GUJCET Mock Test – Physics, Chemistry & Mathematics Practice Paper

Subject	No. of Questions	Marks per Question	Total Marks	Topics Covered
Physics	35	1	35	Mechanics, Properties of Matter, Thermodynamics, Waves, Optics, Modern Physics, Current Electricity, Magnetism, EM Induction
Chemistry	35	1	35	Physical Chemistry, Inorganic Chemistry, Organic Chemistry, High-difficulty mixed questions
Mathematics	50	1	50	Algebra, Quadratic Equations, Trigonometry, Heights & Distances, Coordinate Geometry, Probability, Vectors, Statistics, Calculus
Total	120	1	120	All major GUJCET topics

Section A: Mechanics & Properties of Matter

Q1. A block slides down a frictionless inclined plane of angle 30° and height 2 m. The speed of the block at the bottom is:
A) 2 m/s
B) 4 m/s
C) $\sqrt{20}$ 20 m/s
D) $2\sqrt{2}$ 22 m/s

Q2. Two masses, 3 kg and 6 kg, are connected by a light string over a frictionless pulley. The acceleration of the system is:
A) 5 m/s²
B) 3.27 m/s²
C) 2.5 m/s²
D) 1 m/s²

Q3. A circular disk rotates with an angular velocity of 10 rad/s. The time taken to complete one full rotation is:
A) 0.1 s
B) 0.314 s
C) 0.628 s
D) 1 s

Q4. A body of mass 2 kg is moving in a circle of radius 1 m with velocity 4 m/s. The centripetal force is:
A) 4 N
B) 8 N
C) 16 N
D) 32 N

Q5. A spring of force constant 100 N/m is compressed by 0.1 m. The potential energy stored in the spring is:
A) 0.5 J
B) 1 J
C) 2 J
D) 5 J

Section B: Thermodynamics & Waves

Q6. One mole of an ideal gas expands isothermally at 300 K from 10 L to 20 L. Work done by the gas is approximately:
A) 1.7 kJ
B) 2.1 kJ
C) 0.7 kJ
D) 3 kJ

Q7. Two sound waves of frequencies 256 Hz and 260 Hz interfere. The beat frequency is:
A) 2 Hz
B) 4 Hz
C) 6 Hz
D) 8 Hz

Q8. The ratio of specific heats $\gamma = \frac{C_p}{C_v}$ γ=CvCp for a monoatomic gas is:
A) 5/3
B) 7/5
C) 4/3
D) 3/2

Q9. A body oscillates in simple harmonic motion with amplitude 5 cm and period 2 s. The maximum speed of the body is:
A) 0.05 m/s
B) 0.078 m/s
C) 0.157 m/s
D) 0.314 m/s

Q10. The frequency of a wave on a string is 50 Hz and wavelength 0.2 m. Its speed is:
A) 10 m/s
B) 20 m/s
C) 25 m/s
D) 100 m/s

Section C: Optics & Modern Physics

Q11. The critical angle for the interface between glass (refractive index 1.5) and air is:
A) 30°
B) 41.8°
C) 45°
D) 48.5°

Q12. Light of wavelength 600 nm falls on a diffraction grating with 5000 lines/cm. The angle for the first-order maximum is:
A) 18°
B) 25°
C) 30°
D) 45°

Q13. In a photoelectric experiment, the stopping potential is 2 V. The kinetic energy of emitted electrons is:
A) 1 eV
B) 2 eV
C) 4 eV
D) 0.5 eV

Q14. The half-life of a radioactive substance is 10 hours. The fraction remaining after 30 hours is:
A) 1/8
B) 1/4
C) 1/2
D) 1/16

Q15. The energy of a photon of wavelength 500 nm is approximately:
A) 2.48 eV
B) 3.0 eV
C) 4.14 eV
D) 1.24 eV

Section D: Electromagnetism & Current Electricity

Q16. A wire of resistance 4 Ω carries a current of 2 A. The potential difference across it is:
A) 2 V
B) 4 V
C) 6 V
D) 8 V

Q17. Two resistors, 6 Ω and 3 Ω, are connected in parallel. The equivalent resistance is:
A) 2 Ω
B) 3 Ω
C) 4 Ω
D) 9 Ω

