OUAT Mathematics Group Mock Test

Physics (1–20)

1. A particle starts from rest and moves with uniform acceleration. Distance covered in time t is proportional to:
A) t
B) t²
C) 1/t
D) √t

2. Work done by a centripetal force is always:
A) positive
B) negative
C) zero
D) infinite

3. The slope of velocity-time graph represents:
A) displacement
B) acceleration
C) force
D) momentum

4. A body projected at angle 45° has maximum range because:
A) sinθ is maximum
B) cosθ is maximum
C) sin2θ is maximum
D) velocity is zero

5. Escape velocity is independent of:
A) mass of planet
B) radius of planet
C) mass of object
D) gravitational constant

6. SI unit of impulse is:
A) N
B) N·s
C) J
D) W

7. In SHM, acceleration is proportional to:
A) displacement
B) velocity
C) time
D) mass

8. The phase difference between velocity and displacement in SHM is:
A) 0
B) π/2
C) π
D) 2π

9. The resistance of a conductor increases with:
A) decrease in length
B) increase in area
C) increase in temperature
D) decrease in temperature

10. Kirchhoff’s second law is based on conservation of:
A) mass
B) charge
C) energy
D) momentum

11. The magnetic field inside a long solenoid is:
A) zero
B) uniform
C) non-uniform
D) circular

12. A transformer works on:
A) DC only
B) AC only
C) both AC and DC
D) heat energy

13. Photoelectric effect proves:
A) wave nature of light
B) particle nature of light
C) sound nature of light
D) heat nature of light

14. Unit of Planck’s constant is:
A) J
B) J·s
C) N·m
D) W·s

15. In circular motion, centripetal force acts:
A) outward
B) tangentially
C) toward center
D) away from center

16. Dimensional formula of force is:
A) MLT⁻²
B) MLT⁻¹
C) ML²T⁻²
D) M⁻¹LT⁻²

17. Sound waves in air are:
A) transverse
B) longitudinal
C) electromagnetic
D) stationary

18. Doppler effect is related to:
A) reflection
B) interference
C) frequency change
D) polarization

19. SI unit of power is:
A) Joule
B) Watt
C) Newton
D) Pascal

20. Efficiency of a machine is always:
A) >100%
B) =100%
C) <100%
D) =0%

21. The work-energy theorem relates work done to change in:
A) momentum
B) kinetic energy
C) potential energy
D) force

22. If velocity of a body is doubled, its kinetic energy becomes:
A) 2 times
B) 3 times
C) 4 times
D) unchanged

23. In uniform circular motion, acceleration is:
A) zero
B) tangential
C) radial inward
D) random

24. The moment of inertia depends on:
A) mass distribution
B) velocity
C) time
D) force

25. Angular momentum is conserved when:
A) external force acts
B) external torque is zero
C) velocity is zero
D) energy is lost

26. Pressure at a depth in liquid depends on:
A) surface area
B) density and depth
C) shape of container
D) volume

27. Bernoulli’s theorem is based on conservation of:
A) mass
B) energy
C) momentum
D) charge

28. A body floats when its density is:
A) greater than liquid
B) equal to liquid
C) less than liquid
D) zero

29. Heat transfer by direct contact is:
A) convection
B) radiation
C) conduction
D) reflection

30. Stefan-Boltzmann law relates radiation to:
A) temperature
B) pressure
C) volume
D) mass

31. The unit of thermal conductivity is:
A) W/mK
B) J/kg
C) N/m²
D) W

32. In a perfect gas, internal energy depends only on:
A) pressure
B) volume
C) temperature
D) density

33. First law of thermodynamics is based on conservation of:
A) mass
B) energy
C) momentum
D) charge

34. Entropy of an isolated system always:
A) decreases
B) increases
C) remains zero
D) becomes negative

35. Frequency of wave is measured in:
A) meter
B) hertz
C) joule
D) watt

36. In Young’s double slit experiment, fringe width depends on:
A) intensity
B) wavelength
C) mass
D) pressure

37. Diffraction is significant when slit size is comparable to:
A) wavelength
B) frequency
C) amplitude
D) speed

38. Polarization proves that light is:
A) longitudinal
B) transverse
C) sound wave
D) mechanical wave

39. In a semiconductor, majority carriers are:
A) electrons only
B) holes only
C) electrons or holes depending on type
D) ions

