JEE ADVANCED TYPE 2 - Start Exam

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JEE ADVANCED TYPE 2

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1 / 108

1. Select all correct statements about ideal transformers (Set-02):

1) Voltage ratio equals turns ratio (Vp/Vs = Np/Ns).

2) Power input equals power output (no losses).

3) Transformer works on electrostatic induction.

4) In ideal transformer, current ratio is inverse of turns ratio (Ip/Is = Ns/Np).

2 / 108

2. Select all correct statements about SN1 reactions (Set-02):

1) Rate depends only on substrate concentration.

2) A stable carbocation intermediate is formed.

3) Inversion of configuration always occurs.

4) Racemization can occur for chiral centers.

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3. If vectors a and b are perpendicular, then a·b equals

1) −|a||b|

2) 1

3) |a||b|

4) 0

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4. If sinθ=3/5 (θ acute), then value of sin(2θ) is

1) 12/25

2) 1

3) 24/25

4) 7/25

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5. Match (List-I) with the correct count formula (List-II).

1. Subsets of n-set

2. Diagonals in n-gon

3. Permutations of n distinct items

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6. How many grams of NaCl are present in 0.5 mol? (M=58.5 g/mol)

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7. ∫ x^4 dx equals

1) x^4 + C

2) ln x + C

3) 4x^3+C

4) x^5/5 + C

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8. Compute: lim_{x→0} (sin 5x)/x.

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9. A charged particle moves in a circle of radius 0.4 m in uniform magnetic field B=0.5 T with speed 6×10^6 m/s. The magnitude of q/m equals (q/m = v/(Br))

1) 0.0 C/kg

2) 15000000.0 C/kg

3) 30000000.0 C/kg

4) 15000000.0 C/kg

10 / 108

10. A wire carries current 3 A for 120 s. Charge passed (C) is

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11. Match the quantity (List-I) with its SI unit (List-II).

1. Capacitance

2. Electric potential

3. Magnetic field B

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12. An inductor of inductance 0.6 H carries current 6 A. Energy stored is

1) 10.8 J

2) 3.6 J

3) 0.1 J

4) 10.0 J

13 / 108

13. If a vector has components (2,3,6), find its magnitude (rounded to 2 decimals).

14 / 108

14. Match (List-I) with the correct trend (List-II).

1. Electronegativity down a group

2. Ionization energy down a group

3. Atomic radius across a period

15 / 108

15. Select all correct statements about projectile motion (Set-02):

1) Time to reach highest point depends on initial vertical component.

2) Horizontal component of velocity remains constant.

3) Vertical acceleration is constant and equals g downward.

4) At highest point, acceleration becomes zero.

16 / 108

16. If P(A)=0.4 and P(B)=0.25 and independent, compute P(A∩B).

17 / 108

17. Which compound gives iodoform test?

1) CH3COCH3

2) HCHO

3) CH3COOH

4) CH3CH2OH

18 / 108

18. A conducting loop is moved out of a uniform magnetic field region with constant speed. The induced emf is non-zero because

1) Magnetic flux through the loop changes with time

2) Area of loop changes randomly

3) Resistance of loop changes

4) Electric field outside is zero

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19. A sound wave of frequency 350 Hz travels in air at 340 m/s. Wavelength is

1) 0.971 m

2) 1.942 m

3) 1.0294 m

4) 119000 m

20 / 108

20. Select all correct statements about heat transfer (Set-02):

1) Convection involves bulk motion of fluid.

2) Convection occurs only in solids.

3) Conduction requires a material medium.

4) Radiation can occur in vacuum.

21 / 108

21. Select all correct statements about induced emf (Set-02):

1) A changing flux can be due to changing B, area, or orientation.

2) Direction of induced current opposes the change in flux producing it.

3) Induced emf is proportional to rate of change of magnetic flux.

4) Induced emf exists even if flux is constant but magnetic field is present.

