JEE MAINS TYPE 1 – Start Exam

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JEE MAINS TYPE 1

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1. Calculate the oxidation number of sulphur in H₂SO₄.

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2. The escape velocity from a planet depends on which of the following parameters?

1) Atmospheric pressure

2) Temperature of the planet

3) Radius of the planet

4) Mass of the planet

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3. Fill in the blank: The longest wavelength in the hydrogen spectrum belongs to the ______ series.

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4. If the displacement of a particle is x = 5cos(2t), what is its angular frequency?

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5. True or False: The value of Planck’s constant is approximately 6.63 × 10⁻³⁴ J·s.

1) False

2) True

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6. Fill in the blank: The SI unit of electric charge is ______.

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7. The velocity-time graph of a particle is a horizontal straight line. What does this indicate?

1) Increasing velocity

2) Zero displacement

3) Zero acceleration

4) Decreasing velocity

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8. Fill in the blank: A solution whose pH is less than 7 is called a(n) ______ solution.

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9. What is the value of the determinant | 1 2 ; 3 4 | ?

1) 2

2) 1

3) 4

4) -2

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10. Which of the following statements about chemical equilibrium are TRUE?

1) Reaction stops completely

2) Rate of forward reaction equals rate of backward reaction

3) Concentration of reactants and products becomes constant

4) Equilibrium constant changes with concentration

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11. A particle starts from rest and moves with a constant acceleration of 3 m/s². What is its velocity after 4 seconds?

1) 6 m/s

2) 12 m/s

3) 9 m/s

4) 15 m/s

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12. Which of the following statements about oxidation and reduction are TRUE?

1) Reduction is gain of electrons

2) Oxidizing agent gets oxidized

3) Oxidation is loss of electrons

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13. True or False: A concave mirror always forms a real image.

1) False

2) True

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14. Fill in the blank: The energy required to remove an electron from an isolated gaseous atom is called ______.

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15. A function f(x)=x²+2x+1 is equal to:

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16. Fill in the blank: The unit of power in the SI system is ______.

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17. True or False: The focal length of a convex lens is always positive.

1) True

2) False

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18. Which statements about p-block elements are correct?

1) Fluorine is the most electronegative element

2) Inert pair effect increases down the group

3) Carbon shows inert pair effect

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19. Which mathematical statements are TRUE?

1) sinθ = 1 always

2) sin²θ + cos²θ = 1

3) tanθ = sinθ/cosθ

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20. If a body moves with velocity v = 4t, what is its acceleration?

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21. Which statements about conductors are correct?

1) Electric field inside a conductor is zero

2) Charges remain at the centre

3) Conductors contain free electrons

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22. A body moves in a circular path with uniform speed. Which of the following is true about its acceleration?

1) Acceleration is zero

2) Velocity is constant vector

3) Acceleration is non-zero

4) No force acts on body

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23. A projectile is launched at 30° with speed 20 m/s. What is its maximum height? (g = 10 m/s²)

1) 10 m

2) 5 m

3) 3 m

4) 7.5 m

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24. Which of the following is NOT a state function?

1) Entropy

2) Enthalpy

3) Heat

4) Internal energy

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25. Find the limit: lim (x→0) (sin x / x).

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26. A block of mass 5 kg is pulled on a frictionless surface with a force of 20 N. What is its acceleration?

1) 4 m/s²

2) 2 m/s²

3) 10 m/s²

4) 5 m/s²

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27. Which statements about buffer solutions are correct?

1) They resist changes in pH

2) They contain a weak acid and its salt

3) They contain strong acid only

4) Buffers lower pH automatically

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28. Which statements about logarithms are correct?

1) log(ab) = log a + log b

2) log(a/b) = log a – log b

3) log(a+b) = log a × log b

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29. Fill in the blank: The power of a lens is measured in ______.

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30. A wire of resistance 5 Ω carries a current of 3 A. What is the potential difference across it?

1) 15 V

2) 8 V

3) 5 V

4) 30 V

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31. Which of the following statements about acids and bases are correct?

1) Acids donate H⁺ ions

2) Bases accept H⁺ ions

3) Acids have pH > 7

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32. The pH of a 1×10⁻⁴ M HCl solution is:

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33. Which function represents an odd function?

1) x²

2) sin(x)

3) e^x

4) cos(x)

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34. Which of the following graphs represents uniform motion?

1) Curve with increasing slope

2) Random fluctuations

3) Straight line in position-time graph

4) Curve with decreasing slope

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35. Which statements about hydrocarbons are correct?

1) Alkenes are fully saturated

2) Alkanes are saturated hydrocarbons

3) Alkynes contain triple bonds

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36. Which of the following compounds shows hydrogen bonding?

1) CH₄

2) NH₃

3) CO₂

4) HCl

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37. Solve: If f(x) = x² − 16, find its zeroes.

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38. Which trigonometric identities are correct?

1) sin²θ + cos²θ = 1

2) cosθ = 1/sinθ

3) tanθ = sinθ/cosθ

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39. Fill in the blank: The energy possessed by a body due to its position is called ______ energy.

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40. The discriminant of the quadratic equation ax² + bx + c = 0 is:

1) b² – 4ac

2) 2ac – b²

3) b² + 4ac

4) 4ab – c²

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41. Which of the following statements about electromagnetic waves are correct?

1) They are longitudinal waves

2) They travel with speed c in vacuum

3) They require a material medium

4) They are transverse waves

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42. Fill in the blank: The molecule with the highest bond order among the following is ______.