40. Energy of photon is proportional to:
A) wavelength
B) frequency
C) mass
D) speed

Chemistry (41–70)

41. The number of moles in 11 g of CO₂ is:
A) 0.1
B) 0.25
C) 0.5
D) 1

42. Molarity is defined as moles of solute per:
A) kg of solvent
B) litre of solution
C) litre of solvent
D) gram of solution

43. The hybridization of carbon in ethyne (C₂H₂) is:
A) sp
B) sp²
C) sp³
D) dsp²

44. Bond angle in water molecule is approximately:
A) 180°
B) 120°
C) 104.5°
D) 90°

45. The strongest intermolecular force is:
A) dipole-dipole
B) hydrogen bonding
C) London force
D) ionic bond

46. In periodic table, electronegativity generally:
A) decreases across period
B) increases across period
C) remains constant
D) random

47. Ionization energy increases with:
A) increase in atomic size
B) decrease in nuclear charge
C) increase in nuclear charge
D) shielding only

48. The most stable oxidation state of oxygen is:
A) -1
B) -2
C) +2
D) 0

49. Which has maximum metallic character?
A) Na
B) Mg
C) Al
D) Si

50. The bond in NaCl is:
A) covalent
B) ionic
C) metallic
D) hydrogen

51. The shape of NH₃ molecule is:
A) linear
B) trigonal planar
C) pyramidal
D) tetrahedral

52. pH of strong acid is generally:
A) 7
B) >7
C) <7
D) 14

53. Buffer solution resists change in:
A) mass
B) pH
C) volume
D) temperature

54. Oxidation is defined as loss of:
A) protons
B) neutrons
C) electrons
D) atoms

55. The oxidation state of Mn in KMnO₄ is:
A) +2
B) +4
C) +7
D) +6

56. In electrolysis, oxidation occurs at:
A) cathode
B) anode
C) both electrodes
D) solution only

57. Standard electrode potential is measured under:
A) 25°C and 1 atm
B) 0°C
C) 100°C
D) room pressure only

58. Rate of reaction increases with:
A) decrease in temperature
B) decrease in concentration
C) increase in temperature
D) decrease in surface area

59. Catalyst works by:
A) increasing activation energy
B) decreasing activation energy
C) increasing mass
D) decreasing temperature