22 / 108

22. A body starts from rest and accelerates uniformly at 4 m/s² for 5 s. Final speed (m/s) is

23 / 108

23. Calculate molarity when 0.25 mol solute is dissolved to make 0.50 L solution.

24 / 108

24. Coefficient of x^8 in (1+x)^10 is

1) 10

2) 46

3) 45

4) 9

25 / 108

25. Select all correct statements about thermodynamics (Set-02):

1) Entropy of the universe always decreases for a spontaneous process.

2) ΔU = q + w (work done on system positive).

3) For an isothermal process of ideal gas, ΔU=0.

4) State functions depend only on initial and final states.

26 / 108

26. Select all correct statements for a body in SHM (Set-02):

1) Speed is maximum at equilibrium position.

2) Acceleration is proportional to displacement and opposite in direction.

3) Total energy changes with time in ideal SHM.

4) Time period is independent of amplitude (for ideal SHM).

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27. Match the physical situation (List-I) with the corresponding principle (List-II).

1. Induced current opposes change

2. No net external force on a system

3. Closed path integral of electrostatic field

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28. Select all correct statements about determinants (Set-02):

1) Interchanging two rows changes sign of determinant.

2) If determinant is non-zero, the matrix is singular.

3) Adding a multiple of one row to another does not change determinant.

4) If two rows of a determinant are identical, determinant is zero.

29 / 108

29. If pOH=5, pH is

30 / 108

30. Evaluate: ∫_0^1 6x(1−x) dx.

31 / 108

31. A 0.5 kg mass attached to spring executes SHM with k=200 N/m. Angular frequency ω (rad/s) is

32 / 108

32. Select all correct statements about polymers (Set-02):

1) Condensation polymers often eliminate small molecules (like H2O).

2) Addition polymers generally do not eliminate small molecules during formation.

3) Teflon is a condensation polymer.

4) Nylon-6,6 is a condensation polymer.

33 / 108

33. Sum of roots of equation x^2 + 7x + 1 = 0 is

1) 0

2) 7

3) -7

4) 1

34 / 108

34. Select all correct statements about conic sections (Set-02):

1) Parabola is the locus of points equidistant from a fixed point and a fixed line.

2) For ellipse, sum of distances from two foci is constant.

3) Hyperbola has constant product of distances from foci.

4) Circle is a special case of ellipse.

35 / 108

35. Match (List-I) with the correct dimension (List-II).

1. Pressure

2. Energy

3. Impulse

36 / 108

36. Number of σ-bonds in ethane (C2H6) is

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37. Masses 2 kg and 3 kg move along a line with speeds 14 m/s and 8 m/s in same direction. They stick together. Final speed is

1) 10.4 m/s

2) 0.8 m/s

3) 11.0 m/s

4) 22 m/s

38 / 108

38. Match (List-I) with (List-II).

1. ∫ x^n dx (n≠−1)

2. d/dx (sin x)

3. d/dx (ln x)

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39. If P(A)=0.3, P(B)=0.5 and A,B are independent, then P(A∪B) equals

1) 0.8

2) 0.15

3) 0.65

4) 0.2

40 / 108

40. Number of onto functions from a set of 8 elements to a set of 2 elements is

1) 254

2) 2

3) 256

4) 256

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41. Match (List-I) with the correct hybridization (List-II).

1. BeCl2 (g)

2. CH4

3. BF3

42 / 108

42. The number of atoms per unit cell in a BCC lattice is

1) 4

2) 1

3) 2

4) 6

43 / 108

43. Select all correct statements about chemical equilibrium (Set-02):

1) At equilibrium, concentrations of reactants and products are necessarily equal.

2) Equilibrium can be approached from either side (reactants/products).

3) A catalyst speeds up reaching equilibrium but does not change equilibrium composition.

4) At equilibrium, forward and reverse reaction rates are equal.

