JEE ADVANCED TYPE 1

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1 / 108

1. A string under tension 100 N has linear mass density 0.01 kg/m. Wave speed on the string (m/s) is:

2 / 108

2. Let z = (1+i)/(1−i). Then z equals:

1) 1

2) −1

3) −i

4) i

3 / 108

3. Shortest distance from point (2,−1) to line 3x−4y+5=0 is:

1) 4.0

2) 1.5

3) 6.0

4) 3.0

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4. Select all correct statements about chemical kinetics:

1) Half-life of zero-order reaction is independent of initial concentration.

2) Activation energy is the energy difference between reactants and products.

3) Rate constant of a reaction increases with temperature.

4) Order of reaction can be fractional.

5 / 108

5. Select all correct statements regarding periodic trends:

1) Atomic radius generally decreases across a period.

2) Electronegativity generally increases across a period.

3) Ionization enthalpy generally decreases down a group.

4) Electron affinity of noble gases is high.

6 / 108

6. Calculate rms speed (m/s) of nitrogen gas at 300 K. Take molar mass 28 g/mol and R=8.314.

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7. Select all correct statements about electrochemistry:

1) Standard electrode potentials are measured relative to SHE.

2) Cell emf is intensive property.

3) Increasing Q increases E for a galvanic cell.

4) For spontaneous cell reaction, ΔG<0.

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8. Compute S = 1^3 + 2^3 + … + 20^3.

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9. A conducting rod of length 0.4 m moves with speed 8 m/s perpendicular to a uniform magnetic field of 0.5 T. The motional emf induced between its ends is:

1) 1.6 V

2) 2.1 V

3) 3.2 V

4) 0.8 V

10 / 108

10. Match the matrix (List-I) with its determinant (List-II).

1. [[1,2],[2,4]]

2. [[2,1],[5,3]]

3. [[1,0],[0,1]]

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11. A metal has work function 2.2 eV. The threshold wavelength for photoelectric emission is (hc ≈ 1240 eV·nm):

1) 763.6 nm

2) 676.3 nm

3) 450.9 nm

4) 563.6 nm

12 / 108

12. Calculate pH (to 2 decimal places) of 0.1 M weak acid HA with Ka = 1.0×10⁻⁵. (Assume x<

13 / 108

13. For the reaction A(g) ⇌ 2B(g), Kc = 0.5 at 400 K. Calculate Kp (R=0.0821 L·atm·mol⁻¹·K⁻¹).

1) 32.84

2) 8.21

3) 21.42

4) 16.42

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14. A particle moves along x-axis with position x(t)=2t^3−6t^2 (SI units). At what time t>0 does it attain maximum speed for 0

15 / 108

15. Match the process (List-I) with the property that remains constant for an ideal gas (List-II).

1. Isobaric

2. Isochoric

3. Isothermal

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16. A capacitor of capacitance 2 μF is charged to V0 and discharged through a resistor of 5 kΩ. Time taken for the voltage to drop to V0/2 is:

1) 6.931 ms

2) 3.466 ms

3) 10.396 ms

4) 13.862 ms

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17. Volume of the parallelepiped formed by vectors (1,0,2), (0,2,1), (2,1,0) is:

1) 11

2) 18

3) 9

4) 7

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18. Which has the highest first ionization enthalpy?

1) Al

2) Cl

3) Ne

4) Na

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19. Select all correct statements about vectors a,b,c:

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

2) a×(b×c) = b(a·c) − c(a·b).

3) (a×b)·c equals the determinant with rows a,b,c.

4) a·(b×c) = b·(c×a).

20 / 108

20. A solid cylinder rolls without slipping down an incline of angle 30°. Take g = 9.8 m/s². Its linear acceleration is:

1) 4.91 m/s^2

2) 3.27 m/s^2

3) 6.54 m/s^2

4) 2.45 m/s^2

21 / 108

21. A mixture contains 2 mol He and 1 mol O2 in a container. The mole fraction of O2 is:

1) 1/3

2) 1/4

3) 1/2

4) 2/3

22 / 108

22. Number of onto (surjective) functions from a 3‑element set to a 2‑element set is:

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23. For real x, select all x satisfying the inequality x²−5x+6 ≤ 0:

1) x=3

2) x=4

3) x=1

4) x=2.5

24 / 108

24. A source emitting sound of frequency 1000 Hz approaches a stationary observer with speed 20 m/s. Take speed of sound 340 m/s. Observed frequency is:

1) 941.2 Hz

2) 1168.8 Hz

3) 944.4 Hz

4) 1062.5 Hz

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25. A particle executes SHM with amplitude 0.2 m and angular frequency 10 rad/s. Its speed when displacement is 0.12 m from mean position is:

1) 1.6 m/s

2) 2.4 m/s

3) 1.28 m/s

4) 1.92 m/s

26 / 108

26. Select all correct statements about ideal solutions and Raoult’s law:

1) Vapour pressure of solution equals sum of partial vapour pressures.

