NSMQ 2024 MATHEMATICS AND PHYSICS PAST QUESTIONS AND ANSWERS.

PREAMBLE: Find the coordinate of the vertex of the quadratic curve with the equation

1. y = x² – 3x + 1

Ans: (3/2, -5/4)

2. y = x² + x – 1

Ans: (-1/2, -5/4)

3. y = x² – 5x + 6

Ans: (5/2, -1/4)

4. y = x² + 7x + 10

Ans: (-7/2, -9/4)

PREAMBLE: Find the coordinate of the point of inflection of the curve

5. y = x³ – 3x² + 7x – 3

Ans: (1,2)

6. y = x³ + 3x² – 8x – 9

Ans: (-1,1)

7. y =2x³ + 6x² – 8x – 15

Ans: (-1, -3)

8. y = 2x³ – 6x² + 5x + 3

Ans: (1, 4)

Also Read:

• NSMQ 2024 CHEMISTRY PAST QUESTIONS AND ANSWERS.
• NSMQ 2024 SPEED RACE PAST QUESTIONS AND ANSWERS.

PREAMBLE: Solve the absolute value equation, the absolute value of x

9. 3x – 5 = 13

Ans: x = 6 or x = -8/3

10. 2x + 13 = 9

Ans: x = -11 or -2

11. 5x – 17 = 13

Ans: x = 6 or 4/5

12. 4x-7=5

Ans: x = 3 or 1/2

PREAMBLE: Find the length of a diameter of a circle with the equation

13. x² + y² – 4x + 8y – 5 = 0

Ans: 10units

14. x² + y² + 6x + 10y – 15 = 0

Ans: 14units

15. x² + y² – 8x + 12y – 12 = 0

Ans: 16units

16. x² + y² + 2x – 4y – 4 = 0

Ans: 6units

PREAMBLE: Convert the given number to a decimal number

17. 546₈

Ans: 358

18. 674₈

Ans: 444

19. 321₉

Ans: 263

20. 476₉

Ans: 393

PREAMBLE: Two fair dice are thrown, and find the probability that the sum of the scores is

21. 7

Ans: 1/6

22. 6

Ans: 5/36

23. 8

Ans:  5/36

24. 5

Ans: 1/9

25. Find the change in temperature of an object with a heat capacity of 25JK^-1 when it absorbs 500J of heat

Ans: 20K

26. Find the heat capacity of an object whose temperature increases by 15K when it absorbs 480J of heat

Ans: 32JK^-1

27. Find the quantity of heat that increases the temperature of an object by 10K if the heat capacity of the object is 70JK^-1.

Ans: 700J

28. Find the heat capacity of an object whose temperature increases by 8K when it absorbs 80J of heat

Ans: 10JK^-1

Preamble: Find the equation of a straight line passing through the given pair of points in the slope-intercept form

29. A (2,1), B (-1, -2)

Ans: y = x – 1

30. A (-3, 2), and B (2, 3)

Ans: y = -x -1

31. A (4, -5) B (5, -4)

Ans: y = x – 9

32. A (-2, -5) B (-5, -2)

Ans: y = -x -7)

33. A (3, 5) B (5, 3)

Ans: y = -x + 8

PREAMBLE: Find the solution set of the quadratic inequality

34. (x – 4)(x + 3) < 0

Ans: {x: – 3 < x < 4}

35. (x – 4)(x + 5) > 0

Ans: {x: x > 4 or x < -5}

36. (x + 1)(x – 3) < 0

Ans: {x: – 1 < x < 3}

37. (x + 6)(x – 3) > 0

Ans: {x: x < -6 or x < 3}

38. (x – 5)(x + 3) < 0

Ans: {x: – 3 < x < 5}

39. Find the acceleration of a 2kg object when the net force on it is 6iN

Ans: 3ims^-2

40. Find the net force on a 5.0kg object when its acceleration is 24ms^-2

Ans: 120jN

41. Find the acceleration of a 3.0kg object when the net force on it is 36jN

Ans: 12kms^-2

42. Find the net force on a 40kg object when its acceleration is 16ims^-2.

Ans: 64iN

43. Find the acceleration of a 3.0kg object when the net force on it is 49jN

Ans: 14ims^-2

44. Find the magnitude of the impulse of a constant 24N force when it acts for 3.0s

Ans: 72Ns

45. Find the duration of a constant 50N force if the magnitude of its impulse is 75Ns

ANS: 5.0s

46. Find the magnitude force whose impulse has a magnitude of 84N when it acts for 7.0s

Ans: 12N

47. Find the magnitude of the impulse of a constant 18N force that acts for 3.0s

Ans: 54Ns

48. Find the duration of a constant 72N force whose impulse has magnitude 18Ns

Ans: 0.25s

PREAMBLE: Numbers 1,2,3…10 are written on the pieces of paper and placed in a box; a piece of paper is randomly selected. Find the probability that the number on it is

