of amplitude 20 cm. At what distance from the mean position is the ratio of its KE to PE equal? Leave your answer to one place of decimal place

13. n = 1

Ans: 14 cm

14. n = 2

Ans: 11.5 cm      (accept 12 cm)

15. n = 3

Ans: 10 cm

16. n = 4

Ans: 9 cm

Preamble: Name the part of the nuclear reactor that the following description refers

17. Contains all the fuel and generates the heat required for energy

Ans: The Core

18. It eliminates the excess heat that is not converted or transferred

Ans: Cooling Tower

19. The envelope structure that separates the nuclear reactor from the surroundings

Ans: The Containment

20. It passes through the core, absorbing the heat and transferring it into the turbine

Ans: The Coolant

Preamble: Name the type of aestivation found in the following

21. China rose?

 Ans:  Twisted

22. Cotton

Ans:  Twisted

23. Guava

Ans:  Quincuncial

24. Bean

Ans:  Velvet

25. Ama, Akosua, and Yaa together can finish a piece of work in 50 minutes. Ama and Akosua together finish the same work in 60 minutes. In how many minutes can Yaa alone finish that work?

Ans: 300 minutes

26. Kofi alone can do a piece of work in 12 days, and Kwame can do the same piece of work in 4 days. How many days can that work be completed in if they work together?

Ans: 3 days

27. Irene, Betty, and Rose can complete the work in 30 minutes. Irene and Betty together can do the same work in 80 minutes; then, how long would it take for Rose alone to complete the work?

Ans: 48 minutes

28. Wilson completes a work in 12 days, and Benny completes the same work in 15 days. Find the time required to complete the same work if they both work together?

Ans: 60/9 days or 6.67 days (accept 6.7 days)

Arrange the given bonds in increasing order of bond length.

29. C-H, H-F, N-H, O-H

Ans: C-H, N-H, O-H, H-F

30. C-H, C-Br, C-N, C-I

Ans: C-H, C-N, C-Br, C-I

31. C=O, O=O, N=O, C=C

Ans: C=C, C=O, N=O, O=O

32. C≡C, C≡O, N≡N, C≡N

Ans: C≡C, C≡N, N≡N, C≡O

Preamble: You may leave your answer as a simple ratio

33. The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. Its focal length is 12cm. What is the refractive index of the lens?

Ans: 1.5

34. A thin double convex lens has radii of curvature of magnitude 40 cm each and is made of glass with a refractive index of 1.6. Find its focal length

Ans: 33 cm

35. The radii of curvature of the surfaces of a double convex lens are 20 cm and 40 cm, respectively, and its focal length is 20 cm. What is the refractive index of the material of the lens?

Ans: 5/3 or 1.7

36. A double convex lens has a focal length of 40 cm. If the radius of curvature of its refracting surfaces is 10 cm and 20 cm, find the refractive index of the material of the lens.

Ans: 7/6

Preamble: Find the equation of a tangent to the circle

37. x² + y²  = 15 at the point (2, 3)

Ans: 3y = -2x + 13

38. x² + y² – 52 = 0 at the point (6, -4)

Ans: 2y = 3x – 26

39. x² + y²  = 25 at the point (1, 5)

Ans: 5y = -x + 26

40. x² + y²  – 18 = 0 at the point (3, 2)

Ans: 2y = -3x + 13

41. Preamble: give on the role or importance of heterotrophs in the ecosystem

Ans:

• They serve as the consumers in the ecosystem
• By eating organisms in the food chain, heterotrophs recycle nutrients and organic chemicals
• The help in the dispersal and germination of seeds to other areas of an ecosystem
• Heterotrophs fertilize the land and/or water with their feces.
• Consumers or predators keep the population of their prey within reasonable numbers.
• Predators tend to eat older and weaker individuals from their prey and in doing so, keep the population healthier.

42. Upon heating, 2.5 g of calcium carbonate decomposes to give calcium oxide and carbon dioxide. Determine the mass of metal oxide formed.

Ans: 1.4 g

43. Upon heating, 25.0 g of calcium carbonate decomposes to give 11.2 g of calcium oxide. Determine the percentage purity of the carbonate.

Ans: 80.0%

44. Upon heating, 16.8 g of magnesium carbonate decomposes to give magnesium oxide and carbon dioxide. Determine the mass of the metal oxide formed.