2) Azeotropes are formed by ideal solutions.

3) For an ideal solution, ΔHmix=0.

4) For an ideal solution, ΔVmix=0.

27 / 108

27. Match the conic (List-I) with its eccentricity (List-II).

1. Parabola

2. Circle

3. Hyperbola

28 / 108

28. The geometry of [Ni(CN)4]2− is:

1) square planar

2) tetrahedral

3) octahedral

4) trigonal planar

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29. Select all correct statements:

1) If vectors a and b are nonzero and a·b=0, then they are parallel.

2) If f is differentiable on (a,b) and f'(x)=0 for all x in (a,b), then f is constant on (a,b).

3) If det(A)=0 for a square matrix A, then A has an inverse.

4) If a sequence is bounded and monotonic, it converges.

30 / 108

30. Value of Σ_{k=0}^{6} C(6,k)^2 is:

1) 792

2) 924

3) 914

4) 934

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31. In acidic medium, the equivalent weight of KMnO4 as an oxidizing agent is:

1) molar mass/1

2) molar mass/2

3) molar mass/5

4) molar mass/3

32 / 108

32. Evaluate ∫₀¹ ln(1+x) dx (numerical value).

33 / 108

33. Select all correct statements about chemical equilibrium:

1) Catalyst changes equilibrium constant.

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

3) Equilibrium constant depends on temperature.

4) For a given T, K is independent of initial concentrations.

34 / 108

34. Select all correct statements about conics:

1) Director circle of a circle is itself.

2) A parabola has two distinct foci.

3) For hyperbola, difference of distances from foci to any point is constant.

4) For ellipse, sum of distances from foci to any point is constant.

35 / 108

35. Capacitors of 2 μF and 3 μF are connected in series; this combination is connected in parallel with 6 μF. The equivalent capacitance is:

1) 8.2 μF

2) 3.6 μF

3) 7.2 μF

4) 10.8 μF

36 / 108

36. Evaluate I = ∫₀^{π/2} ln(sin x) dx (numerical value).

1) 1.0888

2) -2.1776

3) -1.0888

4) -0.5444

37 / 108

37. Number of non‑negative integer solutions (x,y,z) to x+y+z=12 with x≥2 is:

1) 78

2) 66

3) 45

4) 55

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38. Hybridization of the central atom in SF6 is:

1) sp3

2) d2sp3

3) sp2

4) sp3d2

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39. One mole of an ideal gas at 300 K expands isothermally from volume 2 L to 6 L. Work done by the gas is (R=8.314 J/mol·K):

1) 1370.1 J

2) 5480.4 J

3) 4110.3 J

4) 2740.2 J

40 / 108

40. Match the circuit element (List-I) with the correct impedance magnitude at angular frequency ω (List-II).

1. Capacitor C

2. Resistor R

3. Inductor L

41 / 108

41. Select all correct statements about complex numbers:

1) If z≠0, then |1/z| = 1/|z|.

2) For any complex z, |z|² = z z̄.

3) If |z|=|w|, then z=w.

4) If z is purely imaginary, then z̄ = −z.

42 / 108

42. For parabola y²=8x, equation of tangent with slope m=1 is:

1) y = x − 2

2) y = x + 4

3) y = x + 1

4) y = x + 2

43 / 108

43. Select all correct statements about organic reactions:

1) E2 elimination requires anti-periplanar H and leaving group for maximum rate.

2) SN2 reactions are favored by tertiary alkyl halides.

3) Aldehydes are generally more reactive than ketones towards nucleophilic addition.

4) Carbocations undergo rearrangement if more stable carbocation can form.

44 / 108

44. A reversible engine operates between 600 K and 300 K. Its maximum possible efficiency is:

1) 0.6

2) 0.5

3) 0.4

4) 0.5

45 / 108

45. Number of solutions of sin x = 1/2 in interval [0,4π) is:

46 / 108

46. A first-order reaction has half-life 30 s. Calculate its rate constant k (s⁻¹).

47 / 108

47. A box has 3 red and 2 blue balls. Two balls are drawn without replacement. Probability that the first is red given that the second is red is:

1) 2/3

2) 1/2

3) 4/5

4) 3/5

48 / 108

48. A wire in the form of a semicircle of radius 0.2 m carries current 3 A. Magnetic field at the center due to the semicircular part is:

1) 4.71 μT

2) 7.06 μT

3) 9.42 μT

4) 2.35 μT

49 / 108

49. Select all correct statements in mechanics:

1) In perfectly elastic collision, kinetic energy of system is conserved.

