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
| Q | Ans | Q | Ans | Q | Ans | Q | Ans |
|---|
| 1 | B | 2 | C | 3 | B | 4 | C |
| 5 | C | 6 | B | 7 | B | 8 | B |
| 9 | C | 10 | C | 11 | B | 12 | B |
| 13 | B | 14 | B | 15 | C | 16 | A |
| 17 | B | 18 | C | 19 | B | 20 | C |
| 21 | B | 22 | C | 23 | C | 24 | A |
| 25 | B | 26 | B | 27 | B | 28 | C |
| 29 | C | 30 | A | 31 | A | 32 | C |
| 33 | B | 34 | B | 35 | B | 36 | B |
| 37 | A | 38 | B | 39 | C | 40 | B |
| 41 | A | 42 | B | 43 | A | 44 | C |
| 45 | B | 46 | B | 47 | C | 48 | B |
| 49 | A | 50 | B | 51 | B | 52 | C |
| 53 | B | 54 | C | 55 | C | 56 | B |
| 57 | A | 58 | B | 59 | C | 60 | B |
| 61 | B | 62 | C | 63 | A | 64 | B |
| 65 | C | 66 | B | 67 | B | 68 | B |
| 69 | B | 70 | D | 71 | B | 72 | B |
| 73 | B | 74 | B | 75 | B | 76 | C |
| 77 | B | 78 | B | 79 | A | 80 | A |
| 81 | A | 82 | A | 83 | B | 84 | A |
| 85 | B | 86 | B | 87 | B | 88 | B |
| 89 | B | 90 | B | 91 | A | 92 | B |
| 93 | B | 94 | B | 95 | B | 96 | B |
| 97 | B | 98 | B | 99 | B | 100 | B |
| 101 | A | 102 | B | 103 | B | 104 | A |
| 105 | B | 106 | B | 107 | B | 108 | A |
| 109 | B | 110 | B | 111 | B | 112 | A |
| 113 | A | 114 | B | 115 | B | 116 | B |
| 117 | A | 118 | B | 119 | A | 120 | B |
| 121 | B | 122 | A | 123 | B | 124 | B |
| 125 | A | 126 | B | 127 | A | 128 | A |
| 129 | B | 130 | B | 131 | A | 132 | B |
| 133 | B | 134 | B | 135 | B | 136 | A |
| 137 | B | 138 | B | 139 | B | 140 | B |
| 141 | A | 142 | A | 143 | A | 144 | B |
| 145 | B | 146 | A | 147 | B | 148 | B |
| 149 | B | 150 | A | 151 | B | 152 | B |
| 153 | B | 154 | A | 155 | B | 156 | C |
| 157 | C | 158 | B | 159 | B | 160 | B |
| 161 | B | 162 | B | 163 | B | 164 | A |
| 165 | B | 166 | B | 167 | A | 168 | B |
| 169 | B | 170 | C | 171 | B | 172 | B |
| 173 | B | 174 | A | 175 | B | 176 | B |
| 177 | C | 178 | B | 179 | B | 180 | C |
| 181 | B | 182 | A | 183 | B | 184 | B |
| 185 | B | 186 | B | 187 | A | 188 | A |
| 189 | B | 190 | B | 191 | B | 192 | B |
| 193 | A | 194 | B | 195 | B | 196 | B |
| 197 | B | 198 | B | 199 | B | 200 | B |