JEE ADVANCED TYPE 2

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JEE ADVANCED TYPE 2

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1 / 108

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

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2. Evaluate: ∫_0^1 6x(1−x) dx.

3 / 108

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

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

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

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

4) Every one-one function is onto.

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

5 / 108

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

1. Aldehyde group

2. Unsaturation (C=C)

3. Methyl ketone

6 / 108

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

1) Photon momentum is p=E/c.

2) Increasing intensity increases photon energy at fixed frequency.

3) Photon energy is proportional to frequency.

4) Photoelectric threshold depends on material.

7 / 108

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

1. Total internal reflection

2. Diffraction (single slit)

3. Constructive interference

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

1. Equilibrium constant K

2. Catalyst

3. Rate constant k

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

1) 75°

2) 41.81°

3) 60°

4) 30°

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

1) HClO4

2) HClO

3) CH3COOH

4) H2CO3

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

1) A stable carbocation intermediate is formed.

2) Racemization can occur for chiral centers.

3) Inversion of configuration always occurs.

4) Rate depends only on substrate concentration.

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

1) 1

2) 7

3) 3

4) 11

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13. 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) 3.000002 s

4) 0.000006 s

14 / 108

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

1) Atomic radius generally decreases across a period.

2) Ionization energy generally increases across a period.

3) Electronegativity generally decreases across a period.

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

15 / 108

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

16 / 108

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

17 / 108

17. 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

18 / 108

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

1) 0.971 m

2) 119000 m

3) 1.942 m

4) 1.0294 m

19 / 108

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

1. Diagonals in n-gon

2. Permutations of n distinct items

3. Subsets of n-set

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

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

1) e^x

2) x

3) 1/x

4) ln x

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22. Which oxide is amphoteric?

1) CO2

2) Al2O3

3) SO3

4) Na2O

23 / 108

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

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

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

3) Interchanging two rows changes sign of determinant.

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

24 / 108

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

1) Convection involves bulk motion of fluid.

2) Conduction requires a material medium.

3) Radiation can occur in vacuum.

4) Convection occurs only in solids.

25 / 108

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

26 / 108

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

1) 0.65

2) 0.15

3) 0.2

4) 0.8

27 / 108

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

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

2) log 1 = 0 (any base).

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

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

28 / 108

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

1) 2

2) 1

3) 6

4) 4

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

1. Capacitance

2. Electric potential

3. Magnetic field B

30 / 108

30. 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

31 / 108

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

32 / 108

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

1) Cathode to anode

2) Salt bridge to anode

3) Electrolyte to electrodes equally

4) Anode to cathode

33 / 108

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

1) Resistance of loop changes

2) Electric field outside is zero

3) Magnetic flux through the loop changes with time

4) Area of loop changes randomly

34 / 108

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

35 / 108

35. Which polymer is an addition polymer?

1) Bakelite

2) Polyethylene

3) Terylene

4) Nylon-6,6

36 / 108

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

1) NaBH4

2) HNO3

3) K2Cr2O7/H+

4) KMnO4

37 / 108

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

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

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

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

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

38 / 108

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

39 / 108

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

1) Circle is a special case of ellipse.

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

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

4) Hyperbola has constant product of distances from foci.

40 / 108

40. 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) 0.0802 mol

3) 0.802 mol

4) 0.1604 mol

41 / 108

41. 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

42 / 108

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

1) 10

2) 65

3) 78

4) 66

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

1. d/dx (sin x)

2. ∫ x^n dx (n≠−1)

3. d/dx (ln x)

44 / 108

44. If a matrix A is singular, then

1) det(A)=0

2) trace(A)=0

3) A^-1 exists

4) A is always diagonal

45 / 108

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

1) Viscosity is a colligative property.

2) Freezing point depression depends on molality.

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

4) Osmotic pressure is a colligative property.

46 / 108

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

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

2) Total energy changes with time in ideal SHM.

3) Speed is maximum at equilibrium position.

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

47 / 108

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

1) 1

2) 7

3) -7

4) 0

48 / 108

48. If pOH=5, pH is

49 / 108

49. Oxidation state of S in H2SO4 is

50 / 108

50. 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)^2+(y+7)^2=25

4) (x−5)+(y−7)=25

51 / 108

51. 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) 3.2 m/s²

2) 0 m/s²

3) 4.9 m/s²

4) 6.6 m/s²

52 / 108

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

1) At highest point, acceleration becomes zero.

2) Vertical acceleration is constant and equals g downward.