Ans: 8.00 g

45. Upon heating, 2.1 g of magnesium carbonate decomposes to give magnesium oxide and carbon dioxide. If the percentage yield is 80.0%, determine the mass of metal oxide formed.

Ans: 0.80 g

46. y = x³ – 6x² – 36x + 5

Ans: (2, -83)

47. y = x³ – 3x²  – 4x + 7

Ans: (1, 1)

48. y = -x³ – 6x² + 5x + 10

Ans: (-2, -16)

49. y = -x³ + 3x² + 45x + 8

 Ans: (1, 55)

50. A tuned circuit with a tunable capacitor set to a capacitance of 5 pF has a resonance frequency of 17 kHz. Find the resonance frequency of the circuit when the capacitance is increased to 20 pF.

Ans: 8.5 kHz

51. A tuned circuit with a tunable capacitor set to a capacitance of 9 pF has a resonance frequency of 14 kHz. Find the resonance frequency of the circuit when the capacitance is increased to 36 pF.

Ans: 7 kHz

52. A tuned circuit with a tunable capacitor set to a capacitance of 5 pF has a resonance frequency of 20 kHz. Find the resonance frequency of the circuit when the capacitance is increased to 10 pF.

Ans: 14 kHz

53. A tuned circuit with a tunable capacitor set to a capacitance of 20 pF has a resonance frequency of 30 kHz. Find the resonance frequency of the circuit when the capacitance is increased to 10 pF.

Ans: 42 kHz

State the hybridization of the central atom and the electron geometry of the following species

54. NO^–₃

Ans: hybridization: sp²    Electron geometry: Trigonal

55. SO₃^2-

Ans: hybridization: sp³    Electron geometry: Tetrahedral

56. ClO₃^–

Ans: hybridization: sp³    Electron geometry: Tetrahedral

57. O₃

Ans: hybridization: sp²    Electron geometry: Trigonal

58. Preamble: Give one main adaptive feature of parasites

Ans:

• Presence of adhesive organs (hooks) or suckers
• Loss of digestive system (they absorb the nutrients directly through their skin)
• High reproductive capacity
• Absence of sense organs (they completely depend on their host)

Preamble: Determine the minimum and maximum values of the trigonometric function

59. cos²x – 4 cos x + 1

Ans: m = -2 M = 6

60. sin²x – 6 sin x + 8

Ans: m = 3 M = 15

61. cos²x – 6 cos x + 13

Ans: m = 8 M = 20

62. sin²x – 8 sin x + 4

Ans: m = -1 M = 7

63. The radius of the Helium-4 nucleus is 3.0 fermi. Determine the radius of Sulphur-32

Ans: 6.0 fermi

64. The radius of a nucleus of an isotope ²⁵⁶X is 8.0 fermi. Determine the nucleus of the Helium-4 isotope.

Ans: 2.0 fermi

65. If the radius of an Aluminium-27 is estimated to be 3.6 fermi, what is the radius of Telurium-125 nucleus?

Answer: 6.0 fermi

66. The radius of a nucleus of an isotope ²¹⁶X is 8.0 fermi. Determine the nucleus of an isotope ⁶⁴Y

Ans: 5.3 fermi

67. Preamble: Genetic drift operates in a small, isolated population. Give one major reason for this

Ans:

• A small change in genes can have a high impact.
• By genetic drift, the phenotype of this small population quickly becomes different from the parent population.
• During migration, gene frequency changes in the population as new alleles get lost from the older population.
• Losing genetic variation is much faster than in a large population
• Some versions of genes can be lost due to random chance (Chance factor)

68. For a saturated solution of AB₂ at 25 °C, the concentration of B ions is 3.0 × 10^-4 moldm^-3. Calculate the solubility product of AB₂ at this temperature.

Ans: 1.1 × 10^–10

69. A sparingly soluble salt MXO₃ has a Ksp of 3.6 × 10^-7 at 25 ℃. What is the maximum amount (in grams) of MXO₃ that can be dissolved in 1 dm³ of solution at this temperature, given its molar mass as 125 g/mol?