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44. In a galvanic cell, electrons flow in the external circuit from

1) Cathode to anode

2) Anode to cathode

3) Salt bridge to anode

4) Electrolyte to electrodes equally

45 / 108

45. Compute the value of 12C3.

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46. Which reagent converts an aldehyde to a primary alcohol selectively?

1) HNO3

2) KMnO4

3) K2Cr2O7/H+

4) NaBH4

47 / 108

47. Select all correct statements about coordination compounds (Set-02):

1) Ligands act as Lewis bases.

2) Geometrical isomerism is possible in square planar complexes.

3) Coordination number equals number of donor atoms attached to metal.

4) Oxidation state of metal is always zero.

48 / 108

48. Select all correct statements about colligative properties (Set-02):

1) Boiling point elevation depends on number of solute particles.

2) Osmotic pressure is a colligative property.

3) Viscosity is a colligative property.

4) Freezing point depression depends on molality.

49 / 108

49. A capacitor 3 μF is charged to 40 V. Energy stored in μJ is

50 / 108

50. Which statement is correct for a capacitor connected to a DC source after a long time?

1) Voltage across it is zero

2) It behaves as an open circuit (no steady current)

3) Charge on it is zero

4) It behaves as a short circuit

51 / 108

51. Number of diagonals in a convex polygon with 13 sides is

1) 78

2) 66

3) 10

4) 65

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52. A particle executes SHM with amplitude A=0.04 m and angular frequency ω=25 rad/s. Its maximum speed is

1) 1.0 m/s

2) 25.0 m/s

3) 625.0 m/s

4) 0.0016 m/s

53 / 108

53. A block slides down a rough incline (angle 30°) with coefficient of friction μ=0.2. Take g=9.8 m/s². Acceleration down the plane is

1) 6.6 m/s²

2) 4.9 m/s²

3) 0 m/s²

4) 3.2 m/s²

54 / 108

54. A resistor R=3 Ω is in series with a capacitor C=2 μF. The time constant τ=RC is

1) 0.000006 s

2) 3.000002 s

3) 1500000.000000 s

4) 0.000001 s

55 / 108

55. A wave travels with speed 360 m/s and frequency 120 Hz. Wavelength (m) is

56 / 108

56. Select all correct statements about periodic trends (Set-02):

1) Atomic radius generally decreases across a period.

2) Electron affinity generally becomes more negative across a period (with exceptions).

3) Ionization energy generally increases across a period.

4) Electronegativity generally decreases across a period.

57 / 108

57. Select all correct statements about redox reactions (Set-02):

1) Reducing agent itself gets oxidized.

2) Reduction involves gain of electrons.

3) Oxidation involves increase in oxidation number.

4) Oxidizing agent itself gets oxidized.

58 / 108

58. The pH of a 10^-3 M strong acid solution is closest to

1) 3

2) 7

3) 11

4) 1

59 / 108

59. For the equilibrium N2(g)+3H2(g)⇌2NH3(g), increasing pressure at constant temperature shifts equilibrium

1) Depends only on catalyst

2) Towards N2 and H2

3) Towards NH3

4) No change

60 / 108

60. Which statement best describes a catalyst?

1) It increases equilibrium constant

2) It increases ΔH of reaction

3) It increases rate by lowering activation energy

4) It is consumed stoichiometrically

61 / 108

61. A 2 Ω and 3 Ω resistors are connected in series across 10 V. Current (A) is

62 / 108

62. Evaluate lim(x→0) (e^3x − 0)/x (note: expression is (e^a·x)/x)

1) 20.086

2) 0

3) 1

4) 3

63 / 108

63. Select all correct statements about functions (Set-02):

1) Composition of two one-one functions is one-one.

2) If a function is onto, every element of codomain has a preimage.

3) Every one-one function is onto.

4) If a function is one-one, distinct inputs give distinct outputs.

