CG PET Mock Test Paper with Answer Key

CG PET Mock Test Paper with Answer Key

CG PET – Sample Question Paper 2026

Duration: 3 Hours
Total Questions: 150
Subjects: Physics (50), Chemistry (50), Mathematics (50)
Total Marks: 150
Type: Multiple Choice Questions (MCQs)
Negative Marking: As per official pattern (if applicable)

SECTION A – PHYSICS (1–50)

  1. A particle moves with constant speed in a circle. Its acceleration is:
    A. Zero
    B. Tangential
    C. Centripetal
    D. Constant linear
  2. The dimensional formula of Planck’s constant is:
    A. ML²T⁻¹
    B. ML²T⁻²
    C. MLT⁻¹
    D. ML⁻¹T
  3. Two resistors 6Ω and 3Ω are in parallel. Equivalent resistance is:
    A. 9Ω
    B. 2Ω
    C. 4Ω
    D. 1.5Ω
  4. The escape velocity from Earth is approximately:
    A. 7.9 km/s
    B. 9.8 km/s
    C. 11.2 km/s
    D. 15 km/s
  5. A body projected vertically upward returns to ground in 4 s. Maximum height is (g=10 m/s²):
    A. 5 m
    B. 10 m
    C. 20 m
    D. 40 m
  6. The electric field inside a conductor in electrostatic equilibrium is:
    A. Maximum
    B. Minimum
    C. Zero
    D. Infinite
  7. Work done in moving charge q through potential difference V is:
    A. q/V
    B. V/q
    C. qV
    D. V²/q
  8. Young’s modulus is stress divided by:
    A. Force
    B. Area
    C. Strain
    D. Volume
  9. The unit of magnetic flux is:
    A. Tesla
    B. Weber
    C. Henry
    D. Gauss
  10. If wavelength increases, frequency:
    A. Increases
    B. Decreases
    C. Remains same
    D. Becomes zero
  11. The time period of simple pendulum depends on:
    A. Mass
    B. Amplitude
    C. Length
    D. Density
  12. A convex lens of focal length 20 cm. Power is:
    A. +5 D
    B. −5 D
    C. +0.5 D
    D. −0.5 D
  13. Energy stored in capacitor is:
    A. CV
    B. ½ CV²
    C. C/V
    D. V²/C
  14. The dimensional formula of force is:
    A. MLT⁻²
    B. ML²T⁻²
    C. MLT⁻¹
    D. ML²T⁻¹
  15. A body of mass 2 kg has kinetic energy 100 J. Velocity is:
    A. 5 m/s
    B. 10 m/s
    C. 20 m/s
    D. 25 m/s
  16. The moment of inertia depends on:
    A. Mass only
    B. Shape only
    C. Axis of rotation
    D. Colour
  17. In resonance, amplitude is:
    A. Minimum
    B. Zero
    C. Maximum
    D. Constant
  18. The unit of electric dipole moment is:
    A. Coulomb
    B. Coulomb-meter
    C. Volt
    D. Newton
  19. Gauss’s law relates electric field with:
    A. Charge
    B. Mass
    C. Velocity
    D. Power
  20. Drift velocity is proportional to:
    A. Temperature
    B. Electric field
    C. Resistance
    D. Length
  21. Lenz’s law is based on conservation of:
    A. Charge
    B. Mass
    C. Energy
    D. Momentum
  22. The refractive index is ratio of:
    A. Speeds
    B. Frequencies
    C. Wavelengths
    D. Intensities
  23. The SI unit of inductance is:
    A. Ohm
    B. Henry
    C. Weber
    D. Tesla
  24. Nuclear fission produces:
    A. Light nuclei
    B. Heavy nuclei
    C. Neutrons
    D. Electrons
  25. Angular momentum is conserved when:
    A. Net torque is zero
    B. Force is zero
    C. Mass is zero
    D. Velocity constant
  26. The de Broglie wavelength is inversely proportional to:
    A. Mass
    B. Momentum
    C. Charge
    D. Energy
  27. In AC circuit, average power depends on:
    A. Current only
    B. Voltage only
    C. Power factor
    D. Frequency only
  28. A transformer works on:
    A. DC
    B. AC
    C. Battery
    D. Static charge
  29. Terminal velocity depends on:
    A. Density of fluid
    B. Shape
    C. Radius
    D. All
  30. The intensity of sound is proportional to square of:
    A. Frequency
    B. Amplitude
    C. Velocity
    D. Time
  31. Pressure at 10 m depth in water (ρ=1000 kg/m³):
    A. 10⁵ Pa
    B. 10⁴ Pa
    C. 10⁶ Pa
    D. 10³ Pa
  32. 2μF and 3μF in series. Equivalent:
    A. 5μF
    B. 1.2μF
    C. 6μF
    D. 0.5μF
  33. A wire stretched to double length. Resistance becomes:
    A. R
    B. 2R
    C. 3R
    D. 4R
  34. If KE doubles, momentum becomes:
    A. Double
    B. √2 times
    C. Half
    D. Same
  35. Torque =
    A. rF
    B. r×F
    C. r/F
    D. F/r
  36. The stopping potential depends on:
    A. Intensity
    B. Frequency
    C. Work function only
    D. Temperature
  37. Magnetic field inside solenoid is proportional to:
    A. Length
    B. Current
    C. Resistance
    D. Area
  38. RMS value of AC current is:
    A. I₀
    B. I₀/√2
    C. √2 I₀
    D. I₀/2
  39. Radius of gyration relates to:
    A. I = Mk²
    B. I = M/k²
    C. I = k/M
    D. I = Mk
  40. Mechanical advantage of ideal machine is:
    A. <1
    B. =1
    C. >1
    D. 0
  41. A photon has zero:
    A. Energy
    B. Momentum
    C. Rest mass
    D. Frequency
  42. If gravitational force doubles, distance becomes:
    A. d/√2
    B. 2d
    C. √2 d
    D. d²
  43. SI unit of surface tension:
    A. N/m
    B. N
    C. Pa
    D. J
  44. Critical angle depends on:
    A. Refractive index
    B. Angle of incidence
    C. Thickness
    D. Colour
  45. A body in SHM has maximum velocity at:
    A. Mean position
    B. Extreme
    C. Half amplitude
    D. Anywhere
  46. Electric potential is scalar because:
    A. Has no direction
    B. Has magnitude
    C. Is force
    D. Is energy
  47. The half-life formula relates to:
    A. Linear decay
    B. Exponential decay
    C. Uniform motion
    D. Collision
  48. Bohr model applies to:
    A. Hydrogen atom
    B. Heavy atoms
    C. Molecules
    D. Solids
  49. The work done in isothermal process depends on:
    A. Pressure
    B. Volume
    C. Temperature
    D. Path
  50. Entropy increases in:
    A. Reversible process
    B. Irreversible process
    C. Static process
    D. Ideal process