60. Order of reaction is determined experimentally from:
A) formula
B) stoichiometry
C) rate law
D) periodic table

61. Benzene undergoes mainly:
A) addition reaction
B) substitution reaction
C) decomposition
D) polymerization

62. Functional group of aldehyde is:
A) -OH
B) -COOH
C) -CHO
D) -NH₂

63. IUPAC name of CH₄ is:
A) methane
B) ethane
C) propane
D) butane

64. Alkane general formula is:
A) CnH2n
B) CnH2n+2
C) CnHn
D) CnH2n-2

65. Isomers have same:
A) structure
B) properties
C) molecular formula
D) mass number

66. The gas used in welding is:
A) oxygen
B) acetylene
C) nitrogen
D) helium

67. Haber process is used to manufacture:
A) HCl
B) NH₃
C) CO₂
D) SO₂

68. Contact process produces:
A) nitric acid
B) sulphuric acid
C) hydrochloric acid
D) acetic acid

69. Hard water contains salts of:
A) sodium
B) calcium and magnesium
C) potassium
D) iron only

70. The most reactive halogen is:
A) iodine
B) bromine
C) chlorine
D) fluorine

MATHEMATICS

71. If f(x) = x² + 3x, then f'(x) is:
A) x + 3
B) 2x + 3
C) 2x
D) x²

72. Limit lim(x→0) (sin x / x) equals:
A) 0
B) 1
C) ∞
D) -1

73. If A is a singular matrix, then det(A) is:
A) 1
B) 0
C) -1
D) undefined

74. The derivative of constant is:
A) 1
B) 0
C) constant
D) x

75. ∫ x dx equals:
A) x
B) x²/2 + C
C) 2x
D) ln x

76. If vectors a and b are perpendicular, then a·b equals:
A) 1
B) -1
C) 0
D) 2

77. Cross product gives:
A) scalar
B) vector
C) number
D) zero always

78. Unit vector has magnitude:
A) 0
B) 1
C) 2
D) infinity

79. Equation of a line in slope form is:
A) y = mx + c
B) ax + by = c
C) x² + y²
D) y² = x

80. Distance between two points uses:
A) Pythagoras theorem
B) algebra
C) integration
D) probability

81. Equation of circle is:
A) x² + y² = r²
B) x + y = r
C) xy = r
D) x² – y²

82. Parabola standard form is:
A) x² = 4ay
B) x² + y² = 1
C) xy = 1
D) x + y = 0

83. Ellipse equation is:
A) x² + y² = 1
B) x²/a² + y²/b² = 1
C) xy = 1
D) x² – y² = 1

84. Hyperbola equation is:
A) x²/a² – y²/b² = 1
B) x² + y² = 1
C) xy = 1
D) x + y = 1

85. If D > 0 in quadratic equation, roots are:
A) equal
B) real and distinct
C) imaginary
D) zero

86. If D = 0, roots are:
A) imaginary
B) equal
C) distinct
D) complex

87. Probability of impossible event is:
A) 1
B) 0
C) -1
D) 2

88. Mean of data is:
A) most frequent
B) average
C) middle
D) range

89. Median is:
A) average
B) middle value
C) sum
D) product

90. Mode is:
A) least value
B) most frequent value
C) average
D) zero

91. Permutation formula is:
A) nCr
B) nPr
C) n!
D) r!

92. Combination formula is:
A) nPr
B) nCr
C) n!
D) r!

93. Value of 5! is:
A) 24
B) 120
C) 60
D) 100

94. log(ab) equals:
A) log a + log b
B) log a – log b
C) log a × log b
D) log a / log b

95. a^m × a^n equals:
A) a^(m+n)
B) a^(m-n)
C) a^(mn)
D) a^(m/n)

