JEE ADVANCED TYPE 3 – Start Exam

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JEE ADVANCED TYPE 3

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1 / 108

1. log10(10^5)=x, then x is

1) 1

2) 5

3) 0

4) 10

2 / 108

2. determinant of [[2,1],[5,3]] is

3 / 108

3. If t1/2=200 s (first order), k=0.693/t1/2 (s^-1) is

4 / 108

4. If z=5−12i, then |z| equals

1) 17

2) 144

3) 13

4) 7

5 / 108

5. Select all correct statements about coordinate geometry (Set-03):

1) Midpoint formula averages coordinates

2) Distance formula uses √[(Δx)^2+(Δy)^2]

3) Slope of vertical line is 0

4) Slope of horizontal line is 0

6 / 108

6. Conjugate base of H2CO3 is

1) H2CO3−

2) CO3^2−

3) HCO3−

4) H3CO3+

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7. Select all correct statements about SHM (Set-03):

1) At mean position acceleration is zero.

2) a and x are opposite in direction in SHM.

3) At extreme position acceleration magnitude is maximum.

4) At extreme position speed is maximum.

8 / 108

8. Tollens’ test is positive for

1) HCHO

2) Benzene

3) CH3COOH

4) CH3COCH3

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9. Select all correct statements about probability (Set-03):

1) P(A∩B)≤P(A)

2) P(A∪B)=P(A)+P(B)+P(A∩B)

3) If A⊆B then P(A)≤P(B)

4) P(∅)=0

10 / 108

10. Select all correct statements about periodicity (Set-03):

1) Effective nuclear charge increases across a period.

2) Ionization energy decreases down a group.

3) Atomic radius increases down a group.

4) Electronegativity increases down a group.

11 / 108

11. Select all correct statements about vectors (Set-03):

1) Dot product is scalar.

2) a×b=b×a.

3) If a ∥ b then a×b=0

4) Cross product is vector.

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12. Match quantity with SI unit.

1. Magnetic flux

2. Power

3. Charge

13 / 108

13. A charged particle moves with velocity parallel to a uniform magnetic field. Magnetic force on it is

1) Depends on charge only

2) Zero

3) Always non-zero

4) Maximum

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14. Select all correct statements about buffers (Set-03):

1) Buffer resists pH change for small additions.

2) Henderson equation relates pH, pKa and ratio.

3) Buffer contains weak acid and its conjugate base.

4) Buffer keeps pH constant for any amount of acid/base.

15 / 108

15. Select all correct statements about optics (Set-03):

1) Critical angle exists only when light goes from denser to rarer.

2) Refractive index n=c/v.

3) TIR can occur for any incidence angle.

4) Frequency of light remains unchanged during refraction.

16 / 108

16. Select all correct statements about electrostatics (Set-03):

1) Electric field is conservative in electrostatics.

2) Potential difference is path independent.

3) Capacitance depends on charge stored only.

4) For a capacitor, Q ∝ V.

17 / 108

17. Number of subsets of a set with 6 elements is

1) 32

2) 36

3) 12

4) 64

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18. Oxidizing agent is the species that

1) Always has oxygen

2) Gets oxidized

3) Gets reduced

4) Loses electrons

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19. A circuit draws current 3.2 A from a 24 V source. Equivalent resistance (Ω) is

1) 9.5

2) 0.133

3) 7.5

4) 76.8

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20. Match (List-I) with dimensional formula (List-II).

1. Charge

2. Pressure

3. Energy

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21. Highest lattice energy among the following is

1) KBr

2) NaCl

3) CsI

4) MgO

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22. ∫ 3x^2 dx equals

1) ln x + C

2) x^3 + C

3) 3x + C

4) x^2 + C

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23. A parallel-plate capacitor remains connected to a battery. On inserting a dielectric fully, the charge on capacitor

1) Remains same

2) Increases

3) Decreases

4) Becomes zero

24 / 108

24. Number of π bonds in benzene is

25 / 108

25. Match acid-base term with definition.

1. Lewis acid

2. Brønsted acid

3. Lewis base

26 / 108

26. A resistor 10 Ω carries 2 A. Voltage (V) is

27 / 108

27. Strong electrolyte in water is

1) NH4OH

2) NaNO3

3) CH3COOH

4) Glucose

28 / 108

28. Match phenomenon with law.

1. Induction

2. Reflection

3. Refraction

29 / 108

29. If det(A)=0 for a square matrix A, then A is

1) Diagonal

2) Singular

3) Identity

4) Orthogonal

30 / 108

30. lim_{x→0} (sin x)/x is

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31. Match colligative property with effect.