2) If net external force on a system is zero, total momentum of the system is conserved.

3) Static friction always equals μsN.

4) Centripetal force does no work in uniform circular motion.

50 / 108

50. A fair coin is tossed 5 times. Probability of getting exactly 2 heads is:

51 / 108

51. AgCl has Ksp = 1.8×10⁻¹⁰ at 298 K. Its molar solubility in pure water (M) is:

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52. Ozonolysis of propene followed by reductive work-up (Zn/H2O) gives:

1) ethanal and methanal

2) ethanoic acid and methanal

3) ethanal only

4) propanone only

53 / 108

53. A particle of mass 0.5 kg moves in a vertical circle of radius 2 m with speed 6 m/s at the lowest point. Tension in the string at the lowest point (g=9.8) is:

1) 18.8 N

2) 10.43 N

3) 13.9 N

4) 9.0 N

54 / 108

54. Match the compound (List-I) with the type of hybridization of central atom (List-II).

1. SF6

2. BF3

3. NH3

55 / 108

55. A satellite moves in a circular orbit of height 1.6×10^6 m above Earth’s surface. Take Earth radius 6.4×10^6 m and GM = 3.986×10^14 SI. Its orbital period is approximately:

1) 2.98 h

2) 1.58 h

3) 1.98 h

4) 2.38 h

56 / 108

56. In Young’s double slit experiment, slit separation is 0.5 mm, screen distance 1.5 m and wavelength 600 nm. Fringe width is:

1) 3.6 mm

2) 2.7 mm

3) 0.9 mm

4) 1.8 mm

57 / 108

57. Which of the following is aromatic?

1) cyclooctatetraene (C8H8)

2) cyclopentadienyl anion (C5H5−)

3) cyclobutadiene (C4H4)

4) cyclohexane

58 / 108

58. Two point charges +2 μC and -1 μC are placed at two vertices A and B of an equilateral triangle of side 0.3 m. Find the magnitude of the electric field at the centroid of the triangle due to these two charges (k=9×10^9 SI).

1) 396862.7 N/C

2) 1587450.78 N/C

3) 793725.39 N/C

4) 992156.74 N/C

59 / 108

59. For Daniell cell (Zn|Zn2+ || Cu2+|Cu), E°=1.10 V at 298 K. If [Zn2+]=0.01 M and [Cu2+]=1.0 M, cell potential E is:

60 / 108

60. Select all correct statements about geometrical/wave optics:

1) Angular magnification of a simple microscope increases when final image is at infinity.

2) In thin film reflection, a phase change of π occurs on reflection from a denser medium.

3) In YDSE, fringe width increases if slit separation increases.

4) For a convex lens, real image can be formed only if object is beyond focal length.

61 / 108

61. Using bond energies (kJ/mol): H–H=436, Cl–Cl=243, H–Cl=431. Estimate ΔH (kJ/mol) for H2(g)+Cl2(g)→2HCl(g).

62 / 108

62. For a particle in ideal simple harmonic motion, select all correct statements:

1) In SHM, acceleration is proportional to displacement and opposite in direction.

2) Phase difference between velocity and displacement in SHM is π/2.

3) At mean position, kinetic energy is minimum.

4) Total energy in ideal SHM depends on amplitude squared.

63 / 108

63. Standard enthalpy of combustion of CH4 is −890 kJ/mol. The enthalpy change (kJ) for burning 11.2 L CH4 at STP is:

1) −222.5

2) −445

3) −1780

4) −890

64 / 108

64. Evaluate lim_{x→0} (sin x − x)/x³.

1) 0

2) -1.0002

3) -0.1667

4) 0.1667

65 / 108

65. At 298 K, a cell has E° = 1.1 V for a 2e⁻ reaction. If reaction quotient Q = 10, the cell potential E is:

1) 1.04 V

2) 1.1 V

3) 1.1 V

4) 1.07 V

66 / 108

66. A 2 kg mass is raised vertically by 5 m (g=9.8). Increase in gravitational potential energy (J) is:

67 / 108

67. Match the reagent (List-I) with the major product formed (List-II).

1. Ethanol + PCC

2. Aniline + NaNO2/HCl (0-5°C)

3. Propene + HBr (peroxide present)

68 / 108

68. For a sparingly soluble hydroxide M(OH)2, Ksp = 1.0×10⁻¹² at 298 K. Its molar solubility in pure water is:

1) 6e-05 M

2) 3e-05 M

3) 0.00012 M

4) 0.0006 M

69 / 108

69. Number of solutions of sin x = cos 2x in [0, 2π) is:

1) 3

2) 1

3) 4

4) 2

70 / 108

70. An electrolyte AB dissociates into A+ and B−. If its van’t Hoff factor i=1.8, the degree of dissociation α is:

71 / 108

71. Select all correct statements (ideal gas / thermodynamics):

1) In a cyclic process, ΔU is non-zero.