3) Horizontal component of velocity remains constant.

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

53 / 108

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

54 / 108

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

1) In an AP, nth term is a+(n−1)d.

2) In a GP, nth term is ar^{n−1}.

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

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

55 / 108

55. Compute: lim_{x→0} (sin 5x)/x.

56 / 108

56. Which compound gives iodoform test?

1) HCHO

2) CH3CH2OH

3) CH3COCH3

4) CH3COOH

57 / 108

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

58 / 108

58. 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) 15000000.0 C/kg

4) 0.0 C/kg

59 / 108

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

1) 10.0 J

2) 0.1 J

3) 10.8 J

4) 3.6 J

60 / 108

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

61 / 108

61. 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).

62 / 108

62. 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.

63 / 108

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

1) 8.167

2) 0.012

3) 0.122

4) 1.220

64 / 108

64. ∫ x^4 dx equals

1) ln x + C

2) 4x^3+C

3) x^5/5 + C

4) x^4 + C

65 / 108

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

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

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

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

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

66 / 108

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

67 / 108

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

68 / 108

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

69 / 108

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

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

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

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

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

70 / 108

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

1) 3.429

2) 3.5

3) 4.667

4) 4

71 / 108

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

1) 9

2) 46

3) 45

4) 10

72 / 108

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

73 / 108

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

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

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

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

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

74 / 108

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

75 / 108

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

1) 7

2) 5

3) 4

4) 6

76 / 108

76. Which of the following has maximum bond order?

1) N2

2) O2

3) Ne2

4) F2

77 / 108

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

1) 64

2) 112

3) 25

4) 113

78 / 108

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

79 / 108

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

1) 12/25

2) 24/25

3) 1

4) 7/25

80 / 108

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

1) Initial speed and angle (and g)

2) Mass of projectile

3) Initial speed only (independent of angle)

4) Horizontal range only

81 / 108

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

1) It behaves as a short circuit

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

3) Charge on it is zero

4) Voltage across it is zero

82 / 108

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

1) P(A^c)=1−P(A).

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

83 / 108

83. Which pair represents coordination isomerism?

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

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

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

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

84 / 108

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

85 / 108

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

1. Energy

2. Impulse

3. Pressure

86 / 108

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

1. CH4

2. BF3

3. BeCl2 (g)

87 / 108

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

1. Circle

2. Parabola

3. Ellipse

88 / 108

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

1) π (or (2n+1)π)

2) 3π/2

3) 0 (or 2πn)

4) π/2

89 / 108

89. 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) 22 m/s

2) 10.4 m/s

3) 0.8 m/s

4) 11.0 m/s

90 / 108

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

1) 256

2) 254

3) 256

4) 2

91 / 108

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

1) 3

2) 3

3) 2

4) 1

92 / 108

92. The correct order of increasing electronegativity is

1) Na < Al < Mg < Si

2) Na < Mg < Al < Si

3) Mg < Na < Al < Si

4) Si < Al < Mg < Na

93 / 108

93. Compute the value of 12C3.

94 / 108

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

1) Towards NH3

2) Towards N2 and H2

3) Depends only on catalyst

4) No change

95 / 108

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

1) Geometrical isomerism is possible in square planar complexes.

2) Ligands act as Lewis bases.

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

4) Oxidation state of metal is always zero.

96 / 108

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

1. A is singular

2. A is identity

3. det(A)≠0

97 / 108

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

1) Retention of configuration

2) Inversion of configuration

3) Racemization always

4) No effect on stereochemistry

98 / 108

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

1) Always large

2) 0

3) Negative

4) Positive

99 / 108

99. 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).

100 / 108

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

1) 1.38 eV

2) 450 eV

3) 5.51 eV

4) 2.76 eV

101 / 108

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

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

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

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

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

102 / 108

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

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

4) a·b = |a||b|cosθ.

103 / 108

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

1) −|a||b|

2) 1

3) |a||b|

4) 0

104 / 108

104. Which statement best describes a catalyst?

1) It increases equilibrium constant

2) It increases rate by lowering activation energy

3) It increases ΔH of reaction

4) It is consumed stoichiometrically

105 / 108

105. 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) 625.0 m/s

3) 0.0016 m/s

4) 25.0 m/s

106 / 108

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

1) 216 W

2) 36 W

3) 1.0 W

4) 1.0 W

107 / 108

107. 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).

108 / 108

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

1) 20.086

2) 1

3) 3

4) 0

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