49. Odd and greater than 4

Ans: 3/10

50. Odd or greater than 4

Ans: 12/5

51. Even and less than 7

Ans: 3/10

52. Even or less than 5

Ans: 9/10

PREAMBLE: The acceleration of a particle is constant and equals 5. O Jms^-2.

53. Find the velocity of the particle 2.0s after its velocity attained 3.0Jms^-1

Ans: 13Jm/s

54. Find the velocity of the particle 2.0s before its velocity attains 24Jm/s

Ans: 14Jm/s

55. Find the velocity of the particle 3.0s after its velocity attains 27Jm/s

Ans: 12Jm/s

56. Find the velocity of the particle 3.0s after its velocity attains 4.0Jm/s

Ans: 19Jm/s

PREAMBLE: Find the positive integer solution by factorizing the right-hand side

57. x² (x + 5) = 250

Ans: x = 5

58. x² (x + 3) = 490

Ans: 7

59. x² (x + 4) = 360

Ans: 6

60. x² (x – 2) = 245

Ans: x = 7

PREAMBLE: Find the energy stored in a capacitor of the given capacitance C when the voltage across it is V

61. C = 25mF, V= 16v

Ans: 3.2J

62. C = 48mF, V = 25v

Ans: 15J

63. C = 32mF, V = 15v

Ans: 3.6J

64. C = 72mF, V = 5.0v

Ans: 0.90J

65. Find the pressure on a 2.0m³ surface over which a 400N force acts uniformly

Ans: 230Pa

66. Find the area of a surface over which a 36N force acts as a pressure of120Pa

Ans: 0.30m²

67. Find the pressure on a 0.25m² surface over which a 6.0N force act uniformly

Ans: 24Pa

68. Find the area of a surface over which a 64N force exert a pressure of 0.20Pa

Ans: 3.2m²

69. Find the pressure on a 0.30m² surface over which 96N force acts uniformly

Ans: 320Pa

PREAMNBLE: Find the mass of a particle whose kinetic energy is K and its speed is V

70. K= 18J, V= 2.0ms^-1

Ans: 9.0Kg

71. K= 72J, and V= 3.0ms^-1

Ans: 16Kg

72. K= 54J, and V= 6.0ms^-1

Ans: 3.0Kg

73. K= 32J, and V= 8.0ms^-1

Ans: 1.0Kg

74. K= 96J, and V= 4.0ms^-1

Ans: 12Kg

PREAMBLE: Find an expression for the function f (x) given that

75. f (3x + 2) = x

Ans: x – 2/3

76. f (3 – 2x) = x

Ans: 3 – x/2

77. f (5x – 7) = x

Ans: x + 7/5

78. f (4 – 3x) = x

Ans: 4 – x/3

79. f (2x + 5) = x

Ans: x – 5/2

Preamble: Find the length of a diagonal of a rhombus given that aside measures

80. 13cm and the second diagonal measure 10cm

Ans: 24cm

81. 10cm and 12cm

Ans: 16cm

82. 17cm and 30cm

Ans: 16cm

83. 10cm and 16cm

Ans: 12cm

84. 13cm and 24cm

Ans: 10cm

PREAMBLE: Find the equivalent resistance for the given resistor network,

85. A 12Ω resistor in series with 15Ω resistor

Ans: 27 ohmsΩ

86. A 12Ω resistor in parallel with a 28Ω resistor

Ans: 8.4Ω

87. A 14Ω resistor in series with a 17Ω resistor

Ans: 31Ω

88. A 16Ω resistor in parallel with a 24Ω resistor

Ans: 9.6Ω

89. Find the magnitude of a centripetal acceleration of an object moving at 4.0ms^-2 in a circle of radius of 2m

Ans: 8.0ms^-1

90. Find the radius of a circle in which an object moves with 15ms^-2 centripetal acceleration when its speed is 6.0m/s

Ans: 2.4m

91. Find the magnitude of the centripetal acceleration of an object moving at 3.0ms^-1 in a circle of radius 2.0m

Ans: 4.5ms^-2

92. Find the radius of a circle in which an object moves with a 4.0ms^-2 centripetal acceleration when its speed is 0.80ms^-1

