JEE ADVANCED TYPE 2 - Start Exam

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JEE ADVANCED TYPE 2

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1 / 108

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

1) 2

2) 1

3) 3

4) 3

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2. 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) 30000000.0 C/kg

2) 15000000.0 C/kg

3) 0.0 C/kg

4) 15000000.0 C/kg

3 / 108

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

1) At highest point, acceleration becomes zero.

2) Horizontal component of velocity remains constant.

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

4) Vertical acceleration is constant and equals g downward.

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

1. Aldehyde group

2. Methyl ketone

3. Unsaturation (C=C)

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

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

1) 7

2) 6

3) 4

4) 5

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

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

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

1) 36 W

2) 1.0 W

3) 1.0 W

4) 216 W

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

1) Positive

2) 0

3) Always large

4) Negative

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

1) 256

2) 256

3) 2

4) 254

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

1) No effect on stereochemistry

2) Racemization always

3) Retention of configuration

4) Inversion of configuration

14 / 108

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

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

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

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

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

15 / 108

15. 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.

16 / 108

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

17 / 108

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

1. Energy

2. Impulse

3. Pressure

18 / 108

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

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

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

1) Convection occurs only in solids.

2) Convection involves bulk motion of fluid.

3) Radiation can occur in vacuum.

4) Conduction requires a material medium.

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21. ∫ x^4 dx equals

1) 4x^3+C

2) x^5/5 + C

3) ln x + C

4) x^4 + C

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

1) 3.5

2) 3.429

3) 4

4) 4.667

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

1) 1.220

2) 0.012

3) 8.167

4) 0.122

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

25 / 108

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

1) K2Cr2O7/H+

2) NaBH4

3) KMnO4

4) HNO3

26 / 108

26. 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) 0 m/s²

3) 3.2 m/s²

4) 4.9 m/s²

27 / 108

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

1) 7

2) 1

3) 3

4) 11

28 / 108

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

1) H2CO3

2) CH3COOH

3) HClO

4) HClO4

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

1) (x−5)^2+(y−7)^2=5

2) (x−5)^2+(y−7)^2=25

3) (x−5)+(y−7)=25

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

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

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31. Compute: lim_{x→0} (sin 5x)/x.

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32. If pOH=5, pH is

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

1) Oxidation state of metal is always zero.

2) Geometrical isomerism is possible in square planar complexes.

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

4) Ligands act as Lewis bases.

34 / 108

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

1. Equilibrium constant K

2. Rate constant k

3. Catalyst

35 / 108

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

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

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

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

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

36 / 108

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

1. Electric potential

2. Capacitance

3. Magnetic field B

37 / 108

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

1. Ellipse

2. Parabola

3. Circle

38 / 108

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

1) 1/x

2) x

3) ln x

4) e^x

39 / 108

39. 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

40 / 108

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

41 / 108

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

1) 0

2) 1

3) −|a||b|

4) |a||b|

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

1) In an AP, nth term is a+(n−1)d.

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

3) In a GP, nth term is ar^{n−1}.

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

43 / 108

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

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

2) Total energy changes with time in ideal SHM.

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

4) Speed is maximum at equilibrium position.

44 / 108

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

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

2) Electronegativity generally decreases across a period.

3) Atomic radius generally decreases across a period.

4) Ionization energy generally increases across a period.

45 / 108

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

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

1) Anode to cathode

2) Cathode to anode

3) Salt bridge to anode

4) Electrolyte to electrodes equally

47 / 108

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

1) Depends only on catalyst

2) Towards NH3

3) No change

4) Towards N2 and H2

48 / 108

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

1) 0

2) -7

3) 7

4) 1

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

1) 60°

2) 41.81°

3) 30°

4) 75°

50 / 108

50. Which of the following has maximum bond order?

1) O2

2) F2

3) Ne2

4) N2

51 / 108

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

1) 0.000001 s

2) 1500000.000000 s

3) 0.000006 s

4) 3.000002 s

52 / 108

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

53 / 108

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

1. CH4

2. BeCl2 (g)

3. BF3

54 / 108

54. 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) 0.0016 m/s

4) 625.0 m/s

55 / 108

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

1. ∫ x^n dx (n≠−1)

2. d/dx (sin x)

3. d/dx (ln x)

56 / 108

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

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

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

3) Interchanging two rows changes sign of determinant.