Q18. A coil of inductance 2 H carries a current increasing at 3 A/s. The induced emf is:
A) 2 V
B) 4 V
C) 6 V
D) 8 V

Q19. A capacitor of 10 μF is connected to 100 V DC. The energy stored is:
A) 0.05 J
B) 0.5 J
C) 5 J
D) 50 J

Q20. The current in a series RC circuit is maximum at:
A) Resonance
B) Cut-off frequency
C) Zero frequency
D) Infinite frequency

Section E: Magnetism & Electromagnetic Induction

Q21. A magnetic field of 0.2 T acts perpendicular to a 0.5 m long wire carrying 3 A. The magnetic force on the wire is:
A) 0.1 N
B) 0.2 N
C) 0.3 N
D) 0.5 N

Q22. Two long parallel wires carry equal currents in opposite directions. The force per unit length between them is:
A) Attractive
B) Repulsive
C) Zero
D) Varies with distance

Q23. The flux linked with a coil changes from 0.5 Wb to 0.1 Wb in 0.2 s. The induced emf is:
A) 2 V
B) 1 V
C) 4 V
D) 0.5 V

Q24. A solenoid of 50 turns/m carries current of 2 A. Magnetic field inside is approximately:
A) 0.13 T
B) 0.63 T
C) 0.13 mT
D) 0.63 mT

Q25. The unit of magnetic moment is:
A) A·m²
B) T·m²
C) N·m
D) Wb

Section F: High-Difficulty & Conceptual Questions

Q26. Two identical capacitors are connected in series and charged to a voltage V. The energy stored in each capacitor is:
A) Same as in a single capacitor
B) Half of a single capacitor
C) Double of a single capacitor
D) Zero

Q27. The ratio of electric field at the center to that at the edge of a uniformly charged ring is:
A) 1:1
B) 2:1
C) 1:2
D) 0

Q28. In a plane electromagnetic wave in vacuum, the ratio of electric to magnetic field amplitude is:
A) c²
B) c
C) 1/c
D) 1

Q29. The power factor of a purely inductive AC circuit is:
A) 0
B) 0.5
C) 1
D) –1

Q30. A particle of charge q moves in a circular path under a uniform magnetic field. The magnetic force does:
A) Positive work
B) Negative work
C) Zero work
D) Variable work

Section G: Mixed PYQ-Style Questions

Q31. A resistor of 10 Ω is connected in series with a 20 μF capacitor to 100 V DC. The initial current is:
A) 5 A
B) 10 A
C) 0 A
D) 2 A

Q32. A ray of light passes from air into a medium of refractive index 1.5. If the incident angle is 30°, the angle of refraction is approximately:
A) 19.5°
B) 20°
C) 25°
D) 30°

Q33. A metal rod of length 0.5 m moves perpendicular to a magnetic field of 0.3 T with velocity 4 m/s. The induced emf is:
A) 0.6 V
B) 0.3 V
C) 0.2 V
D) 1.2 V

Q34. The de Broglie wavelength of an electron moving at 10⁶ m/s is approximately:
A) 7.27 pm
B) 72.7 pm
C) 0.727 nm
D) 7.27 nm

Q35. The stopping potential in a photoelectric effect experiment is doubled. The maximum kinetic energy of emitted electrons:
A) Doubles
B) Halves
C) Remains same
D) Quadruples

Section A: Physical Chemistry (1–15)

Q1. The first ionization energy of an element is 578 kJ/mol. The element most likely belongs to:
A) Alkali metals
B) Alkaline earth metals
C) Halogens
D) Noble gases

Q2. The solubility product (Ksp) of AgCl at 25°C is 1.6 × 10⁻¹⁰. The solubility in mol/L is approximately:
A) 1.3 × 10⁻⁵
B) 1.6 × 10⁻⁵
C) 2 × 10⁻⁵
D) 5 × 10⁻⁶

Q3. The van’t Hoff factor (i) for 0.1 M Na₂SO₄ in water is:
A) 1
B) 2
C) 3
D) 4

Q4. The order of reaction is determined by plotting:
A) Concentration vs. Time
B) ln[Concentration] vs. Time
C) 1/[Concentration] vs. Time
D) Any of the above, depending on order