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43. Fill in the blank: The process of conversion of solid directly into gas is called ______.

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44. The work done in moving a charge q across a potential difference V is:

1) V/q

2) q/V

3) qV

4) q²V

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45. A current of 2 A flows through a resistor of 10 Ω. What is the power dissipated?

1) 4 W

2) 10 W

3) 20 W

4) 40 W

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46. Fill in the blank: The law that relates pressure and volume at constant temperature is ______ law.

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47. Fill in the blank: The derivative of e^x is ______.

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48. Fill in the blank: The derivative of sin(x) is ______.

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49. For a first-order reaction, which of the following statements are correct?

1) Half-life decreases as concentration increases

2) Half-life is independent of initial concentration

3) Rate ∝ concentration

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50. Which statements about pH are correct?

1) pH < 7 indicates an acid

2) pH = 7 is neutral

3) pH measures temperature

4) pH > 7 indicates a base

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51. A function f(x) = 2x² + 3 is evaluated at x = 4. What is the value?

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52. Which statements about atomic orbitals are TRUE?

1) p-orbitals are dumbbell shaped

2) d-orbitals are linear

3) f-orbitals have only two lobes

4) s-orbital is spherical

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53. Find the value of √75 simplified.

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54. Which of the following statements about matrices are TRUE?

1) Matrix multiplication is commutative

2) Identity matrix acts as multiplicative identity

3) Matrix multiplication is associative

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55. Evaluate: ∫ x dx.

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56. True or False: The magnetic field inside a long solenoid is uniform.

1) False

2) True

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57. True or False: Mole fraction of all components in a mixture always adds up to 1.

1) True

2) False

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58. The bond angle in methane (CH₄) is approximately:

1) 104.5°

2) 109.5°

3) 90°

4) 120°

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59. True or False: Work done by centripetal force is always zero.

1) True

2) False

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60. Identify the correct statements about vectors.

1) Speed is a vector

2) Displacement is a vector

3) Scalar product gives a vector

4) Vector has both magnitude and direction

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61. A 2 kg block slides down a smooth incline of height 5 m. What is its speed at the bottom? (g = 10 m/s²)

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62. Identify the correct statements about water’s anomalous expansion.

1) Ice is denser than water

2) Water contracts below 4°C

3) Water expands below 4°C

4) Density maximum at 4°C

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63. Which of the following options correctly classify the functions?

1) sin(x) is odd

2) cos(x) is even

3) sin(x) is even

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64. Evaluate the derivative of ln(x).

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65. Which of the following statements are true regarding SHM?

1) Acceleration is opposite to displacement

2) SHM acceleration ∝ displacement

3) Velocity is constant

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66. Which statements about thermodynamics are true?

1) Reversible work is maximum work

2) Heat is a state function

3) ΔU = q + w

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67. True or False: The magnetic flux through a surface depends on the angle between magnetic field and area vector.

1) True

2) False

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68. Which of the following relations hold true for permutation and combination?

1) nPr = nCr × r!

2) nPr = nCr / r!

3) nCr = nPr × r!

4) nPr = nCr

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69. What is the oxidation number of Mn in KMnO₄?

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70. A body is projected vertically upward with speed 30 m/s. How long will it take to come back to the ground? (g = 10 m/s²)

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71. Fill in the blank: The slope of a distance-time graph gives ______.

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72. True or False: The escape velocity on Earth is approximately 11.2 km/s.

1) False

2) True

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73. Calculate the value of ³√27.

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74. Fill in the blank: The line that touches a circle at exactly one point is called a ______.

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75. Fill in the blank: The integral of cos(x) dx is ______.

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76. Which of the following is the correct inverse function of f(x)=e^x?

1) sin(x)

2) x²

3) ln(x)

4) 1/x

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77. Select the correct statements about electromagnetic induction.

1) Direction of EMF opposes change in flux

2) EMF is produced when magnetic flux changes

3) Lenz’s law gives magnitude of EMF

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78. If a capacitor of capacitance 10 µF is charged to 50 V, what is the energy stored in it?

1) 0.050 J

2) 0.0125 J

3) 0.125 J

4) 0.025 J

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79. Fill in the blank: The curve y = x² represents a ______ function.

80 / 90

80. Fill in the blank: The element with the highest first ionization energy is ______.

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81. True or False: The direction of current is always opposite to electron flow.

1) True

2) False

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82. Which statements about ideal gas are TRUE?

1) Real gases behave ideally at high pressure

2) Obeys PV=nRT

3) Volume of molecules is significant

4) No intermolecular forces

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83. A metal sphere is heated from 27°C to 127°C. If its radius becomes R’, then R’ = ______ (assume small expansion).

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84. A body is thrown upwards with velocity 20 m/s. (g = 10 m/s²). What is the time taken to reach maximum height?

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85. Find the derivative of x³ − 5x.

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86. If log₁₀2 = 0.301, what is log₁₀8?

1) 0.699

2) 0.903

3) 1.301

4) 2.903

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87. Find the value of (sin30° + cos60°).

1) 1/2

2) 0

3) 2

4) 1

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88. Select all correct statements about gravitational potential energy.

1) It increases with height

2) It is maximum at ground level

3) It is equal to mgh near Earth's surface

89 / 90

89. Which of the following statements about the periodic table are correct?

1) Electronegativity decreases across a period

2) Ionization energy decreases across a period

3) Atomic radius increases down a group

4) Atomic radius decreases across a period

90 / 90

90. Fill in the blank: The force that opposes the relative motion between two surfaces is called ______.

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