Ans: 0.075 g

70. The solubility product of silver ethanoate is 4.90 x 10^-3 at 30.0 0C. Calculate the mass of the salt needed to prepare 10.0 liters of its saturated solution at 30.0 °C. silver ethanoate (AgCH₃CO₂) = 167 g/mol

Ans: 117 g

71. The solubility of YX₂ at 25 ℃ is 4.00 × 10^-3 moldm^-3. Calculate the solubility product at this temperature

Ans: 2.56 × 10^-7

PREAMBLE: Find the base number ‘n’ if the sum is right

72. 132 + 231 = 1010

Ans: 3

73. 214 + 341 = 1320

Ans: 5

74. 112 + 221 = 1010

Ans: 3

75. 123 + 234 = 1012

Ans: 5

76. 513 + 214 = 1030

Ans: 7

Preamble: A and B are two independent events. Find the P(AnB) given:

77. P(A) = ¾ and P(B) = 2/5

Ans: 3/10

78. P(A) = 1/3 and P(B) = 4/7

Ans: 4/21

79. P(A) = 5/6 and P(B) = ¼

Ans: 5/24

80. P(A) = 2/5 and P(B) = 3/8

Ans: 3/20

81. P(A) = 7/10 and P(B) = 5/9

Ans: 7/18

Preamble: State if the given elements belong to the following description at room temperature: metal, metalloid, gas, or non-metal

82. Arsenic

Ans: metalloid

83. Argon

Ans: non-metal and gas

84. Mercury

Ans: metal

85. Silicon

Ans: metalloid

86. Carbon

Ans: non-metal

87. A 50 cm³ of 1.2 mol/dm³ NaOH solution is diluted to 250 cm³. What is the new concentration of the diluted solution?

Ans: 0.24 mol/dm³

88. A 10 cm³ sample of a concentrated hydrochloric acid (HCl) solution is diluted to 500 cm³. If the concentration after dilution is found to be 0.1 mol/dm³, what was the concentration of the original solution?

Ans: 5 mol/dm³

89. A 100 cm³ of 2.5 mol/dm³ sulfuric acid (H₂SO₄) solution is diluted to 500 cm³. What is the new concentration of the diluted solution?

Ans: 0.50 mol/dm³

90. A 25 cm³ sample of a concentrated sodium hydroxide (NaOH) solution is diluted to 1000 cm³. If the concentration after dilution is found to be 0.05 mol/dm³, what was the concentration of the original solution?

Ans: 2 mol/dm³

91. A 150 cm³ of 0.80 mol/dm potassium hydroxide (KOH) solution is diluted to 750 cm³. What is the new concentration of the diluted solution?

Ans: 0.16 mol/dm³

92. Preamble: Give one general characteristic of Arthropods

Ans:

• They have a hard exoskeleton made of chitin
• They have segmented bodies
• Jointed appendages
• Undergo molting (ecdysis) to grow
• Open circulatory system
• They have respiratory organs such as a trachea and gills
• Well-developed nervous system with a dorsal brain connected to a ventral nerve cord
• Many undergo metamorphosis
• Some live in terrestrial, freshwater, and marine environments

Preamble: The Earth’s atmosphere has 5 main layers. Give the names of the following parts of the atmosphere as described

93. It is the second-lowest layer of the Earth’s atmosphere. It contains the ozone layer.

Ans: stratosphere

94. It is the second-highest layer of the Earth’s atmosphere. It is completely cloudless and free of water vapor.

Ans: thermosphere

• Major Areas to Cover and Basic Principles in Answering True/False, Multiple Choice, And Fill-In-The-Blank Questions.

• NSMQ 2025 TRIER QUESTIONS AND ANSWERS; (RIDDLES ONLY).

• Test Practical on Prawn/Crayfish, Crab, and Woodlouse.

• NSMQ 2024 BIOLOGY PAST QUESTIONS AND ANSWERS.

95. It is the outermost layer of the Earth’s atmosphere. Mainly composed of extremely low densities of hydrogen and helium gas

Ans: exosphere

96. It is the lowest layer of the Earth’s atmosphere. It contains roughly 80% of the mass of the Earth’s atmosphere. It is denser than all its overlying atmospheric layers.

Ans: troposphere

97. It is the third-highest layer of the Earth’s atmosphere. It is the coldest place on Earth.

Ans: mesosphere.

