JEE MAINS TYPE 1 – Start Exam

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JEE MAINS TYPE 1

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1 / 90

1. 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

2 / 90

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

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3. Which trigonometric identities are correct?

1) cosθ = 1/sinθ

2) sin²θ + cos²θ = 1

3) tanθ = sinθ/cosθ

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

1) 3 m

2) 7.5 m

3) 5 m

4) 10 m

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5. Evaluate the derivative of ln(x).

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

1) 120°

2) 90°

3) 109.5°

4) 104.5°

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

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

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

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

1) cos(x) is even

2) sin(x) is even

3) sin(x) is odd

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11. 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) 5 m/s²

4) 10 m/s²

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

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

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

1) Internal energy

2) Heat

3) Entropy

4) Enthalpy

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15. 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

16 / 90

16. Which statements about ideal gas are TRUE?

1) No intermolecular forces

2) Real gases behave ideally at high pressure

3) Obeys PV=nRT

4) Volume of molecules is significant

17 / 90

17. Which function represents an odd function?

1) x²

2) sin(x)

3) cos(x)

4) e^x

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18. Which statements about conductors are correct?

1) Charges remain at the centre

2) Electric field inside a conductor is zero

3) Conductors contain free electrons

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

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

1) True

2) False

22 / 90

22. Select the correct statements about electromagnetic induction.

1) EMF is produced when magnetic flux changes

2) Direction of EMF opposes change in flux

3) Lenz’s law gives magnitude of EMF

23 / 90

23. Evaluate: ∫ x dx.

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24. Which mathematical statements are TRUE?

1) sin²θ + cos²θ = 1

2) tanθ = sinθ/cosθ

3) sinθ = 1 always

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

1) 2ac – b²

2) b² – 4ac

3) 4ab – c²

4) b² + 4ac

26 / 90

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

27 / 90

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

28 / 90

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

1) Bases accept H⁺ ions

2) Acids donate H⁺ ions

3) Acids have pH > 7

29 / 90

29. Which statements about hydrocarbons are correct?

1) Alkenes are fully saturated

2) Alkynes contain triple bonds

3) Alkanes are saturated hydrocarbons

30 / 90

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

31 / 90

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

1) True

2) False

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

1) True

2) False

33 / 90

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

34 / 90

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

1) Velocity is constant

2) SHM acceleration ∝ displacement

3) Acceleration is opposite to displacement

35 / 90

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

36 / 90

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

1) Half-life decreases as concentration increases

2) Rate ∝ concentration

3) Half-life is independent of initial concentration

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

1) 12 m/s

2) 15 m/s

3) 9 m/s

4) 6 m/s

38 / 90

38. Which statements about pH are correct?

1) pH > 7 indicates a base

2) pH measures temperature

3) pH = 7 is neutral

4) pH < 7 indicates an acid

39 / 90

39. Calculate the value of ³√27.

40 / 90

40. Calculate the oxidation number of sulphur in H₂SO₄.

41 / 90

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

42 / 90

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

43 / 90

43. Which of the following compounds shows hydrogen bonding?

1) NH₃

2) CO₂

3) HCl

4) CH₄

44 / 90

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

45 / 90

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

46 / 90

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

1) Zero displacement

2) Increasing velocity

3) Decreasing velocity

4) Zero acceleration

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

48 / 90

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

1) 0.0125 J

2) 0.025 J

3) 0.050 J

4) 0.125 J

49 / 90

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

1) sin(x)

2) x²

3) 1/x

4) ln(x)

50 / 90

50. Which statements about buffer solutions are correct?

1) They resist changes in pH

2) They contain strong acid only

3) Buffers lower pH automatically

4) They contain a weak acid and its salt

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

1) Acceleration is zero

2) No force acts on body

3) Velocity is constant vector

4) Acceleration is non-zero

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52. If log₁₀2 = 0.301, what is log₁₀8?

1) 2.903

2) 0.699

3) 0.903

4) 1.301

53 / 90

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

1) 2

2) 1

3) 0

4) 1/2

54 / 90

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

55 / 90

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

56 / 90

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

1) Radius of the planet

2) Mass of the planet

3) Temperature of the planet

4) Atmospheric pressure

57 / 90

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

1) Inert pair effect increases down the group

2) Carbon shows inert pair effect

3) Fluorine is the most electronegative element

58 / 90

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

1) False

2) True

59 / 90

59. Which statements about logarithms are correct?

1) log(a+b) = log a × log b

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

3) log(a/b) = log a – log b

60 / 90

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

1) 4

2) -2

3) 2

4) 1

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61. Which of the following graphs represents uniform motion?

1) Random fluctuations

2) Straight line in position-time graph

3) Curve with decreasing slope

4) Curve with increasing slope

62 / 90

62. Which statements about thermodynamics are true?

1) ΔU = q + w

2) Heat is a state function

3) Reversible work is maximum work

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

1) nPr = nCr

2) nCr = nPr × r!

3) nPr = nCr × r!

4) nPr = nCr / r!

64 / 90

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

1) 20 W

2) 4 W

3) 40 W

4) 10 W

65 / 90

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

1) Concentration of reactants and products becomes constant

2) Rate of forward reaction equals rate of backward reaction

3) Reaction stops completely

4) Equilibrium constant changes with concentration

66 / 90

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

1) Matrix multiplication is commutative

2) Matrix multiplication is associative

3) Identity matrix acts as multiplicative identity

67 / 90

67. 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

68 / 90

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

69 / 90

69. Identify the correct statements about vectors.

1) Scalar product gives a vector

2) Displacement is a vector

3) Vector has both magnitude and direction

4) Speed is a vector

70 / 90

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

71 / 90

71. Find the derivative of x³ − 5x.

72 / 90

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

1) False

2) True

73 / 90

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

74 / 90

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

1) False

2) True

75 / 90

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

1) False

2) True

76 / 90

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

1) Water expands below 4°C

2) Water contracts below 4°C

3) Density maximum at 4°C

4) Ice is denser than water

77 / 90

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

78 / 90

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

79 / 90

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

80 / 90

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

81 / 90

81. 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)

82 / 90

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

1) They travel with speed c in vacuum

2) They are transverse waves

3) They are longitudinal waves

4) They require a material medium

83 / 90

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

84 / 90

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

85 / 90

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

86 / 90

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

1) Oxidizing agent gets oxidized

2) Reduction is gain of electrons

3) Oxidation is loss of electrons

87 / 90

87. Find the value of √75 simplified.

88 / 90

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

1) q/V

2) q²V

3) qV

4) V/q

89 / 90

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

1) True

2) False

90 / 90

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

1) Ionization energy decreases across a period

2) Atomic radius decreases across a period

3) Electronegativity decreases across a period

4) Atomic radius increases down a group

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