JEE ADVANCED TYPE 3 - Start Exam

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JEE ADVANCED TYPE 3

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1 / 108

1. Match phenomenon with law.

1. Induction

2. Reflection

3. Refraction

2 / 108

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

1) Slope of horizontal line is 0

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

3) Midpoint formula averages coordinates

4) Slope of vertical line is 0

3 / 108

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

1) Cyclobutadiene is aromatic.

2) Aromatic species are necessarily neutral.

3) Aromatic systems are planar.

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

4 / 108

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

1) Speed decreases and wavelength decreases; frequency unchanged

2) Speed increases and wavelength increases

3) Frequency decreases

4) Frequency increases

5 / 108

5. Sigma bonds in benzene (C6H6) are

1) 18

2) 9

3) 6

4) 12

6 / 108

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

7 / 108

7. Oxidizing agent is the species that

1) Gets reduced

2) Always has oxygen

3) Gets oxidized

4) Loses electrons

8 / 108

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

1) In isolated system, momentum is conserved.

2) Impulse equals change in momentum.

3) Momentum is a vector.

4) Momentum is always conserved even with external forces.

9 / 108

9. Derivative of (sin x) is

1) −cos x

2) −sin x

3) sin x

4) cos x

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

1) If a ∥ b then a×b=0

2) Cross product is vector.

3) Dot product is scalar.

4) a×b=b×a.

11 / 108

11. Highest lattice energy among the following is

1) CsI

2) KBr

3) NaCl

4) MgO

12 / 108

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

1) 0.044

2) 0.088

3) 13.75

4) 0.176

13 / 108

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

1) Octahedral complexes cannot show geometrical isomerism.

2) Ligands may be neutral/anionic.

3) Coordination number equals donor atoms bonded.

4) Square planar often involves dsp2 hybridization.

14 / 108

14. Ozonolysis of alkenes uses

1) LiAlH4

2) NaBH4

3) O3 then Zn/H2O

4) H2/Pd

15 / 108

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

16 / 108

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

1) Changing area of loop can induce emf.

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

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

4) Induced current supports the change in flux.

17 / 108

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

1) cos2θ=cos^2θ−sin^2θ

2) sin2θ=sinθ+cosθ

3) tanθ=sinθ/cosθ

4) sin^2θ+cos^2θ=1

18 / 108

18. Conjugate base of H2CO3 is

1) H3CO3+

2) H2CO3−

3) HCO3−

4) CO3^2−

19 / 108

19. 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

20 / 108

20. 0.75 mol of substance with molar mass 80 g/mol has mass (g)

1) 80

2) 6

3) 600

4) 60

21 / 108

21. Match geometry item with formula.

1. Triangle area

2. Circle area

3. Rectangle area

22 / 108

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

1) 0.497

2) 79.477

3) 0.248

4) 0.994

23 / 108

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

1) 2

2) 4

3) 3

4) 1

24 / 108

24. Colligative properties depend on

1) Number of solute particles

2) Nature of solute only

3) Solvent identity only

4) Pressure only

25 / 108

25. Molarity for 1 mol solute in 4 L is

26 / 108

26. If cosθ=1, θ could be

1) π/4

2) π/3

3) π/2

4) 0

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

1) 0.3

2) 1.7

3) 0

4) 0.7

28 / 108

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

1) Continuity implies differentiability.

2) If LHL=RHL, limit exists.

3) Continuity implies limit equals function value.

4) Polynomials are continuous everywhere.

29 / 108

29. Geometry of XeF4 is

1) Linear

2) Trigonal bipyramidal

3) Tetrahedral

4) Square planar

30 / 108

30. Match probability term with meaning.

1. Complement

2. Independent events

3. Mutually exclusive

31 / 108

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

1) 1

2) 0

3) 2

4) Infinite

32 / 108

32. Strong electrolyte in water is

1) NH4OH

2) CH3COOH

3) Glucose

4) NaNO3

33 / 108

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

34 / 108

34. ∫ 3x^2 dx equals

1) x^3 + C

2) ln x + C

3) x^2 + C

4) 3x + C

35 / 108

35. Match quantity with SI unit.

1. Power

2. Charge

3. Magnetic flux

36 / 108

36. Tollens’ test is positive for

1) HCHO

2) CH3COCH3

3) CH3COOH

4) Benzene

37 / 108

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

1) Angle of incidence is greater than critical angle

2) Angle of incidence is less than critical angle

3) Angle of refraction is zero always

4) Refractive index of denser medium is smaller

38 / 108

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

39 / 108

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

40 / 108

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

1) 39.39

2) 80.0

3) 157.56

4) 78.78

41 / 108

41. Match colligative property with effect.

1. Osmotic pressure

2. Freezing point depression

3. Boiling point elevation

42 / 108

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

1) Mechanical energy always

2) Linear momentum

3) Speed of each body

4) Kinetic energy

43 / 108

43. Atoms per unit cell in BCC is

44 / 108

44. Which acts as a Lewis acid?

1) OH−

2) BF3

3) NH3

4) Cl−

45 / 108

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

1) Magnetic force is q(v×B).

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

3) If v ∥ B, force is zero.

4) If v ⟂ B, force magnitude is qvB.

46 / 108

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

47 / 108

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

1) If A⊆B then P(A)≤P(B)

2) P(A∪B)=P(A)+P(B)+P(A∩B)

3) P(∅)=0

4) P(A∩B)≤P(A)

48 / 108

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

1) Potential difference is path independent.

2) For a capacitor, Q ∝ V.