98. The coefficient of static friction between a block and a horizontal surface is 0.30. A force of 50 N is applied horizontally to the block. The normal force acting on the block is 100 N. Determine the static friction force acting on the block.

Ans: 30 N

99. The coefficient of kinetic friction between a sled and the snow is 0.15. Determine the force needed to pull the sled at a constant velocity if the normal force acting on the sled is 200 N.

Ans: 30 N

100. Two blocks are stacked on top of each other. The coefficient of static friction between the two blocks is 0.40. If a horizontal force of 20 N is applied to the bottom block, and the normal force between the two blocks is 50N, calculate the static friction force between the blocks.

Ans: 20 N

101. A box is being pushed across a floor with a coefficient of kinetic friction of 0.25. If the normal force acting on the box is 80 N, determine the force required to keep the box moving at a steady speed.

Ans: 20 N

102. An object requires a 15 N horizontal force to move steadily across a rough surface. If the normal force acting on the object is 80 N, calculate the coefficient of kinetic friction.

Ans: 0.19

103. The primary winding of a 15:1 step-down transformer is excited at 330V RMS. Find the RMS output voltage.

Ans: 22 V

104. The output power of a 10:1 step-down transformer is 50W when the input consumes 60W. Find the efficiency of the transformer.

Ans: 83%

105. The primary winding of a 10:1 step-down transformer is excited at 120V RMS. Find the RMS output voltage.

Ans: 12 V

106. The output power of a 5:1 step-down transformer is 200W when the input consumes 250W. Find the efficiency of the transformer.

Ans: 80%

107. The secondary winding of a 10:1 step-down transformer gives an output of 15V RMS. Find the RMS input voltage.

Ans: 150 V

108. Preamble: Name one of the physical phenomena employed in the construction of thermometers.

Ans:

• Thermal expansion
• Thermoelectric effect
• Resistance change
• Radiation
• Liquid crystals
• Gas expansion

Preamble: Given f(x) = 4x³ -3x³ + 2x – 1, evaluate

109. f(2)

Ans: 23

110. f(-1)

Ans: -10

111. f(-2)

Ans: -49

112. f(1)

Ans: 2

113. f(3)

Ans: 86

Preamble: Given that log 2=0.301 and log 3=0.477, evaluate to 3 d.p

114. log(3/2)

Ans: 0.176

115. log 4

Ans: 0.602

116. log 9

Ans: 0.954

117. log ½

Ans: -0.301

118. log 12

Ans: 1.079

119. A 10.0 L gas cylinder initially filled with gas at 300 kPa is allowed to expand to 25 L at the same temperature. Calculate the new pressure in the cylinder.

Ans: 120 kPa

120. A balloon initially filled with air at 25.0°C and a pressure of 150 kPa has a volume of 15.0 L. If the pressure is increased to 180 kPa while keeping the temperature constant, what was the initial volume of the gas?

Ans: 12.5 L

121. A gas sample occupies 50.0 L at a pressure of 200 kPa. If the volume is compressed to 20.0 L at constant temperature, what is the new pressure?

Ans: 500 kPa

122. A gas initially occupies a volume of 10.0 L at a pressure of 200 kPa and a temperature of 25°C. If the pressure is increased to 300 kPa while keeping the temperature constant, what was the initial volume of the gas?

Ans: 6.7 L

123. A gas tank contains 30.0 L of gas at a pressure of 250 kPa. If the volume of the gas is reduced to 10.0 L, what is the new pressure assuming constant temperature?

Ans: 750 kPa

Preamble: Write the equilibrium constant expression for the following equilibrium reactions. Consider all species to be in their standard states at room temperature

124. Dissociation of gaseous hydrogen iodide to give hydrogen gas and iodine

Ans: Kc = [H₂]/[HI]²

125. Formation of carbon monoxide from carbon dioxide and carbon

Ans: Kc = [CO]²/[CO₂]

126. Formation of ammonium chloride from ammonia and hydrochloric acid

Ans: Kc = 1/[NH₃][HCl]

127. Dissociation of a water molecule to give hydrogen gas and oxygen gas

Ans: Kc = [H₂]²[O₂]

128. Formation of ammonia using the Haber process by reaction of nitrogen gas and hydrogen gas

Ans: Kc = [NH₃]²/[N₂][H₂]³

(NB: Kc is not written for solids and liquids in an equilibrium expression)

129. A 1.0 kg ball moving at 6.0 m/s collides with a stationary wall and rebounds with a speed of 4.0 m/s. Find the coefficient of restitution.