Ans: 0.16m

PREAMBLE: Find the coordinate of the centre(C) and the radius (r) of the circle with equation

93. x² + y² – 10x + 12y – 20 = 0

Ans: Centre (5, -6), radius (9) units

94. x² + y² + 4x + 6y – 23 = 0

Ans: Centre (-2, -3), radius (6) units

95. x² + y² – 6x – 8y + 9 = 0

Ans:  Centre (-3, 4), radius (4) units

96. x² + y² + 2x – 8y – 8 = 0

Ans: Centre (-1, 4), radius (5) units

PREAMBLE: Find a quadratic equation of the form f(x) = mx² + nx + p given that it cuts the x – axis and the y – axis at the given points. m, n, p are constants.

97. (-2, 0), (3, 0) and (0, -18)

Ans: f(x) = 3x² – 3x – 18

98. (1, 0), (-2, 0) and (0, 12)

Ans: f(x) = – 6x² – 6x + 12

99. (3, 0), (5, 0) and (0, -30)

Ans: f(x) = – 2x² + 16x – 30

100. (-1, 0), (- 5, 0) and (0, 15)

Ans: f(x) = 3x² + 18x + 15

PREAMBLE: Find the equivalent resistance of a circuit composed of resistor ₁ in parallel with resistor ₂ given that.

101. ₁ = 15 and ₂ = 25 .

Ans: 9.4

102. ₁ = 16 and ₂ = 18 .

Ans: 8. 5

103. ₁ = 9.0 and ₂ = 12 .

Ans: 5. 1

104. ₁ = 5.0 and ₂ = 25 .

Ans: 4. 2

PREAMBLE: Find the work done by the net force on an object of mass when its speed changes from to given that:                     

105. = 15 g, = 1 ^-1 and = 3 ^-1.

Ans: 60 J

106. = 24 g, = 2 ^-1 and = −2 ^-1.

Ans: 0 J

107. = 16 g, = 6 ^-1 and = 2 ^-1.

Ans: −256

108. = 13 g, = 5 ^-1 and = 9 ^-1.

Ans: 429

109. The surface gravity of a round celestial object of radius 770 m is 0.70 m^-2. Find the gravitational potential on the object’s surface.

Ans: −.9 × ^{5 -1}

110. The mean terrestrial surface gravity is 9.80 m^-2. Assuming the earth is spherical and of radius 6480 m, what is earth’s surface gravitational potential?

Ans: −. × ^{7 -1}

111. The moon, earth’s only natural satellite, has a mean radius of 1770 m and a surface gravity of 1.80 m^-1. Find the moon’s surface gravitational potential assuming it is spherical.

Ans: −. × ^{6 -1}

112. The mean terrestrial surface gravity is 9.90 m^-2. Assuming the earth is spherical and of radius 6420 m, what is earth’s surface gravitational potential?

Ans: −. × ^{7 -1}

113. Find the Young modulus of a substance for which a tensile stress of 2.8 MPa produces a strain of 0.020 %.

Ans: 14 Pa

114. If the Young modulus of a substance is 18 Pa, what tensile stress is required to produce a 0.050 % tensile strain in a wire made of the substance?