64 / 108

64. For light going from glass (n=1.50) to air (n=1.00), the critical angle is closest to

1) 60°

2) 75°

3) 41.81°

4) 30°

65 / 108

65. Which pair represents coordination isomerism?

1) linkage in [Co(NH3)5NO2]Cl2

2) [Co(NH3)5Br]SO4 and [Co(NH3)5SO4]Br

3) cis/trans in [Pt(NH3)2Cl2]

4) optical in [Co(en)3]3+

66 / 108

66. Match (List-I) with the correct test (List-II).

1. Unsaturation (C=C)

2. Methyl ketone

3. Aldehyde group

67 / 108

67. Select all correct statements about capacitors in series (Set-02):

1) Potential difference across each capacitor is same in series combination.

2) Total potential difference is sum of individual potential differences.

3) Charge on each capacitor is same in series combination.

4) Equivalent capacitance is less than the smallest individual capacitance.

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68. For ideal gas: n=1 mol, T=300 K, R=0.082 L·atm/mol·K. Find PV (L·atm).

69 / 108

69. Which oxide is amphoteric?

1) SO3

2) Al2O3

3) CO2

4) Na2O

70 / 108

70. In interference, for two waves of equal amplitude, resultant intensity is maximum when phase difference is

1) π/2

2) 0 (or 2πn)

3) π (or (2n+1)π)

4) 3π/2

71 / 108

71. A lens has focal length 20 cm. Power (D) is

72 / 108

72. Match the conic (List-I) with the standard form (List-II).

1. Ellipse

2. Parabola

3. Circle

73 / 108

73. In BCC lattice, number of atoms per unit cell is

74 / 108

74. A circle has radius 7. Its area (in terms of π) equals

75 / 108

75. Match (List-I) with the correct statement (List-II).

1. Equilibrium constant K

2. Rate constant k

3. Catalyst

76 / 108

76. If the roots of x^2−7x+10=0 are α,β, compute α^2+β^2.

77 / 108

77. For first order reaction, if half-life t1/2=693 s, k (s^-1) equals (k=0.693/t1/2).

78 / 108

78. Which polymer is an addition polymer?

1) Nylon-6,6

2) Polyethylene

3) Bakelite

4) Terylene

79 / 108

79. Select all correct statements about sequences (Set-02):

1) In a GP, nth term is ar^{n−1}.

2) Sum of first n natural numbers is n^2.

3) Sum of first n natural numbers is n(n+1)/2.

4) In an AP, nth term is a+(n−1)d.

80 / 108

80. Select all correct statements about limits (Set-02):

1) If lim x→a f(x)=L and lim x→a g(x)=M, then lim x→a (f(x)+g(x))=L+M.

2) If lim x→a f(x) exists, then f(a) must be defined.

3) If lim x→a f(x) exists, left and right limits at a are equal.

4) If f is continuous at a, then lim x→a f(x)=f(a).

81 / 108

81. In SN2 reactions, stereochemistry at the chiral center typically shows

1) No effect on stereochemistry

2) Inversion of configuration

3) Retention of configuration

4) Racemization always

82 / 108

82. Select all correct statements about probability (Set-02):

1) P(A∪B)=P(A)+P(B) when A and B are mutually exclusive.

2) P(A^c)=1−P(A).

3) 0 ≤ P(A) ≤ 1 for any event A.

4) If A and B are independent, then P(A∩B)=P(A)+P(B).

83 / 108

83. Monochromatic light of wavelength 450 nm has photon energy (use 1240 eV·nm).

1) 5.51 eV

2) 2.76 eV

3) 450 eV

4) 1.38 eV

84 / 108

84. For y=ln x, the derivative dy/dx is

1) 1/x

2) e^x

3) ln x

4) x

85 / 108

85. A mass 2.0 kg is raised vertically by 10 m (take g=9.8). Increase in potential energy is

1) 20.0 J

2) 20.0 J

3) 196.0 J

4) 98.0 J

86 / 108

86. Select all correct statements about vectors (Set-02):

1) a·b = |a||b|cosθ.

2) If a·b=0, then a and b are perpendicular (or one is zero vector).