Q5. At 25°C, Kw for water is 1 × 10⁻¹⁴. The pH of pure water is:
A) 6
B) 6.5
C) 7
D) 7.5

Q6. Which of the following gases deviates most from ideal behavior?
A) H₂
B) He
C) CO₂
D) Ne

Q7. The entropy change is maximum in which process?
A) Freezing of water
B) Melting of ice
C) Condensation of steam
D) Sublimation of solid

Q8. The rate constant of a reaction doubles when temperature increases from 300 K to 310 K. The activation energy is approximately:
A) 50 kJ/mol
B) 42 kJ/mol
C) 35 kJ/mol
D) 25 kJ/mol

Q9. Which of the following solutions shows maximum colligative effect?
A) 0.1 M NaCl
B) 0.1 M K₂SO₄
C) 0.1 M Urea
D) 0.1 M Glucose

Q10. The conductivity of a solution decreases with:
A) Increasing dilution
B) Increasing temperature
C) Increasing solute concentration
D) Both B and C

Q11. The density of 2 mol/L H₂SO₄ solution is 1.2 g/cm³. Mass of H₂SO₄ in 100 mL solution is:
A) 19.6 g
B) 24 g
C) 20 g
D) 12 g

Q12. The energy change for vaporization of 1 mole of water at 100°C is:
A) 40.7 kJ/mol
B) 4.18 kJ/mol
C) 2260 kJ/mol
D) 18 kJ/mol

Q13. For an endothermic reaction, increasing temperature:
A) Increases K
B) Decreases K
C) No effect
D) Initially increases then decreases K

Q14. The oxidation state of Cr in $K_2Cr_2O_7$ K2Cr2O7 is:
A) +3
B) +6
C) +4
D) +2

Q15. The bond dissociation enthalpy of H–H is 436 kJ/mol. The energy required to break 2 moles of H₂ is:
A) 436 kJ
B) 872 kJ
C) 218 kJ
D) 109 kJ

Section B: Inorganic Chemistry (16–25)

Q16. The most reactive metal with water is:
A) Mg
B) Na
C) Fe
D) Zn

Q17. The compound which is a strong oxidizing agent in acidic medium is:
A) $KMnO_4$ KMnO4
B) $K_2Cr_2O_7$ K2Cr2O7
C) $H_2O_2$ H2O2
D) All of the above

Q18. Which of the following is amphoteric?
A) Al(OH)₃
B) NaOH
C) HCl
D) MgO

Q19. The common oxidation state of Mn in compounds:
A) +2
B) +4
C) +7
D) All of the above

Q20. The major product of $Na_2CO_3 + CaCl_2$ Na2CO3+CaCl2 reaction is:
A) CaCO₃ precipitate
B) NaCl precipitate
C) CaCl₂ solution
D) CO₂ gas

Q21. Which halogen shows least reactivity?
A) F₂
B) Cl₂
C) Br₂
D) I₂

Q22. The color of $Fe^{3+}$ Fe3+ ion in solution is:
A) Green
B) Yellow
C) Violet
D) Brown

Q23. The number of unpaired electrons in $O_2$ O2 molecule is:
A) 0
B) 1
C) 2
D) 4

Q24. The formula of basic bauxite is:
A) Al₂O₃·2H₂O
B) Al₂O₃·3H₂O
C) Al(OH)₃
D) Al₂O₃

Q25. The strongest acid among the following is:
A) HF
B) HCl
C) HBr
D) HI

Q26. The major product of the reaction: $CH_3CH_2Br + KOH (alc.) \rightarrow ?$ CH3CH2Br+KOH(alc.)→?