Ans: 36 Pa

115. Find the Young modulus of a substance for which a tensile stress of 1.5 Pa produces a strain of 0.0033 %.

Ans: 45 Pa

116. Find the Young modulus of a substance for which a tensile stress of 4.50 Pa produces a strain of 0.00330 %.

Ans: 135 Pa

PREAMBLE: Find the least value and greatest value of the given function in the given interval

117. y = |2x – 10|in the interval {−7 ≤ < 5}

Ans: L = 2, G = 24

118. y = |6x – 18|in the interval {−3 < ≤ 3}

Ans: L = 0, G = 30

119. y = |4x – 8|in the interval {− 4 < < 2}

Ans: L = 4, G = 20

120. y = |2x + 2|in the interval {− 1 < ≤ 4}

Ans: L = 2, G = 10

PREAMBLE: Find the image of the circle (x – 4)² + (y + 3)² = 16 under the translation vector V, given that

121. V is (3, -1)

Ans: (x – 7)² + (y + 4)² = 16

122. V is (- 3, 2)

Ans: (x – 1)² + (y + 1)² = 16

123. V is (2, 5)

Ans: (x – 6)² + (y – 2)² = 1

124. V is (- 5, 3)

Ans: (x + 1)² + y² = 16.

Preamble: Find the ratio of the interior angle to the exterior angle of a regular

125. undecagon

Ans: 9 : 2

126. octagon

Ans: 3 : 1

127. Septagon

Ans: 5 : 2

128. icosagon

Ans: 9 : 1

PREAMBLE: Where needed, you may take the Wien constant as 2.899 × 10^-3 , the Stefan-Boltzmann constant as 5.67 × 10^{-8 -2-4}, and the Boltzmann constant as 1.38 × 10⁻²³JK^-1

129. The emissivity of the surface of a spherical object of radius 0.500 is 0.960. Find the net rate of radiation from the object when its temperature is 400 and the temperature of its surroundings is 300

Ans: . W

130. The emissivity of the surface of another spherical object of radius 0.250 is 0.800. Find the net rate of radiation from the object when its temperature is 500 and the temperature of its surroundings is 400 .

Ans: . W

131. The emissivity of the surface of a third spherical object of radius 0.300 is 1. Find the net rate of radiation from the object when its temperature is 500 and the temperature of its surroundings is 300

Ans: . W

132. The emissivity of the surface of another spherical object of radius 0.250 is 0.400. Find the net rate of radiation from the object when its temperature is 500 and the temperature of its surroundings is 300 .

Ans: . W

PREAMBLE: Find the refractive index of the material of a 60° prism for which the angle of minimum deviation is as given.

133. The angle of minimum deviation equals 32.0°.

Ans: .

134. The angle of minimum deviation equals 37.0°.

Ans: .

135. The angle of minimum deviation equals 36.0°.

Ans: .

136. The angle of minimum deviation equals 33.0°.

Ans: .

PREAMBLE: Find the coefficient of x⁶ in the expansion of the given binomial expression 

137. (x² + 2)⁶

Ans: 160

138. (3 – x²)⁵

Ans: – 90

139. (5 – x²)⁵

Ans: – 250

140. (x² + 3)⁷

Ans: 2835

PREAMBLE: Find x

141. log₅ 512 x log_x 125 = 27

Ans: x = 2

142. log₈16 x log_x 512 = 6

Ans: x = 4

143. log₆512 x log_x216 = 9

Ans: x = 8

144. Log_x16 x log₄729 = 4

Ans: x = 27

Preamble: Find the centroid of the triangle ABC with the given point of A, B and C

145. A (1,2), B (3, 4), and C (5, 6)

Ans: (3, 4)

146. A (−2, 3), B (4, −1), and C (0, 5)

Ans: (2/3 ,7/3)

147. A (−1, −2), B (2, −3), and C (−4, 1)

Ans: (-1, -4/3)

148. A (5, 7), B (−3, 2) and C (1, −4)

Ans: (1, 5/3)

Preamble: A music class of five girls and four boys is having a recital. If each member is to perform once, how many ways can the program be arranged if,

149. All girls must perform first.

Ans: 2880 ways

150. All girls must perform first and a specific boy must perform last.

Ans: 720 ways

151. The performance must start and end with a girl.

Ans: 100800

152. The entire program will alternate between boys and girls

Ans: 2880 ways

153. A car accelerates uniformly from 10 m/s to 30 m/s in 5.0 seconds while moving along a circular track of radius 50 m. Calculate the tangential acceleration.

Ans: 4.0m/s²

154. A wheel increases its angular velocity from 2.0 rad/s to 8.0 rad/s in 3.0 seconds. If the wheel has a radius of 0.40 m, what is the tangential acceleration?

Ans: 0.80m/s²

155. A particle moves in a circular path of radius 2.0 m. Its speed changes from 5.0 m/s to 9.0 m/s in 2.0 seconds. Find the tangential acceleration.