1. Boiling point elevation

2. Osmotic pressure

3. Freezing point depression

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32. For ideal gas at constant volume, pressure is directly proportional to

1) Density only

2) Molar mass

3) Absolute temperature

4) Volume

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33. Atoms per unit cell in BCC is

34 / 108

34. If N=150, ΔΦ=0.06 Wb in 0.02 s, induced emf (V)

35 / 108

35. Match geometry item with formula.

1. Triangle area

2. Rectangle area

3. Circle area

36 / 108

36. Select all correct statements about momentum (Set-03):

1) Momentum is a vector.

2) Momentum is always conserved even with external forces.

3) Impulse equals change in momentum.

4) In isolated system, momentum is conserved.

37 / 108

37. In photoelectric effect, maximum kinetic energy of photoelectrons depends on

1) Temperature only

2) Intensity only

3) Frequency of incident light

4) Surface area only

38 / 108

38. Ozonolysis of alkenes uses

1) H2/Pd

2) O3 then Zn/H2O

3) LiAlH4

4) NaBH4

39 / 108

39. If P(A)=0.7, then P(A^c) equals

1) 0.3

2) 1.7

3) 0.7

4) 0

40 / 108

40. For a first-order reaction, the unit of rate constant is

1) s^-1

2) dimensionless

3) L mol^-1 s^-1

4) mol L^-1 s^-1

41 / 108

41. Select all correct statements about EMI (Set-03):

1) Induced emf depends on rate of change of flux.

2) Lenz’s law gives direction of induced current.

3) Changing area of loop can induce emf.

4) Induced current supports the change in flux.

42 / 108

42. Geometry of XeF4 is

1) Tetrahedral

2) Trigonal bipyramidal

3) Linear

4) Square planar

43 / 108

43. Select all correct statements about trigonometry (Set-03):

1) sin^2θ+cos^2θ=1

2) sin2θ=sinθ+cosθ

3) tanθ=sinθ/cosθ

4) cos2θ=cos^2θ−sin^2θ

44 / 108

44. A charge 2 μC at potential 50 V has potential energy (in μJ)

45 / 108

45. Molarity for 1 mol solute in 4 L is

46 / 108

46. Magnitude of vector (2,1,2) is

47 / 108

47. Select all correct statements about kinetics (Set-03):

1) Rate law is experimental.

2) Molecularity can be fractional.

3) Order can be fractional.

4) Higher activation energy generally lowers rate at given T.

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48. Select all correct statements about continuity (Set-03):

1) Continuity implies limit equals function value.

2) Continuity implies differentiability.

3) If LHL=RHL, limit exists.

4) Polynomials are continuous everywhere.

