JEE MAINS TYPE 1

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JEE MAINS TYPE 1

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1 / 90

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

2 / 90

2. 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

3 / 90

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

1) False

2) True

4 / 90

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

5 / 90

5. Which statements about hydrocarbons are correct?

1) Alkenes are fully saturated

2) Alkanes are saturated hydrocarbons

3) Alkynes contain triple bonds

6 / 90

6. 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

7 / 90

7. Which function represents an odd function?

1) x²

2) cos(x)

3) e^x

4) sin(x)

8 / 90

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

1) Rate ∝ concentration

2) Half-life is independent of initial concentration

3) Half-life decreases as concentration increases

9 / 90

9. Evaluate: ∫ x dx.

10 / 90

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

11 / 90

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

12 / 90

12. Find the value of √75 simplified.

13 / 90

13. Which mathematical statements are TRUE?

1) sinθ = 1 always

2) tanθ = sinθ/cosθ

3) sin²θ + cos²θ = 1

14 / 90

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

1) False

2) True

15 / 90

15. 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

16 / 90

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

17 / 90

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

1) 104.5°

2) 90°

3) 120°

4) 109.5°

18 / 90

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

1) Entropy

2) Internal energy

3) Heat

4) Enthalpy

19 / 90

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

1) True

2) False

20 / 90

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

1) b² + 4ac

2) b² – 4ac

3) 2ac – b²

4) 4ab – c²

21 / 90

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

1) True

2) False

22 / 90

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

23 / 90

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

24 / 90

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

1) True

2) False

25 / 90

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

1) 30 V

2) 15 V

3) 8 V

4) 5 V

26 / 90

26. Calculate the oxidation number of sulphur in H₂SO₄.

27 / 90

27. Find the derivative of x³ − 5x.

28 / 90

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

1) They are transverse waves

2) They travel with speed c in vacuum

3) They require a material medium

4) They are longitudinal waves

29 / 90

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

30 / 90

30. Which of the following graphs represents uniform motion?

1) Straight line in position-time graph

2) Curve with increasing slope

3) Curve with decreasing slope

4) Random fluctuations

31 / 90

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

32 / 90

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

1) cos(x) is even

2) sin(x) is odd

3) sin(x) is even

33 / 90

33. Which statements about conductors are correct?

1) Electric field inside a conductor is zero

2) Conductors contain free electrons

3) Charges remain at the centre

34 / 90

34. 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) 9 m/s

4) 15 m/s

35 / 90

35. 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) 5 m

3) 10 m

4) 3 m

36 / 90

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

1) Acceleration is non-zero

2) No force acts on body

3) Velocity is constant vector

4) Acceleration is zero

37 / 90

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

38 / 90

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

1) 2

2) 1

3) 1/2

4) 0

39 / 90

39. 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

40 / 90

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

41 / 90

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

42 / 90

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

1) Zero displacement

2) Decreasing velocity

3) Zero acceleration

4) Increasing velocity

43 / 90

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

44 / 90

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

1) Mass of the planet

2) Radius of the planet

3) Atmospheric pressure

4) Temperature of the planet

45 / 90

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

46 / 90

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

1) Bases accept H⁺ ions

2) Acids have pH > 7

3) Acids donate H⁺ ions

47 / 90

47. If log₁₀2 = 0.301, what is log₁₀8?

1) 2.903

2) 1.301

3) 0.903

4) 0.699

48 / 90

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

1) -2

2) 1

3) 2

4) 4

49 / 90

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

1) q²V

2) V/q

3) q/V

4) qV

50 / 90

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

51 / 90

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

1) False

2) True

52 / 90

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

1) sin(x)

2) 1/x

3) ln(x)

4) x²

53 / 90

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

1) Acceleration is opposite to displacement

2) SHM acceleration ∝ displacement

3) Velocity is constant

54 / 90

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

55 / 90

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

1) 0.125 J

2) 0.050 J

3) 0.025 J

4) 0.0125 J

56 / 90

56. Identify the correct statements about vectors.

1) Speed is a vector

2) Vector has both magnitude and direction

3) Scalar product gives a vector

4) Displacement is a vector

57 / 90

57. Which trigonometric identities are correct?

1) tanθ = sinθ/cosθ

2) sin²θ + cos²θ = 1

3) cosθ = 1/sinθ

58 / 90

58. 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

59 / 90

59. 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)

60 / 90

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

1) False

2) True

61 / 90

61. 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

62 / 90

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

1) True

2) False

63 / 90

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

64 / 90

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

65 / 90

65. Which statements about atomic orbitals are TRUE?

1) d-orbitals are linear

2) p-orbitals are dumbbell shaped

3) f-orbitals have only two lobes

4) s-orbital is spherical

66 / 90

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

67 / 90

67. Evaluate the derivative of ln(x).

68 / 90

68. Which statements about thermodynamics are true?

1) Heat is a state function

2) ΔU = q + w

3) Reversible work is maximum work

69 / 90

69. Which statements about pH are correct?

1) pH > 7 indicates a base

2) pH < 7 indicates an acid

3) pH measures temperature

4) pH = 7 is neutral

70 / 90

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

71 / 90

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

72 / 90

72. Which of the following compounds shows hydrogen bonding?

1) CH₄

2) NH₃

3) CO₂

4) HCl

73 / 90

73. Calculate the value of ³√27.

74 / 90

74. 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

75 / 90

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

76 / 90

76. Which statements about ideal gas are TRUE?

1) Volume of molecules is significant

2) Real gases behave ideally at high pressure

3) Obeys PV=nRT

4) No intermolecular forces

77 / 90

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

78 / 90

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

79 / 90

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

80 / 90

80. Which statements about buffer solutions are correct?

1) They contain strong acid only

2) They resist changes in pH

3) They contain a weak acid and its salt

4) Buffers lower pH automatically

81 / 90

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

82 / 90

82. 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

83 / 90

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

1) 10 W

2) 40 W

3) 20 W

4) 4 W

84 / 90

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

85 / 90

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

1) Equilibrium constant changes with concentration

2) Concentration of reactants and products becomes constant

3) Rate of forward reaction equals rate of backward reaction

4) Reaction stops completely

86 / 90

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

1) Ice is denser than water

2) Density maximum at 4°C

3) Water contracts below 4°C

4) Water expands below 4°C

87 / 90

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

1) Atomic radius decreases across a period

2) Electronegativity decreases across a period

3) Atomic radius increases down a group

4) Ionization energy decreases across a period

88 / 90

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

89 / 90

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

90 / 90

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

1) True

2) False

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