Ans: 2.0m/s²

156. A disc starts from rest and reaches an angular speed of 15 rad/s in 5.0 seconds. If a point on the rim is 0.30 m from the center, what is its tangential acceleration?

Ans: 0.90m/s²

Preamble: There are two scenarios, in scenario 1 an ideal heat engine does 120KJ in a cyclic process. In scenario 2, another heat engine undergoes an isothermal process at a constant temperature of 450K of which 120KJ of heat is applied.

157. What is the change in internal energy in scenario 1?

Ans: 0

158. What is the change in internal energy in scenario 2?

Ans: 0

159. What is the quantity of heat applied in scenario 1 if R = 8.314 and 3.00 moles of ideal gas is in the system?

Ans: 120KJ

160. What is the amount of work done in scenario 2 if R = 8.314 and 3.00 moles of ideal gas is in the system?

Ans: 120KJ

161. A uniform meter stick has a mass of 0.100Kg, where should a pivot be placed if a 50.0 g pellet is placed at 0.00cm mark.

Ans: 33.3cm

162. A uniform meter stick weighs 80.0 g. A 40.0 g mass is hung at the 75.0 cm mark. Where should the pivot be placed for balance?

Ans: 58.3cm

163. A uniform meter stick weighs 75.2g. A 15.04 g mass is hung at the 45.0 cm mark. Where should the pivot be placed for balance?

Ans: 49.2cm

164. A non-uniform meter stick has a mass of 0.120Kg, and its center of mass is at the 40.0cm mark. A 60.0g mass is placed at the 10.0 cm mark. Where should the pivot be placed so the stick balances?

Ans: 30.0cm

Preamble: Given that m > n and m and n are positive integer values, form a Pythagorean triple that does not include m and n

165. m = 21, n = 13

Ans: 272, 546, 610

166. m = 27, n = 23,

Ans: 200, 1242, 1258

167. m = 24, n = 17

Ans: 287, 816, 865

168. m = 31, n = 12

Ans: 817, 744, 1105

Preamble: A bag contains 6 red balls, 4 blue balls, 5 green balls, and 3 yellow balls. A person picks balls one at a time randomly without replacement. Find the probability that the

169. First ball is red.

Ans: 1/3

170. Second red given first is red.

Ans: 5/17

171. First ball drawn is green and the second ball is blue.

Ans: 10/153

172. First two balls drawn are of the same colour.

Ans: 34/153

Preamble: Find the equation of the line joining the given points:

173. A (-7, 3) and B (5, 3)

Ans: y = 3

174. C (-2, -4) and D (-2, 3)

Ans: x = -2

175. E (4, 5) and F (4, 4)

Ans: x = 4

176. G (3, 5) and H (4, 5)

Ans: y = 5

Preamble: An alternating current of frequency 50.0 Hertz flows in a circuit containing a resistor. Calculate the peak current for the following r.m.s values.

177. 00

Ans: 5.66A

178. 00

Ans: 8.48A

179. 00

Ans: 11.3A

180. 00

Ans: 12.7A

Preamble: An object is released from rest on a smooth plane inclined at an angle to the horizontal. The point at which the object is released is a height h, above the bottom of the plane.

181. If = 30^o, and h = 5m, find the speed of the object at the bottom of the plane

Ans: 10m/s

182. If = 30^o, and h = 5m, find the magnitude of the acceleration of the object down the plane.

Ans: 5m/s²

183. If = 60^o, and h = 8.0m, find the speed of the object when it is 2.0m above the bottom of the plane

Ans: 11m/s

184. If = 60^o, and h = 11.0m, find the magnitude of the acceleration of the object when it is 2.0m above the bottom of the plane.

Ans: 8.5m/s².

185. Find the centripetal force on a body of mass 25kg moving in a circle of radius 3.0m with a speed of 7.0m/s

Ans: 410N

186. Find the centripetal force on a body of mass 33kg moving in a circle of radius 5.0m with a speed of 6.0m/s

Ans: 240N

187. Find the centripetal force on a body of mass 12kg moving in a circle of radius 14m with a speed of 9.0m/s

Ans: 69N

188. Find the centripetal force on a body of mass 36kg moving in a circle of radius 7.0m with a speed of 11m/s

Ans: 620N

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