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

57 / 108

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

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

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

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

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

58 / 108

58. 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) 0.8 m/s

2) 22 m/s

3) 11.0 m/s

4) 10.4 m/s

59 / 108

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

60 / 108

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

1) Charge on it is zero

2) Voltage across it is zero

3) It behaves as a short circuit

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

61 / 108

61. Evaluate: ∫_0^1 6x(1−x) dx.

62 / 108

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

63 / 108

63. Oxidation state of S in H2SO4 is

64 / 108

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

1. Diagonals in n-gon

2. Subsets of n-set

3. Permutations of n distinct items

65 / 108

65. Which statement best describes a catalyst?

1) It is consumed stoichiometrically

2) It increases equilibrium constant

3) It increases rate by lowering activation energy

4) It increases ΔH of reaction

66 / 108

66. Which compound gives iodoform test?

1) CH3COCH3

2) CH3CH2OH

3) CH3COOH

4) HCHO

67 / 108

67. 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

68 / 108

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

69 / 108

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

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

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

3) 0 ≤ P(A) ≤ 1 for any event A.

4) P(A^c)=1−P(A).

70 / 108

70. Which polymer is an addition polymer?

1) Nylon-6,6

2) Bakelite

3) Terylene

4) Polyethylene

71 / 108

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

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

1) 0.15

2) 0.8

3) 0.65

4) 0.2

73 / 108

73. The correct order of increasing electronegativity is

1) Mg < Na < Al < Si

2) Na < Al < Mg < Si

3) Si < Al < Mg < Na

4) Na < Mg < Al < Si

74 / 108

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

1) 20.086

2) 1

3) 3

4) 0

75 / 108

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

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

2) Freezing point depression depends on molality.

3) Viscosity is a colligative property.

4) Osmotic pressure is a colligative property.

76 / 108

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

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

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

3) log 1 = 0 (any base).

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

77 / 108

77. Which oxide is amphoteric?

1) SO3

2) Na2O

3) Al2O3

4) CO2

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

1) Initial speed and angle (and g)

2) Initial speed only (independent of angle)

3) Horizontal range only

4) Mass of projectile

79 / 108

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

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

1. No net external force on a system

2. Closed path integral of electrostatic field

3. Induced current opposes change

81 / 108

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

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

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

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

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

82 / 108

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

1) 10

2) 78

3) 65

4) 66

83 / 108

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

1) 6

2) 4

3) 1

4) 2

84 / 108

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

1) 113

2) 112

3) 64

4) 25

85 / 108

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

86 / 108

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

1. Atomic radius across a period

2. Ionization energy down a group

3. Electronegativity down a group

87 / 108

87. Compute the value of 12C3.

88 / 108

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

1) 0.1 J

2) 3.6 J

3) 10.0 J

4) 10.8 J

89 / 108

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

1. A is singular

2. det(A)≠0

3. A is identity

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

1) Racemization can occur for chiral centers.

2) Inversion of configuration always occurs.

3) Rate depends only on substrate concentration.

4) A stable carbocation intermediate is formed.

92 / 108

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

1) 5.51 eV

2) 1.38 eV

3) 2.76 eV

4) 450 eV

93 / 108

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

94 / 108

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

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

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

3) a·b = |a||b|cosθ.

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

95 / 108

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

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

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

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

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

96 / 108

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

1) Density of field lines indicates field strength.

2) Field lines are always closed loops in electrostatics.

3) Two electric field lines can never intersect.

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

97 / 108

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

1) Transformer works on electrostatic induction.

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

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

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

98 / 108

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

1) 0 (or 2πn)

2) 3π/2

3) π/2

4) π (or (2n+1)π)

99 / 108

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

100 / 108

100. 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) Electric field outside is zero

3) Area of loop changes randomly

4) Resistance of loop changes

101 / 108

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

1) 46

2) 9

3) 45

4) 10

102 / 108

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

1) Photon momentum is p=E/c.

2) Photon energy is proportional to frequency.

3) Photoelectric threshold depends on material.

4) Increasing intensity increases photon energy at fixed frequency.

103 / 108

103. If a matrix A is singular, then

1) A^-1 exists

2) trace(A)=0

3) det(A)=0

4) A is always diagonal

104 / 108

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

1) Oxidation involves increase in oxidation number.

2) Oxidizing agent itself gets oxidized.

3) Reducing agent itself gets oxidized.

4) Reduction involves gain of electrons.

105 / 108

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

1) 98.0 J

2) 196.0 J

3) 20.0 J

4) 20.0 J

106 / 108

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

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

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

3) Teflon is a condensation polymer.

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

107 / 108

107. Which pair represents coordination isomerism?

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

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

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

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

108 / 108

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

1) Hyperbola has constant product of distances from foci.

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

3) Circle is a special case of ellipse.

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

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