JEE MAINS TYPE 1 - Start Exam

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JEE MAINS TYPE 1

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1 / 90

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

2 / 90

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

1) 0

2) 2

3) 1

4) 1/2

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

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4. 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

5 / 90

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

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

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

1) Atomic radius decreases across a period

2) Ionization energy decreases across a period

3) Electronegativity decreases across a period

4) Atomic radius increases down a group

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8. Which trigonometric identities are correct?

1) sin²θ + cos²θ = 1

2) tanθ = sinθ/cosθ

3) cosθ = 1/sinθ

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

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10. Evaluate: ∫ x dx.

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

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12. Which function represents an odd function?

1) cos(x)

2) sin(x)

3) x²

4) e^x

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

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

1) Reduction is gain of electrons

2) Oxidation is loss of electrons

3) Oxidizing agent gets oxidized

16 / 90

16. Which statements about ideal gas are TRUE?

1) Obeys PV=nRT

2) Real gases behave ideally at high pressure

3) Volume of molecules is significant

4) No intermolecular forces

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

18 / 90

18. Calculate the oxidation number of sulphur in H₂SO₄.

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

1) Carbon shows inert pair effect

2) Fluorine is the most electronegative element

3) Inert pair effect increases down the group

20 / 90

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

1) False

2) True

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21. Select all correct statements about gravitational potential energy.

1) It is maximum at ground level

2) It increases with height

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

22 / 90

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

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

24 / 90

24. 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)

25 / 90

25. Find the value of √75 simplified.

26 / 90

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

1) True

2) False

27 / 90

27. Evaluate the derivative of ln(x).

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28. 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

29 / 90

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

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

1) Temperature of the planet

2) Mass of the planet

3) Atmospheric pressure

4) Radius of the planet

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

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32. Which statements about hydrocarbons are correct?

1) Alkanes are saturated hydrocarbons

2) Alkenes are fully saturated

3) Alkynes contain triple bonds

33 / 90

33. 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 require a material medium

4) They are longitudinal waves

34 / 90

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

1) 30 V

2) 8 V

3) 5 V

4) 15 V

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35. Which statements about pH are correct?

1) pH = 7 is neutral

2) pH measures temperature

3) pH > 7 indicates a base

4) pH < 7 indicates an acid

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

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

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

1) Acids have pH > 7

2) Acids donate H⁺ ions

3) Bases accept H⁺ ions

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

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40. 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

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

42 / 90

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

1) Water expands below 4°C

2) Ice is denser than water

3) Density maximum at 4°C

4) Water contracts below 4°C

43 / 90

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

1) True

2) False

44 / 90

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

1) True

2) False

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

1) False

2) True

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46. 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) No force acts on body

4) Acceleration is non-zero

47 / 90

47. 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

48 / 90

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

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49. Which statements about thermodynamics are true?

1) Heat is a state function

2) Reversible work is maximum work

3) ΔU = q + w

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

1) Zero acceleration

2) Decreasing velocity

3) Zero displacement

4) Increasing velocity

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

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

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

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

1) False

2) True

55 / 90

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

56 / 90

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

1) 2 m/s²

2) 4 m/s²

3) 5 m/s²

4) 10 m/s²

57 / 90

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

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

1) Velocity is constant

2) SHM acceleration ∝ displacement

3) Acceleration is opposite to displacement

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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

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60. Which of the following graphs represents uniform motion?

1) Curve with increasing slope

2) Random fluctuations

3) Curve with decreasing slope

4) Straight line in position-time graph

61 / 90

61. Which of the following compounds shows hydrogen bonding?

1) CO₂

2) CH₄

3) HCl

4) NH₃

62 / 90

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

1) 2

2) 1

3) 4

4) -2

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

64 / 90

64. Calculate the value of ³√27.

65 / 90

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

66 / 90

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

1) 7.5 m

2) 3 m

3) 10 m

4) 5 m

68 / 90

68. 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

69 / 90

69. Which statements about atomic orbitals are TRUE?

1) f-orbitals have only two lobes

2) s-orbital is spherical

3) d-orbitals are linear

4) p-orbitals are dumbbell shaped

70 / 90

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

1) nPr = nCr / r!

2) nCr = nPr × r!

3) nPr = nCr × r!

4) nPr = nCr

71 / 90

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

1) Entropy

2) Enthalpy

3) Internal energy

4) Heat

72 / 90

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

1) 120°

2) 90°

3) 104.5°

4) 109.5°

73 / 90

73. Find the derivative of x³ − 5x.

74 / 90

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

1) False

2) True

75 / 90

75. Which statements about buffer solutions are correct?

1) They resist changes in pH

2) They contain strong acid only

3) They contain a weak acid and its salt

4) Buffers lower pH automatically

76 / 90

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

77 / 90

77. Select the correct statements about electromagnetic induction.

1) Lenz’s law gives magnitude of EMF

2) Direction of EMF opposes change in flux

3) EMF is produced when magnetic flux changes

78 / 90

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

1) q²V

2) q/V

3) qV

4) V/q

79 / 90

79. Identify the correct statements about vectors.

1) Displacement is a vector

2) Speed is a vector

3) Scalar product gives a vector

4) Vector has both magnitude and direction

80 / 90

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

1) False

2) True

81 / 90

81. 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) 6 m/s

3) 15 m/s

4) 9 m/s

82 / 90

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

1) 4ab – c²

2) b² + 4ac

3) b² – 4ac

4) 2ac – b²

83 / 90

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

84 / 90

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

1) True

2) False

85 / 90

85. If log₁₀2 = 0.301, what is log₁₀8?

1) 0.903

2) 1.301

3) 2.903

4) 0.699

86 / 90

86. Which statements about conductors are correct?

1) Charges remain at the centre

2) Conductors contain free electrons

3) Electric field inside a conductor is zero

87 / 90

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

88 / 90

88. Which mathematical statements are TRUE?

1) tanθ = sinθ/cosθ

2) sinθ = 1 always

3) sin²θ + cos²θ = 1

89 / 90

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

1) 10 W

2) 40 W

3) 4 W

4) 20 W

90 / 90

90. 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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