A) CH₂=CH₂
B) CH₃CH₂OH
C) CH₃CH₃
D) CH₃CHO

Q27. The monomer of nylon-6 is:
A) Hexamethylenediamine
B) Caprolactam
C) Adipic acid
D) Aniline

Q28. The compound that exhibits both keto and enol forms is:
A) CH₃COCH₃
B) CH₃CH₂OH
C) HCHO
D) CH₃COOH

Q29. Which reagent converts an aldehyde into a carboxylic acid?
A) NaBH₄
B) LiAlH₄
C) Tollens’ reagent
D) KMnO₄

Q30. The number of sigma bonds in benzene molecule is:
A) 6
B) 9
C) 12
D) 18

Q31. The major product of $CH_3CH=CH_2 + HBr$ CH3CH=CH2+HBr in presence of peroxide is:
A) CH₃CHBrCH₃
B) CH₃CH₂CH₂Br
C) CH₃CBr=CH₂
D) CH₂BrCH=CH₂

Q32. The type of isomerism shown by CH₃CH₂OH and CH₃OCH₃ is:
A) Chain isomerism
B) Functional group isomerism
C) Position isomerism
D) Tautomerism

Q33. The reaction $C_6H_6 + Cl_2/FeCl_3 \rightarrow ?$ C6H6+Cl2/FeCl3→? produces:
A) Chlorobenzene
B) Benzyl chloride
C) Dichlorobenzene
D) Chlorocyclohexane

Q34. Which of the following is most reactive towards nucleophilic substitution?
A) CH₃Br
B) CH₃CH₂Br
C) (CH₃)₃CBr
D) C₆H₅CH₂Br

Q35. In the reaction $CH_3COCH_3 + I_2/NaOH$ CH3COCH3+I2/NaOH, the product is:
A) CHI₃
B) CH₃COI
C) CH₃CHI₂
D) CH₃CH₂I

Section A: Algebra & Quadratic Equations (1–10)

Q1. If $x^2 – 5x + 6 = 0$ x2−5x+6=0, then the sum of the reciprocals of the roots is:
A) 5
B) 6
C) 3
D) 1

Q2. The roots of $x^2 – 7x + 12 = 0$ x2−7x+12=0 are:
A) 3, 4
B) 4, 3
C) -3, -4
D) Both A and B

Q3. If $\alpha$ α and $\beta$ β are roots of $x^2 – 3x + 2 = 0$ x2−3x+2=0, then $\alpha^3 + \beta^3 = ?$ α3+β3=?
A) 9
B) 11
C) 17
D) 19

Q4. The sum of the squares of roots of $2x^2 – 5x + 3 = 0$ 2×2−5x+3=0 is:
A) 4
B) 25/4
C) 17/4
D) 9/4

Q5. The quadratic equation whose roots are $3\alpha$ 3α and $3\beta$ 3β, where $\alpha, \beta$ α,β are roots of $x^2 – 2x + 3 = 0$ x2−2x+3=0, is:
A) $x^2 – 6x + 27 = 0$ x2−6x+27=0
B) $x^2 – 6x + 3 = 0$ x2−6x+3=0
C) $x^2 – 2x + 9 = 0$ x2−2x+9=0
D) $x^2 – 18x + 27 = 0$ x2−18x+27=0

Q6. If one root of $x^2 + px + q = 0$ x2+px+q=0 is double the other, then:
A) $p^2 = 8q$ p2=8q
B) $p^2 = 4q$ p2=4q
C) $p^2 = 2q$ p2=2q
D) $p^2 = q$ p2=q

Q7. If $\alpha + \beta = 7$ α+β=7 and $\alpha\beta = 12$ αβ=12, then $\alpha^2 + \beta^2 = ?$ α2+β2=?
A) 13
B) 25
C) 49
D) 37

Q8. The roots of $x^2 – 4x + 4 = 0$ x2−4x+4=0 are:
A) 2, 2
B) -2, -2
C) 4, 0
D) 0, 4

Q9. If $x^2 – 5x + k = 0$ x2−5x+k=0 has equal roots, then k = ?
A) 25
B) 6.25
C) 12.5
D) 0

Q10. The equation $x^2 + bx + c = 0$ x2+bx+c=0 has roots in the ratio 2:3. If sum of roots = 10, then c = ?
A) 12
B) 16
C) 20
D) 24

Section B: Trigonometry & Heights/Distances (11–20)

Q11. If $\sin A + \cos A = 1$ sinA+cosA=1, then $\sin^2 A + \cos^2 A = ?$ sin2A+cos2A=?
A) 1
B) 0
C) 2
D) 0.5

Q12. The value of $\tan 75°$ tan75° is:
A) $2 + \sqrt{3}$ 2+3
B) $2 – \sqrt{3}$ 2−3
C) $\sqrt{3} + 1$ 3+1
D) $\sqrt{3} – 1$ 3−1