SECTION B – CHEMISTRY (51–100)

  1. The number of moles in 44 g CO₂:
    A. 1
    B. 2
    C. 0.5
    D. 22
  2. pH of 10⁻³ M HCl:
    A. 1
    B. 2
    C. 3
    D. 11
  3. Oxidation number of S in H₂SO₄:
    A. +4
    B. +6
    C. −2
    D. 0
  4. Hybridization of carbon in CH₄:
    A. sp
    B. sp²
    C. sp³
    D. dsp²
  5. The unit of rate constant for first order reaction:
    A. s⁻¹
    B. mol L⁻¹
    C. L mol⁻¹ s⁻¹
    D. s
  6. Faraday constant is:
    A. 96500 C
    B. 8.314
    C. 6.023×10²³
    D. 1.6×10⁻¹⁹
  7. Strongest reducing agent:
    A. Na
    B. Cu
    C. Ag
    D. Au
  8. Boyle’s law:
    A. PV=constant
    B. V/T=constant
    C. P/T=constant
    D. PT=constant
  9. Atomic radius decreases across period due to:
    A. Shielding
    B. Nuclear charge
    C. Electrons
    D. Mass
  1. Number of atoms in 1 mole is:
    A. 6.023×10²³
    B. 6.023×10²²
    C. 9.8×10²³
    D. 1.6×10⁻¹⁹
  2. Standard temperature is:
    A. 273 K
    B. 298 K
    C. 300 K
    D. 0 K
  3. Catalyst changes:
    A. ΔH
    B. Rate
    C. Equilibrium
    D. Products
  4. The shape of NH₃:
    A. Trigonal planar
    B. Tetrahedral
    C. Trigonal pyramidal
    D. Linear
  5. Strongest acid:
    A. HF
    B. HCl
    C. HBr
    D. HI