3) a×b is perpendicular to both a and b.

4) If a×b=0, then a and b are perpendicular.

87 / 108

87. A 2 kg block is pulled horizontally with force 14 N on a frictionless surface. Find acceleration (m/s²).

88 / 108

88. Value of determinant |1 1 1; 1 5 1; 1 1 5| is

1) 113

2) 25

3) 112

4) 64

89 / 108

89. Select all correct statements about logarithms (Set-02):

1) log 1 = 0 (any base).

2) log(a+b)=log a + log b always.

3) log(a^k)=k log a (a>0).

4) log(ab)=log a + log b (same base).

90 / 108

90. Match the wave phenomenon (List-I) with the key condition (List-II).

1. Constructive interference

2. Total internal reflection

3. Diffraction (single slit)

91 / 108

91. If a matrix A is singular, then

1) trace(A)=0

2) A^-1 exists

3) A is always diagonal

4) det(A)=0

92 / 108

92. An ideal gas at P=1.0×10^5 Pa and V=2.0×10^-3 m³ has temperature 300 K. Number of moles is (use PV=nRT, R=8.314)

1) 0.00802 mol

2) 0.1604 mol

3) 0.0802 mol

4) 0.802 mol

93 / 108

93. Number of moles in 12 g of a substance with molar mass 98 g/mol (rounded to 3 decimals) is

1) 0.012

2) 1.220

3) 8.167

4) 0.122

94 / 108

94. Select all correct statements about photons (Set-02):

1) Photon energy is proportional to frequency.

2) Photon momentum is p=E/c.

3) Photoelectric threshold depends on material.

4) Increasing intensity increases photon energy at fixed frequency.

95 / 108

95. Which of the following is a stronger acid in aqueous solution?

1) HClO4

2) H2CO3

3) HClO

4) CH3COOH

96 / 108

96. Which of the following has maximum bond order?

1) F2

2) O2

3) Ne2

4) N2

97 / 108

97. For an ideal solution, the enthalpy change of mixing (ΔHmix) is

1) 0

2) Always large

3) Positive

4) Negative

98 / 108

98. Sum of infinite GP with first term 4 and common ratio 1/7 is

1) 3.429

2) 4

3) 4.667

4) 3.5

99 / 108

99. A current 6 A passes through resistance 6 Ω. Power dissipated is

1) 1.0 W

2) 216 W

3) 36 W

4) 1.0 W

100 / 108

100. For a projectile (no air resistance), time of flight depends on

1) Mass of projectile

2) Horizontal range only

3) Initial speed and angle (and g)

4) Initial speed only (independent of angle)

101 / 108

101. Compute determinant of matrix [[2,3],[5,7]].

102 / 108

102. Oxidation state of S in H2SO4 is

103 / 108

103. Equation of the circle with center (5,7) and radius 5 is

1) (x−5)^2+(y−7)^2=25

2) (x−5)^2+(y−7)^2=5

3) (x−5)+(y−7)=25

4) (x+5)^2+(y+7)^2=25

104 / 108

104. Find the remainder when (32^2 + 16) is divided by 14.

1) 5

2) 7

3) 4

4) 6

105 / 108

105. Match the matrix property (List-I) with the implication (List-II).

1. A is singular

2. det(A)≠0

3. A is identity

106 / 108

106. The correct order of increasing electronegativity is

1) Na < Mg < Al < Si

2) Na < Al < Mg < Si

3) Mg < Na < Al < Si

4) Si < Al < Mg < Na

107 / 108

107. Let f(x)=ax+b with a=2, b=3. If f(f(x)) = 4x + 9, then a equals

1) 3

2) 2

3) 1

4) 3

108 / 108

108. Select all correct statements about electric field lines (Set-02):

1) Electric field lines start on positive charges and end on negative charges (or infinity).

2) Density of field lines indicates field strength.

3) Two electric field lines can never intersect.

4) Field lines are always closed loops in electrostatics.

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