Ans: 0.67

• Major Areas to Cover and Basic Principles in Answering True/False, Multiple Choice, And Fill-In-The-Blank Questions.

• NSMQ 2025 TRIER QUESTIONS AND ANSWERS; (RIDDLES ONLY).

• Test Practical on Prawn/Crayfish, Crab, and Woodlouse.

• NSMQ 2024 BIOLOGY PAST QUESTIONS AND ANSWERS.

130. A 0.3 kg ball moving at 8 m/s collides directly with a stationary wall and rebounds with a speed of 5 m/s. Find the impulse of the force on the ball.

Ans: -0.9 Ns or kgm/s

131. A 0.20 kg tennis ball moving at 15 m/s collides with a wall and rebounds with a speed of 10 m/s. Find the coefficient of restitution.

Ans: 0.67

132. A 0.60 kg truck moves at 12 m/s and collides with a stationary wall, bouncing back with a speed of 9.0 m/s. Calculate the impulse of the force on the truck.

Ans: -1.8 Ns or kgm/s

133. A 0.50 kg hockey puck moving at 12 m/s collides with a wall and rebounds with a speed of 9.0 m/s. Find the coefficient of restitution.

Ans: 0.75

Preamble: Simplify by rationalizing the denominator

134. 1/(√2 – 1)

Ans: √2 + 1

135. 3/(1+√5)

Ans: (3√5 – 3) / 4

136. 2/(√3 – 1)

Ans: √3 + 1

137. 5/(√6 – √2)

Ans: (5√6 + 5√2) / 4

138. 4/(3 – √7)

Ans: 6 + 2√7

Preamble: State the molecular formula of the following alkanes

139. 2,2,4-trimethylpentane

Ans: C₈H₁₈

140. 3-ethyl-2-methylhexane

Ans: C₉H₂₀

141. 2,3-diethylbutane

Ans: C₈H₁₈

142. 4-propylheptane

Ans: C₁₀H₂₂

143. 2,2-dimethylpropane

Ans: C₅H₁₂

144. When nitrogen-14 (atomic number 7) is bombarded with a certain nuclear particle, it forms oxygen-17 (atomic number 8) and emits a proton. What is this nuclear particle?

Ans: alpha particle

145. When thorium-232 (atomic number 90) absorbs a neutron, it produces two nuclides and emits 2 neutrons. If one of the daughter nuclides is xenon-137 with atomic number 54, what are the atomic mass and atomic number of the second nuclide?

Ans: mass number = 94, atomic number = 36

146. When nitrogen-14 (atomic number 7) is bombarded with a certain nuclear particle, it forms carbon-14 (atomic number 6) and a proton. What is this nuclear particle?

Ans: neutron

147. When plutonium-239 (atomic number 94) absorbs a neutron, it produces two nuclides and emits 3 neutrons. If one of the daughter nuclides is technetium-99 with atomic number 43, what are the atomic mass and atomic number of the second nuclide?

Ans: mass number = 138, atomic number = 51

148. When oxygen-18 (atomic number 8) is bombarded with a certain nuclear particle, it forms nitrogen-15 (atomic number 7) and an alpha particle (Helium-4). What is this nuclear particle?

Ans: proton

149. Give the term used to describe the adult stage of an insect after it has undergone metamorphosis, especially in species that undergo complete metamorphosis

Ans: imago

150. What is the name of the process of shedding the outer layer of the exoskeleton in arthropods and some other invertebrates?

Ans: ecdysis or molting

151. Name the immature stage of development in insects that undergo incomplete metamorphosis

Ans: nymph

152. What is the name of the protective egg case or capsule produced by certain invertebrates, particularly insects and some mollusks?

Ans: ootheca (plural: oothecae)

153. Name the polysaccharide that forms the main component of the exoskeleton of insects

Ans: chitin

Preamble: State the main respiratory organs found in the following organisms

154. Birds

Ans: lungs (accept air sacs)

155. Mammals

Ans: lungs

156. Fish

Ans: gills

157. Insects

Ans: trachea

158. Reptiles

Ans: lungs

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