96. If function is continuous, graph is:
A) broken
B) smooth
C) jump
D) undefined

97. dy/dx of x³ is:
A) 2x
B) 3x²
C) x³
D) x²

98. ∫1 dx is:
A) 0
B) x + C
C) 1
D) x²

99. Maximum value of sin x is:
A) 0
B) 1
C) -1
D) 2

100. cos 0° equals:
A) 0
B) 1
C) -1
D) 2

101. If f(x) = sin x, then f'(x) is:
A) cos x
B) -cos x
C) sin x
D) -sin x

102. ∫ x² dx equals:
A) x³
B) x³/3 + C
C) 2x
D) ln x

103. If A is invertible matrix, then det(A) is:
A) 0
B) non-zero
C) 1 only
D) negative only

104. Gradient of a function gives:
A) slope
B) area
C) volume
D) distance

105. Maximum value of cos x is:
A) 0
B) 1
C) -1
D) 2

106. If two lines are parallel, slopes are:
A) reciprocal
B) equal
C) negative
D) zero

107. Distance formula is derived from:
A) integration
B) Pythagoras theorem
C) differentiation
D) probability

108. Vector addition follows:
A) triangle law
B) division law
C) subtraction law
D) none

109. Scalar product results in:
A) vector
B) scalar
C) matrix
D) zero always

110. Cross product results in:
A) scalar
B) vector
C) number
D) zero only


🔺 3D GEOMETRY

111. Direction cosines satisfy:
A) sum = 1
B) sum of squares = 1
C) product = 1
D) difference = 0

112. Equation of plane is:
A) ax + by + cz = d
B) x² + y² = z²
C) xy = z
D) x + y + z

113. Angle between two vectors uses:
A) dot product
B) cross product
C) integration
D) determinant

114. Unit vector has magnitude:
A) 0
B) 1
C) 2
D) infinity


📊 PROBABILITY & STATISTICS

115. Probability of sure event is:
A) 0
B) 1
C) -1
D) 2

116. Mean is also called:
A) median
B) average
C) mode
D) range

117. Median divides data into:
A) equal halves
B) quarters
C) thirds
D) none

118. Mode is:
A) least frequent
B) most frequent
C) average
D) middle

119. Variance measures:
A) central value
B) spread
C) frequency
D) sum

120. Standard deviation is:
A) variance²
B) √variance
C) variance/2
D) 2×variance


🔢 SEQUENCES & SERIES

121. AP nth term is:
A) a + nd
B) a + (n−1)d
C) arⁿ
D) n!

122. GP nth term is:
A) a + nd
B) arⁿ⁻¹
C) a/n
D) n²

123. Sum of AP formula is:
A) n/2[2a + (n−1)d]
B) a + b
C) n²
D) ar

124. Sum of GP is valid when:
A) r = 1
B) |r| < 1
C) r > 1
D) r = 0 only


🔥 CALCULUS APPLICATIONS

125. Increasing function has:
A) positive derivative
B) negative derivative
C) zero derivative
D) infinite derivative

126. Decreasing function has:
A) positive slope
B) negative slope
C) zero slope
D) constant slope

127. Maximum occurs when:
A) f'(x)=0 and f”(x)<0
B) f'(x)=1
C) f(x)=0
D) derivative undefined

128. Minimum occurs when:
A) f'(x)=0 and f”(x)>0
B) f'(x)=1
C) f(x)=0
D) slope infinite


📐 CONICS

129. Eccentricity of circle is:
A) 0
B) 1
C) >1
D) <0

130. Parabola eccentricity is:
A) 0
B) 1
C) >1
D) <1

131. Hyperbola eccentricity is:
A) <1
B) =1
C) >1
D) 0


🧮 ADVANCED ALGEBRA

132. If log a + log b = log(ab), it is based on:
A) multiplication law
B) addition law
C) subtraction law
D) division law

133. a^m / a^n =
A) a^(m+n)
B) a^(m−n)
C) a^(mn)
D) a^(m/n)

134. (a+b)³ expansion has:
A) 2 terms
B) 3 terms
C) 4 terms
D) 6 terms


INTEGRATION & DIFFERENTIATION

151. ∫ 1/x dx equals:
A) x
B) ln x + C
C) 1/x²
D) eˣ

152. Derivative of eˣ is:
A) 0
B) eˣ
C) x eˣ
D) 1

153. If y = x² + 2x, dy/dx =
A) x + 2
B) 2x + 2
C) 2x
D) x²

154. ∫ eˣ dx =
A) eˣ + C
B) xeˣ
C) 1/eˣ
D) 0

155. Maximum value of sin x is:
A) 0
B) 1
C) -1
D) 2

156. Minimum value of cos x is:
A) 1
B) 0
C) -1
D) 2

157. If f'(x)=0, function is:
A) increasing
B) decreasing
C) stationary
D) undefined


📐 VECTORS & 3D GEOMETRY

158. Dot product of perpendicular vectors is:
A) 1
B) 0
C) -1
D) 2

159. Cross product gives:
A) scalar
B) vector
C) number
D) zero always

160. Magnitude of unit vector is:
A) 0
B) 1
C) 2
D) infinity

161. Scalar triple product gives:
A) vector
B) scalar
C) matrix
D) zero always

162. Volume of parallelepiped uses:
A) dot product
B) scalar triple product
C) integration
D) determinant only

163. Direction ratios represent:
A) magnitude
B) direction
C) area
D) force

164. Equation of line in 3D uses:
A) one point + direction vector
B) only slope
C) only intercept
D) only origin


📊 PROBABILITY (ADVANCED)