49 / 108

49. Derivative of (sin x) is

1) −cos x

2) −sin x

3) sin x

4) cos x

50 / 108

50. A wave of frequency 250 Hz and wavelength 1.2 m has speed (m/s)

51 / 108

51. pH of 1×10^-3 M HCl (strong acid) is

52 / 108

52. For normal incidence on a plane mirror, the angle of reflection is

1) 180°

2) 90°

3) 45°

4) 0°

53 / 108

53. A mass 5 kg moves at 4 m/s. Kinetic energy (J) is

54 / 108

54. Moles in 22 g CO2 (M=44 g/mol) is

55 / 108

55. Match probability term with meaning.

1. Independent events

2. Complement

3. Mutually exclusive

56 / 108

56. Remainder when 37^2 is divided by 9 is

1) 3

2) 2

3) 4

4) 1

57 / 108

57. If Kc=9 for A⇌B, then Kc for B⇌A is

58 / 108

58. Value of 6! is

1) 120

2) 1440

3) 360

4) 720

59 / 108

59. When light enters a medium with higher refractive index, its

1) Frequency increases

2) Speed increases and wavelength increases

3) Speed decreases and wavelength decreases; frequency unchanged

4) Frequency decreases

60 / 108

60. Aromatic species is

1) Cyclobutadiene

2) C5H5+

3) C5H5−

4) COT

61 / 108

61. Match trig identity.

1. sin^2θ+cos^2θ

2. 1+cot^2θ

3. 1+tan^2θ

62 / 108

62. Select all correct statements about magnetic force (Set-03):

1) If v ⟂ B, force magnitude is qvB.

2) Magnetic force can do work and change speed always.

3) Magnetic force is q(v×B).

4) If v ∥ B, force is zero.

63 / 108

63. If cosθ=1, θ could be

1) π/3

2) π/4

3) 0

4) π/2

64 / 108

64. If two resistors 6Ω and 3Ω are in parallel, equivalent resistance is

1) 4.5 Ω

2) 1 Ω

3) 9 Ω

4) 2 Ω

65 / 108

65. Select all correct statements about permutations (Set-03):

1) nPr=nCr always.

2) nC0=1

3) Permutations of n objects is n!.

4) nPr=n!/(n−r)!

66 / 108

66. Work done by centripetal force in uniform circular motion over any displacement is

1) Positive

2) Negative

3) Depends on mass

4) Zero

67 / 108

67. If x=3, evaluate 4x^2.

68 / 108

68. A projectile is fired with speed 28 m/s at angle 40°. (g=9.8 m/s²). Find its range (m).

1) 80.0

2) 78.78

3) 39.39

4) 157.56

69 / 108

69. Distance between (1,2) and (7,10) is

70 / 108

70. 0.75 mol of substance with molar mass 80 g/mol has mass (g)

1) 80

2) 600

3) 6

4) 60

71 / 108

71. If u=−20 cm and v=40 cm, focal length f (cm) from 1/f=1/v−1/u

72 / 108

72. A mass 2 kg attached to a spring of constant 320 N/m performs SHM. Time period (s) is

1) 0.497

2) 0.994

3) 0.248

4) 79.477

73 / 108

73. Sigma bonds in benzene (C6H6) are

1) 18

2) 12

3) 6

4) 9

74 / 108

74. A loop of area 0.08 m² is in a magnetic field increasing at 1.1 T/s. Induced emf (V) is

1) 0.176

2) 0.088

3) 13.75

4) 0.044

75 / 108

75. Select all correct statements about redox (Set-03):

1) Oxidation is loss of electrons.

2) Oxidizing agent is reduced.

3) Reducing agent is reduced.

4) Reduction is gain of electrons.

76 / 108

76. For ideal solutions, Raoult’s law states

1) p_i = x_i p_i°

2) p_i independent of x_i

3) Applies only to solids

4) ΔHmix always positive

77 / 108

77. Select all correct statements about integration (Set-03):

1) ∫0 dx = C

2) ∫1/x dx = 1/x + C

3) ∫(f+g)=∫f+∫g

4) ∫(cf)=c∫f

78 / 108

78. For vectors a=(1,2,0), b=(2,0,1), the dot product a·b equals

1) 3

2) 4

3) 1

4) 2

79 / 108

79. Complex showing cis-trans isomerism is

1) [Fe(CN)6]4−

2) [Pt(NH3)2Cl2]

3) [Ni(CO)4]

4) [Co(NH3)6]3+

80 / 108

80. If GP has a=2, r=3, the 4th term is

81 / 108

81. Select all correct statements about circuits (Set-03):

1) Equivalent resistance of parallel is greater than each resistor.

2) In parallel, voltage is same across branches.

3) Power dissipated in resistor is I^2R.

4) In series, current is same in each element.