3) Electric field is conservative in electrostatics.

4) Capacitance depends on charge stored only.

49 / 108

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

50 / 108

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

1) 411.0

2) 102.8

3) 205.5

4) 0

51 / 108

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

1) 10

2) 5

3) 0

4) 1

52 / 108

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

1) Acceleration is non-zero and directed toward center

2) Acceleration is zero

3) Speed necessarily changes

4) Velocity is constant

53 / 108

53. If f(x)=2x+1, then f(−4) equals

1) −7

2) 7

3) −9

4) 9

54 / 108

54. Aromatic species is

1) Cyclobutadiene

2) C5H5−

3) C5H5+

4) COT

55 / 108

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

1) mol L^-1 s^-1

2) L mol^-1 s^-1

3) dimensionless

4) s^-1

56 / 108

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

1) 32

2) 12

3) 36

4) 64

57 / 108

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

1) 6

2) 8

3) 24

4) 12

58 / 108

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

1) Vapour pressure lowering is colligative.

2) Molarity depends on temperature.

3) Ideal solution has large ΔHmix.

4) Molality is temperature independent.

59 / 108

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

60 / 108

60. lim_{x→0} (sin x)/x is

61 / 108

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

62 / 108

62. Match function with inverse (domain restricted).

1. x^2 (x≥0)

2. x+5

3. 3x

63 / 108

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

1) Reduction is gain of electrons.

2) Oxidizing agent is reduced.

3) Oxidation is loss of electrons.

4) Reducing agent is reduced.

64 / 108

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

1) Depends on mass

2) Zero

3) Positive

4) Negative

65 / 108

65. Number of π bonds in benzene is

66 / 108

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

67 / 108

67. Match trig identity.

1. 1+tan^2θ

2. 1+cot^2θ

3. sin^2θ+cos^2θ

68 / 108

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

1) Increases

2) Remains same

3) Decreases

4) Becomes zero

69 / 108

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

1) At extreme position acceleration magnitude is maximum.

2) At extreme position speed is maximum.

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

4) At mean position acceleration is zero.

70 / 108

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

71 / 108

71. Slope of line 2x−y+3=0 is

1) −1/2

2) 1/2

3) −2

4) 2

72 / 108

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

1) Effective nuclear charge increases across a period.

2) Electronegativity increases down a group.

3) Atomic radius increases down a group.

4) Ionization energy decreases down a group.

73 / 108

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

1) SN2

2) E2

3) SN1

4) E1

74 / 108

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

1) Molecularity can be fractional.

2) Rate law is experimental.

3) Order can be fractional.

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

75 / 108

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

76 / 108

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

77 / 108

77. For ideal solutions, Raoult’s law states

1) Applies only to solids

2) ΔHmix always positive

3) p_i independent of x_i

4) p_i = x_i p_i°

78 / 108

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

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

2) At constant V, P proportional to T.

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

4) PV=nRT

79 / 108

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

80 / 108

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

1) In parallel, voltage is same across branches.

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

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

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

81 / 108

81. Match condition with statement.

1. TIR

2. Centripetal acceleration

3. Resonance (LC)

82 / 108

82. Compute 10C3.

83 / 108

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

1) 4.5 Ω

2) 1 Ω

3) 2 Ω

4) 9 Ω

84 / 108

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

85 / 108

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

1) 1

2) 2

3) 3

4) 4

86 / 108

86. 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.

87 / 108

87. Value of 6! is

1) 1440

2) 120

3) 720

4) 360

88 / 108

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

89 / 108

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

1. Charge

2. Energy

3. Pressure

90 / 108

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

1) 0°

2) 180°

3) 45°

4) 90°

91 / 108

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

92 / 108

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

93 / 108

93. If z=5−12i, then |z| equals

1) 13

2) 144

3) 7

4) 17

94 / 108

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

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

2) Sound in air is longitudinal.

3) Frequency changes when wave enters another medium.

4) v=fλ

95 / 108

95. Match acid-base term with definition.

1. Brønsted acid

2. Lewis acid

3. Lewis base

96 / 108

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

1) Identity

2) Orthogonal

3) Diagonal

4) Singular

97 / 108

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

1) ∫(f+g)=∫f+∫g

2) ∫(cf)=c∫f

3) ∫0 dx = C

4) ∫1/x dx = 1/x + C

98 / 108

98. Match lattice with atoms per unit cell.

1. BCC

2. SC

3. FCC

99 / 108

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

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

2) Henderson equation relates pH, pKa and ratio.

3) Buffer contains weak acid and its conjugate base.

4) Buffer resists pH change for small additions.

100 / 108

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

1) Temperature only

2) Surface area only

3) Intensity only

4) Frequency of incident light

101 / 108

101. Complex showing cis-trans isomerism is

1) [Fe(CN)6]4−

2) [Co(NH3)6]3+

3) [Ni(CO)4]

4) [Pt(NH3)2Cl2]

102 / 108

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

1) 240

2) 210

3) 255

4) 30

103 / 108

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

1) nPr=nCr always.

2) nC0=1

3) nPr=n!/(n−r)!

4) Permutations of n objects is n!.

104 / 108

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

1) 0.133

2) 76.8

3) 7.5

4) 9.5

105 / 108

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

1) Maximum

2) Depends on charge only

3) Zero

4) Always non-zero

106 / 108

106. Match test with compound class.

1. Iodoform

2. Tollens

3. Bromine water

107 / 108

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

108 / 108

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

1) Density only

2) Volume

3) Absolute temperature

4) Molar mass

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