165. Probability value lies between:
A) -1 to 1
B) 0 to 1
C) 1 to 2
D) 0 to 100

166. If A and B are independent:
A) P(A∩B)=P(A)+P(B)
B) P(A∩B)=P(A)P(B)
C) P(A∪B)=0
D) P(A)=P(B)

167. Conditional probability is:
A) P(A|B)
B) P(A+B)
C) P(A−B)
D) P(AB) only

168. Total probability theorem is used for:
A) single event
B) multiple partitions
C) geometry
D) vectors


🔢 MATRICES & DETERMINANTS

169. If det(A)=0, matrix is:
A) invertible
B) singular
C) identity
D) diagonal

170. Inverse exists when determinant is:
A) 0
B) 1
C) non-zero
D) negative

171. Identity matrix has diagonal elements:
A) 0
B) 1
C) 2
D) -1

172. Rank of matrix depends on:
A) size only
B) independent rows/columns
C) determinant only
D) trace


📘 SEQUENCES & SERIES

173. Infinite GP converges when:
A) r>1
B) |r|<1
C) r=1
D) r=0 only

174. Sum of infinite GP is:
A) a/(1-r)
B) a(1-r)
C) ar
D) a+r

175. Arithmetic mean is:
A) product/n
B) sum/n
C) difference
D) ratio


🔥 HIGHER FUNCTIONS

176. If f(x)=|x|, derivative at 0 is:
A) 0
B) undefined
C) 1
D) -1

177. Continuity requires:
A) left limit only
B) right limit only
C) both limits equal
D) derivative only


📐 CONICS FINAL

178. Focus of parabola lies:
A) at vertex
B) on axis
C) outside curve
D) at origin always

179. Eccentricity of ellipse is:
A) 0
B) between 0 and 1
C) 1
D) >1

180. Hyperbola has eccentricity:
A) <1
B) =1
C) >1
D) 0


🧠 MIXED ADVANCED MCQs

181. If sin²x + cos²x = ?
A) 0
B) 1
C) 2
D) x

182. tan x = sin x / cos x is valid when:
A) cos x ≠ 0
B) sin x = 0
C) x = 0 only
D) always false

183. log 1 equals:
A) 1
B) 0
C) ∞
D) -1

184. e⁰ equals:
A) 0
B) 1
C) e
D) ∞

185. derivative of constant is:
A) 1
B) 0
C) constant
D) x


🎯 FINAL CONCEPTS

186. If function is increasing:
A) derivative <0
B) derivative >0
C) derivative =0
D) undefined

187. Stationary point occurs when:
A) f'(x)=0
B) f(x)=0
C) f”(x)=0
D) f(x)=1

188. Maximum curvature depends on:
A) f”(x)
B) f(x)
C) f'(x)
D) integral

189. Area under curve uses:
A) differentiation
B) integration
C) algebra
D) vectors

190. Definite integral gives:
A) slope
B) area
C) vector
D) matrix

191. The value of sin 0° is:
A) 1
B) 0
C) -1
D) Undefined

192. The value of cos 0° is:
A) 0
B) 1
C) -1
D) 2

193. The value of tan 0° is:
A) 0
B) 1
C) Undefined
D) -1

194. The limit lim (x → ∞) (1/x) is:
A) 1
B) 0
C) ∞
D) -∞

195. The value of i² in complex numbers is:
A) 1
B) -1
C) 0
D) i

196. The determinant of a matrix geometrically represents:
A) only length
B) scaling factor of area/volume
C) time change
D) probability

197. Derivative of a function represents:
A) total value
B) rate of change
C) area under curve
D) constant value

198. Integral of a function represents:
A) slope
B) accumulation/area under curve
C) difference
D) ratio

199. Probability of an event measures:
A) certainty of error
B) likelihood of occurrence
C) total outcomes
D) average value

200. Mathematics is primarily based on:
A) memory
B) logical reasoning
C) guessing
D) observation only


QAnsQAnsQAnsQAns
1B2C3B4C
5C6B7B8B
9C10C11B12B
13B14B15C16A
17B18C19B20C
21B22C23C24A
25B26B27B28C
29C30A31A32C
33B34B35B36B
37A38B39C40B
41A42B43A44C
45B46B47C48B
49A50B51B52C
53B54C55C56B
57A58B59C60B
61B62C63A64B
65C66B67B68B
69B70D71B72B
73B74B75B76C
77B78B79A80A
81A82A83B84A
85B86B87B88B
89B90B91A92B
93B94B95B96B
97B98B99B100B
101A102B103B104A
105B106B107B108A
109B110B111B112A
113A114B115B116B
117A118B119A120B
121B122A123B124B
125A126B127A128A
129B130B131A132B
133B134B135B136A
137B138B139B140B
141A142A143A144B
145B146A147B148B
149B150A151B152B
153B154A155B156C
157C158B159B160B
161B162B163B164A
165B166B167A168B
169B170C171B172B
173B174A175B176B
177C178B179B180C
181B182A183B184B
185B186B187A188A
189B190B191B192B
193A194B195B196B
197B198B199B200B