65. The SI unit of entropy is:

A. J
B. J/mol
C. J/mol·K
D. J/K

66. The most electronegative element is:

A. Oxygen
B. Nitrogen
C. Fluorine
D. Chlorine

67. Oxidation is defined as:

A. Gain of electrons
B. Loss of electrons
C. Gain of protons
D. Loss of neutrons

68. The unit of molarity is:

A. mol/kg
B. mol/L
C. g/L
D. mol/m³

69. The ideal gas equation is:

A. PV = RT
B. PV = nRT
C. P = nRT
D. V = nRT

70. The order of a reaction is:

A. Molecularity
B. Sum of powers of concentration terms
C. Stoichiometric coefficient
D. Rate constant

71. A buffer solution resists change in:

A. Volume
B. Temperature
C. pH
D. Pressure

72. Temporary hardness of water is due to presence of:

A. NaCl
B. CaSO₄
C. Ca(HCO₃)₂
D. MgCl₂

73. The molecular formula of ozone is:

A. O₂
B. O₃
C. O₄
D. O₅

74. The hybridization of carbon in benzene is:

A. sp
B. sp²
C. sp³
D. dsp²

75. The functional group of aldehydes is:

A. –COOH
B. –OH
C. –CHO
D. –CO–

76. Proteins are polymers of:

A. Glucose
B. Fatty acids
C. Amino acids
D. Nucleotides

77. A galvanic cell converts:

A. Electrical energy to chemical energy
B. Chemical energy to electrical energy
C. Mechanical energy to electrical energy
D. Heat energy to electrical energy

78. A strong electrolyte:

A. Partially ionizes
B. Does not ionize
C. Completely ionizes
D. Forms precipitate

79. Gibbs free energy is given by:

A. ΔG = ΔH + TΔS
B. ΔG = ΔH − TΔS
C. ΔG = TΔS − ΔH
D. ΔG = ΔH/T

80. The particle size in colloids ranges approximately:

A. <1 nm
B. 1–1000 nm
C. >1000 nm
D. >1 mm

81. Avogadro’s number is:

A. 6.023 × 10²³
B. 6.023 × 10²²
C. 9.8 × 10²³
D. 1.6 × 10⁻¹⁹

82. An endothermic reaction:

A. Releases heat
B. Absorbs heat
C. Has ΔH negative
D. Has ΔG negative always

83. Modern periodic law is based on:

A. Atomic mass
B. Atomic number
C. Valency
D. Density

84. Nitrogen dioxide (NO₂) is:

A. Neutral oxide
B. Basic oxide
C. Acidic oxide
D. Amphoteric oxide

85. Rust is chemically:

A. FeO
B. Fe₂O₃
C. Fe₂O₃·xH₂O
D. Fe₃O₄

86. The molecular formula of ethanol is:

A. CH₃OH
B. C₂H₆
C. C₂H₅OH
D. C₃H₇OH

87. According to Le Chatelier’s principle, increasing pressure favors reaction with:

A. More moles of gas
B. Fewer moles of gas
C. Equal moles
D. Solid products

88. Activation energy is:

A. Total energy of system
B. Minimum energy to start reaction
C. Energy of products
D. Energy of reactants

89. Electrolysis requires:

A. AC current
B. DC current
C. Heat
D. Catalyst

90. Aromatic compounds follow:

A. Markovnikov rule
B. Huckel rule
C. Raoult’s law
D. Henry’s law

91. Ammonia in water behaves as:

A. Strong acid
B. Strong base
C. Weak base
D. Neutral

92. Noble gases are chemically:

A. Highly reactive
B. Inert
C. Metallic
D. Acidic

93. In diamond, carbon is:

A. sp
B. sp²
C. sp³
D. dsp²

94. Alkaline earth metals belong to:

A. Group 1
B. Group 2
C. Group 17
D. Group 18

95. Transition elements belong to:

A. s-block
B. p-block
C. d-block
D. f-block

96. A redox reaction involves:

A. Acid-base reaction
B. Only reduction
C. Only oxidation
D. Oxidation and reduction

97. The valency of carbon is:

A. 2
B. 3
C. 4
D. 6

98. Hydrolysis is reaction with:

A. Oxygen
B. Hydrogen
C. Water
D. Acid

99. A covalent bond is formed by:

A. Electron transfer
B. Proton transfer
C. Electron sharing
D. Neutron transfer

100. Isotopes have same:

A. Mass number
B. Atomic number
C. Neutrons
D. Mass

SECTION C – MATHEMATICS (101–150)