Q13. $\sin^4 θ + \cos^4 θ = ?$ sin4θ+cos4θ=?
A) 1 – 2 sin²θ cos²θ
B) 1 + 2 sin²θ cos²θ
C) 1 – sin²2θ
D) 1 + sin²2θ

Q14. In a right triangle, the hypotenuse = 10 cm and one side = 6 cm. The other side is:
A) 8 cm
B) 6 cm
C) 4 cm
D) 5 cm

Q15. If $\sin A = 3/5$ sinA=3/5, then $\cos A = ?$ cosA=?
A) 4/5
B) 3/5
C) 5/3
D) 1/2

Q16. The height of a tower is 50 m. The angle of elevation from a point on the ground is 30°. Distance of the point from the base is:
A) 50√3 m
B) 50/√3 m
C) 100 m
D) 25√3 m

Q17. $\sin 2A = 2 \sin A \cos A$ sin2A=2sinAcosA. Then $\sin 2A$ sin2A if A = 45° is:
A) 1
B) √2
C) 1/2
D) √3/2

Q18. If $\tan θ = 1$ tanθ=1, then θ = ?
A) 30°
B) 45°
C) 60°
D) 90°

Q19. $\sin^2 A – \cos^2 A = ?$ sin2A–cos2A=?
A) –cos 2A
B) cos 2A
C) –sin 2A
D) sin 2A

Q20. The value of $\tan 30°$ tan30° is:
A) 1/√3
B) √3
C) 1
D) √2

Section C: Coordinate Geometry & Probability (21–30)

Q21. The distance between points $A(2, 3)$ A(2,3) and $B(-4, 5)$ B(−4,5) is:
A) √40
B) √36
C) √32
D) √48

Q22. The midpoint of the line segment joining $(1, 2)$ (1,2) and $(3, 6)$ (3,6) is:
A) (2, 4)
B) (1, 4)
C) (2, 3)
D) (0, 4)

Q23. The slope of a line perpendicular to $3x – 4y + 7 = 0$ 3x–4y+7=0 is:
A) 3/4
B) –3/4
C) 4/3
D) –4/3

Q24. The area of a triangle with vertices $(0,0), (4,0), (0,3)$ (0,0),(4,0),(0,3) is:
A) 6
B) 12
C) 7
D) 5

Q25. If the roots of $x^2 – x + p = 0$ x2–x+p=0 are real, then p satisfies:
A) p ≥ 1/4
B) p ≤ 1/4
C) p > 1/4
D) p < 1/4

Q26. A bag contains 5 red and 3 blue balls. Probability of drawing 2 red balls is:
A) 1/2
B) 5/14
C) 5/21
D) 10/28

Q27. Probability of getting a sum 8 with two dice is:
A) 5/36
B) 1/6
C) 1/8
D) 7/36

Q28. The equation of a line passing through (1, 2) with slope 3 is:
A) y – 2 = 3(x – 1)
B) y + 2 = 3(x + 1)
C) y – 1 = 2(x – 3)
D) y = 3x + 2

Q29. The centroid of a triangle with vertices $(2,3),(4,5),(6,7)$ (2,3),(4,5),(6,7) is:
A) (4,5)
B) (12,15)
C) (3,5)
D) (4,6)

Q30. Two dice are rolled. Probability that at least one shows 6 is:
A) 11/36
B) 1/6
C) 25/36
D) 1/2

Section D: Vectors & Statistics (31–40)

Q31. If $\vec{A} = 3\hat{i} + 2\hat{j}$ A=3i^+2j^ and $\vec{B} = \hat{i} – \hat{j}$ B=i^–j^, then $\vec{A}·\vec{B} = ?$ A⋅B=?
A) 1
B) 5
C) 3
D) 7

Q32. Magnitude of vector $2\hat{i} + 3\hat{j}$ 2i^+3j^ is:
A) √13
B) 5
C) √11
D) 6