82 / 108

82. Work done in lifting 80 N weight by 1.5 m (J)

83 / 108

83. [Fallback-8] Evaluate (2+8)^2.

84 / 108

84. Colligative properties depend on

1) Pressure only

2) Number of solute particles

3) Nature of solute only

4) Solvent identity only

85 / 108

85. Select all correct statements about waves (Set-03):

1) Frequency changes when wave enters another medium.

2) Wavelength changes when speed changes (frequency fixed).

3) Sound in air is longitudinal.

4) v=fλ

86 / 108

86. If P(A)=0.25, then P(A^c) is

87 / 108

87. Number of real roots of x^2+4x+5=0 is

1) 2

2) Infinite

3) 1

4) 0

88 / 108

88. Area of triangle with vertices (0,0),(6,0),(0,4) is

1) 6

2) 12

3) 24

4) 8

89 / 108

89. Match lattice with atoms per unit cell.

1. FCC

2. SC

3. BCC

90 / 108

90. Mechanism of CH3Br + OH− → CH3OH + Br− is

1) SN2

2) E2

3) SN1

4) E1

91 / 108

91. Select all correct statements about coordination compounds (Set-03):

1) Square planar often involves dsp2 hybridization.

2) Ligands may be neutral/anionic.

3) Coordination number equals donor atoms bonded.

4) Octahedral complexes cannot show geometrical isomerism.

92 / 108

92. If f(x)=2x+1, then f(−4) equals

1) −7

2) 7

3) −9

4) 9

93 / 108

93. Compute 10C3.

94 / 108

94. In an isolated system, during any collision, which quantity is always conserved?

1) Mechanical energy always

2) Kinetic energy

3) Linear momentum

4) Speed of each body

95 / 108

95. Match function with inverse (domain restricted).

1. 3x

2. x^2 (x≥0)

3. x+5

96 / 108

96. Select all correct statements about gases (Set-03):

1) PV=nRT

2) At constant T, P inversely proportional to V.

3) At constant P, V inversely proportional to T.

4) At constant V, P proportional to T.

97 / 108

97. Select all correct statements about aromaticity (Set-03):

1) Aromatic species are necessarily neutral.

2) Aromatic systems follow (4n+2)π rule.

3) Aromatic systems are planar.

4) Cyclobutadiene is aromatic.

98 / 108

98. In uniform circular motion with constant speed, which statement is correct?

1) Speed necessarily changes

2) Velocity is constant

3) Acceleration is non-zero and directed toward center

4) Acceleration is zero

99 / 108

99. An LC circuit has L=0.15 H and C=4 μF. Resonant frequency (Hz) is closest to

1) 205.5

2) 411.0

3) 102.8

4) 0

100 / 108

100. Select all correct statements about solutions (Set-03):

1) Vapour pressure lowering is colligative.

2) Ideal solution has large ΔHmix.

3) Molarity depends on temperature.

4) Molality is temperature independent.

101 / 108

101. Total internal reflection occurs when light goes from denser to rarer medium and

1) Angle of refraction is zero always

2) Refractive index of denser medium is smaller

3) Angle of incidence is greater than critical angle

4) Angle of incidence is less than critical angle

102 / 108

102. Match condition with statement.

1. Centripetal acceleration

2. Resonance (LC)

3. TIR

103 / 108

103. Select all correct statements about matrices (Set-03):

1) det(A)≠0 implies invertible

2) det(AB)=det(A)det(B)

3) AB=BA implies A=B

4) det(I)=1

104 / 108

104. Sum of first 15 terms of AP with a=3 and d=2 is

1) 255

2) 240

3) 210

4) 30

105 / 108

105. Which acts as a Lewis acid?

1) OH−

2) Cl−

3) NH3

4) BF3

106 / 108

106. Match test with compound class.

1. Bromine water

2. Tollens

3. Iodoform

107 / 108

107. Two capacitors 4 μF and 5 μF in parallel have equivalent (μF)

108 / 108

108. Slope of line 2x−y+3=0 is

1) 1/2

2) −2

3) 2

4) −1/2

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