(Difficult algebra, calculus, coordinate geometry, trigonometry)

  1. If log₁₀2=0.3010, log₁₀5= ?
    A. 0.6990
    B. 0.3010
    C. 1
    D. 0
  2. Determinant of |1 2; 3 4| =
    A. −2
    B. 2
    C. 10
    D. −10
  3. d/dx (x² sinx) =
    A. 2x sinx + x² cosx
    B. x² cosx
    C. 2x cosx
    D. sinx
  4. ∫x dx =
    A. x²
    B. x²/2 + C
    C. 2x
    D. ln x
  5. sin²θ + cos²θ = 1
  6. If A.P. first term 2, d=3, 10th term=?
    A. 29
    B. 30
    C. 32
    D. 35
  7. Equation of circle x²+y²=25 radius=?
    A. 25
    B. 5
    C. √25
    D. 10

108. The probability of getting a head when a fair coin is tossed once is:

A. 0
B. 1
C. 1/2
D. 1/4

109. Matrix multiplication AB is possible if:

A. Rows of A = Rows of B
B. Columns of A = Columns of B
C. Columns of A = Rows of B
D. Rows of A = Columns of B

110. The roots of quadratic equation ax² + bx + c = 0 are given by:

A. (−b ± √(b² − 4ac)) / a
B. (b ± √(b² − 4ac)) / 2a
C. (−b ± √(b² − 4ac)) / 2a
D. (−b ± √(4ac − b²)) / 2a

111. lim⁡x→0sin⁡xx=\lim_{x→0} \frac{\sin x}{x} =limx→0​xsinx​=

A. 0
B. 1
C. ∞
D. −1

112. The identity for cos(A − B) is:

A. cosA cosB − sinA sinB
B. cosA cosB + sinA sinB
C. sinA cosB − cosA sinB
D. sinA sinB + cosA cosB

113. The value of tan 45° is:

A. 0
B. 1
C. √3
D. −1

114. If determinant of coefficient matrix is zero, system of linear equations is:

A. Always consistent
B. Always inconsistent
C. May have infinitely many or no solutions
D. Unique solution

115. The dot product of two perpendicular vectors is:

A. 1
B. −1
C. 0
D. Infinite

116. Distance between points (x₁,y₁) and (x₂,y₂) is:

A. (x₂−x₁)+(y₂−y₁)
B. √[(x₂−x₁)²+(y₂−y₁)²]
C. (x₂−x₁)²+(y₂−y₁)²
D. √(x₁x₂+y₁y₂)

117. The value of e⁰ is:

A. 0
B. 1
C. e
D. −1

118. ln(1) equals:

A. 0
B. 1
C. e
D. −1

119. Slope of line passing through (1,2) and (3,6) is:

A. 1
B. 2
C. 3
D. 4

120. The value of ⁵C₂ is:

A. 5
B. 10
C. 15
D. 20

121. In binomial expansion of (1 + x)ⁿ, coefficient of x is:

A. n
B. n²
C. 1
D. n/2

122. If z = a + ib, then |z| equals:

A. a + b
B. √(a² + b²)
C. a² + b²
D. a − b

123. Equation of straight line with slope m and intercept c is:

A. y = mx
B. x = my + c
C. y = mx + c
D. x + y = c

124. ∫ eˣ dx equals:

A. eˣ
B. eˣ + C
C. ln x
D. x eˣ

125. Arithmetic mean of n observations is:

A. Σx
B. Σx/n
C. n/Σx
D. Σx²

126. Variance is:

A. Square root of mean
B. Mean of deviations
C. Mean of squared deviations
D. Square of mean

127. The cosine rule is:

A. a² = b² + c² − 2bc cosA
B. a² = b² + c² + 2bc cosA
C. a² = b² − c²
D. a = b + c

128. Derivative of eˣ is:

A. x eˣ
B. eˣ
C. ln x
D. 1/x

129. Integration by parts formula is:

A. ∫u dv = uv + ∫v du
B. ∫u dv = uv − ∫v du
C. ∫u dv = u/v
D. ∫u dv = v/u

130. If A is 2×2 matrix, |kA| equals:

A. k|A|
B. k²|A|
C. |A|/k
D. |A|

131. The cross product of two parallel vectors is:

A. 1
B. Infinite
C. 0
D. −1

132. The inverse of matrix A exists if:

A. |A| = 0
B. |A| ≠ 0
C. A is square
D. A is symmetric

133. The domain of 1/(x − 2) is:

A. All real numbers
B. x ≠ 2
C. x = 2
D. x > 2

134. Range of sinθ is:

A. (−∞,∞)
B. [0,1]
C. [−1,1]
D. (0,1)

135. Geometric mean of a and b is:

A. (a+b)/2
B. √(ab)
C. ab
D. a−b

136. Standard deviation is:

A. Variance
B. Square root of variance
C. Mean
D. Median

137. Identity 1 + tan²θ equals:

A. sec²θ
B. cosec²θ
C. cos²θ
D. sin²θ

138. Angle between two lines with slopes m₁ and m₂ is given by:

A. tanθ = m₁ + m₂
B. tanθ = (m₁ − m₂)/(1 + m₁m₂)
C. tanθ = (m₁ + m₂)/(1 − m₁m₂)
D. tanθ = m₁m₂

139. Order of differential equation is:

A. Power of derivative
B. Highest derivative
C. Degree of function
D. Variable

140. Probability of an impossible event is:

A. 1
B. −1
C. 0
D. 1/2

141. Sample space represents:

A. Favorable outcomes
B. Total possible outcomes
C. Required outcomes
D. None

142. For independent events A and B:

A. P(A∪B)=P(A)+P(B)
B. P(A∩B)=P(A)P(B)
C. P(A|B)=P(A)
D. P(A)=P(B)

143. Relation between HCF and LCM of two numbers is:

A. Product = HCF + LCM
B. Product = HCF × LCM
C. HCF = LCM
D. None

144. Rationalizing denominator means removing:

A. Numerator
B. Fraction
C. Surd from denominator
D. Variable

145. log(ab) equals:

A. log a − log b
B. log a + log b
C. log a × log b
D. log a / log b

146. The transpose of matrix A is denoted by:

A. A⁻¹
B. |A|
C. Aᵀ
D. adj A

147. Rank of a matrix is:

A. Determinant
B. Number of rows
C. Maximum number of linearly independent rows/columns
D. Trace

148. If a function is one-one and onto, it is:

A. Injective
B. Surjective
C. Bijective
D. Constant

149. Sum of infinite GP with |r|<1 is:

A. a/(1−r)
B. a/(1+r)
C. ar/(1−r)
D. a+r

150. If f(x)=x³, then f′(2) equals:

A. 6
B. 8
C. 12
D. 4

Disclaimer

“This is a sample paper created for practice purposes only. It is inspired by CG Vyapam syllabus and previous year trends, and is not an official exam paper.

Answer

Complete Answer Key (1–150)

Q.NoAnsQ.NoAnsQ.NoAnsQ.NoAnsQ.NoAns
1C31A61C91C121A
2A32B62B92B122B
3B33D63C93C123C
4C34B64D94B124B
5C35B65C95C125B
6C36C66C96D126C
7C37B67B97C127A
8C38B68B98C128B
9B39A69B99C129B
10B40C70B100B130B
11C41C71C101B131C
12A42C72C102A132C
13B43A73B103A133B
14A44A74B104B134B
15B45A75C105A135B
16C46A76C106A136B
17C47B77B107B137A
18B48A78C108C138B
19A49D79B109C139B
20B50B80B110C140C
21C51A81A111B141B
22B52C82B112B142B
23A53B83B113B143B
24C54C84C114C144C
25A55A85C115C145B
26B56A86C116B146C
27C57A87B117B147C
28B58A88B118A148C
29D59B89B119B149A
30B60A90B120B150B