Q33. Mean of first 10 natural numbers is:
A) 5
B) 5.5
C) 6
D) 4.5

Q34. Variance of numbers 2, 4, 6, 8, 10 is:
A) 8
B) 10
C) 6
D) 5

Q35. If $\vec{A} = 2\hat{i} + 3\hat{j}$ A=2i^+3j^ and $\vec{B} = –\hat{i} + 2\hat{j}$ B=–i^+2j^, then $\vec{A} × \vec{B} = ?$ A×B=?
A) 7 k̂
B) –7 k̂
C) 4 k̂
D) –4 k̂

Q36. Median of numbers 3, 7, 5, 9, 11 is:
A) 5
B) 7
C) 6
D) 8

Q37. Range of numbers 2, 4, 9, 5, 7 is:
A) 7
B) 5
C) 9
D) 11

Q38. If $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ A=i^+j^+k^, magnitude = ?
A) √2
B) √3
C) 3
D) 1

Q39. The sum of deviations of a data set from its mean is:
A) Positive
B) Negative
C) Zero
D) Depends on data

Q40. The coefficient of correlation between perfectly positively correlated data is:
A) 0
B) 1
C) –1
D) Undefined

Section E: Calculus & Miscellaneous (41–50)

Q41. If $f(x) = x^2$ f(x)=x2, then $f'(x) = ?$ f′(x)=?
A) x
B) 2x
C) x²
D) 2

Q42. If $y = sin x$ y=sinx, then $dy/dx = ?$ dy/dx=?
A) cos x
B) sin x
C) –sin x
D) –cos x

Q43. $\int 2x dx = ?$ ∫2xdx=?
A) x² + C
B) 2x + C
C) x + C
D) x³ + C

Q44. Derivative of $e^x$ ex is:
A) e^x
B) x e^x
C) ln x
D) 1/x

Q45. $\int cos x dx = ?$ ∫cosxdx=?
A) sin x + C
B) –sin x + C
C) cos x + C
D) –cos x + C

Q46. The slope of tangent to y = x² at x = 2 is:
A) 2
B) 4
C) 1
D) 8

Q47. If $y = x^3 – 3x^2 + 2$ y=x3–3×2+2, then dy/dx = ?
A) 3x² – 6x
B) 3x² – 6x + 2
C) x² – 6x + 2
D) 3x² + 6x

Q48. Maximum value of sin²x + cos²x is:
A) 0
B) 1
C) 2
D) √2

Q49. The derivative of ln x is:
A) ln x
B) 1/x
C) x
D) e^x

Q50. If f(x) = x² + 3x – 4, f(2) = ?
A) 4
B) 6
C) 2
D) 0

Section	Q.No	Answer
Physics	1	C
	2	C
	3	B
	4	C
	5	B
	6	A
	7	B
	8	A
	9	C
	10	C
	11	B
	12	A
	13	B
	14	A
	15	A
	16	D
	17	A
	18	C
	19	B
	20	A
	21	C
	22	B
	23	A
	24	A
	25	A
	26	A
	27	C
	28	B
	29	A
	30	C
	31	A
	32	A
	33	A
	34	B
	35	A
Chemistry	1	A
	2	A
	3	C
	4	D
	5	C
	6	C
	7	D
	8	B
	9	B
	10	A
	11	A
	12	A
	13	A
	14	B
	15	B
	16	B
	17	D
	18	A
	19	D
	20	A
	21	D
	22	D
	23	C
	24	B
	25	D
	26	A
	27	B
	28	A
	29	D
	30	A
	31	A
	32	B
	33	A
	34	C
	35	A
Mathematics	1	C
	2	A
	3	B
	4	C
	5	A
	6	A
	7	B
	8	A
	9	B
	10	D
	11	A
	12	A
	13	A
	14	A
	15	A
	16	A
	17	A
	18	B
	19	B
	20	A
	21	A
	22	A
	23	C
	24	A
	25	B
	26	C
	27	A
	28	A
	29	A
	30	C
	31	B
	32	A
	33	B
	34	A
	35	A
	36	B
	37	A
	38	B
	39	C
	40	B
	41	B
	42	A
	43	A
	44	A
	45	A
	46	B
	47	A
	48	B
	49	B
	50	A

Disclaimer:
This mock test is created for educational purposes only. Questions are original and inspired by previous GUJCET papers, but this is not an official exam. Answers are provided for reference and practice.