2) For a reversible process, entropy generation is zero.

3) In an adiabatic process for ideal gas, PV^γ is constant.

4) For an ideal gas, internal energy depends only on temperature.

72 / 108

72. When 2-bromobutane reacts with aqueous KOH (polar protic) at moderate temperature, the major product is:

1) 2-methoxybutane

2) but-2-ene (only trans)

3) butan-1-ol

4) butan-2-ol (racemic mixture)

73 / 108

73. Evaluate lim_{n→∞} (1+1/n)^n (numerical value up to 4 decimals).

74 / 108

74. Match the wave phenomenon (List-I) with the condition/feature (List-II).

1. Beats

2. Doppler effect

3. Standing wave

75 / 108

75. Compute |(1,2,2) × (2,0,1)|.

76 / 108

76. 2.0 g of a non-electrolyte is dissolved in 100 g of water. The freezing point depression is 0.372 K (Kf=1.86 K·kg·mol⁻¹). Molar mass of the solute is:

1) 120.0 g/mol

2) 150.0 g/mol

3) 80.0 g/mol

4) 100.0 g/mol

77 / 108

77. An inductor of inductance 0.5 H is connected in series with a resistor of 20 Ω. Time constant of the RL circuit (in seconds) is:

78 / 108

78. Select all correct statements about modern physics:

1) De Broglie wavelength decreases when particle momentum increases.

2) For a given transition, emitted photon energy equals difference of energy levels.

3) In photoelectric effect, stopping potential depends on intensity of light only.

4) Compton shift depends on the scattering angle.

79 / 108

79. A particle tied to a string of length 1.5 m moves in a vertical circle. Minimum speed at the top to keep the string just taut (m/s) is:

80 / 108

80. A first-order reaction has rate constant k = 0.231 s⁻¹. Its half-life is:

1) 4.33 s

2) 1.5 s

3) 3.0 s

4) 6.0 s

81 / 108

81. A capacitor of capacitance 4 μF is charged to 200 V and then isolated. Energy stored in it (in joules) is:

82 / 108

82. Evaluate ∫₀¹ 1/(1+√x) dx.

1) 0.1137

2) 1.1137

3) 0.6137

4) 1.2274

83 / 108

83. Select all correct statements about acids and bases:

1) pH of 0.01 M HCl is 2.

2) A stronger acid has smaller Ka.

3) For a weak acid HA, Ka=[H+][A−]/[HA].

4) At 25°C, pH+pOH=14.

84 / 108

84. Match the type of solid (List-I) with its characteristic (List-II).

1. Covalent network solid

2. Ionic solid

3. Molecular solid

85 / 108

85. Select all correct statements about electrostatics:

1) In electrostatic equilibrium, electric field inside a conductor is zero.

2) Electric field is always perpendicular to equipotential surfaces.

3) Work done in moving a test charge in an electrostatic field depends on the path.

4) Electric potential is a scalar quantity.

86 / 108

86. Evaluate ∫₀¹ x e^x dx.

1) 1.0

2) 2.0

3) 0.0

4) 2.0

87 / 108

87. A thin convex lens of focal length 20 cm forms a real image of an object placed 30 cm in front of it. The image distance (from the lens) is:

1) 7.0 cm

2) 12.0 cm

3) 24.0 cm

4) 22.0 cm

88 / 108

88. Number of real solutions of |x−2| + |x−5| = 7 is:

1) 2

2) 1

3) 3

4) 0

89 / 108

89. A solution contains 10 g water and 46 g ethanol (C2H5OH). Mole fraction of water is:

90 / 108

90. Select all correct statements about electromagnetic induction:

1) Lenz’s law is a consequence of conservation of energy.

2) Self-inductance of a coil depends on the current through it.

3) Mutual inductance depends on relative orientation of coils.

4) Induced emf can be produced by changing magnetic flux through a circuit.

91 / 108

91. Match the integral (List-I) with its value (List-II).

1. ∫₀¹ x/(1+x²) dx

2. ∫₀^π sin x dx

3. ∫₀¹ ln(1+x) dx

92 / 108

92. Match each physical quantity (List-I) with its SI unit (List-II).

1. Electric field (E)

2. Capacitance (C)

3. Magnetic flux (Φ)

93 / 108

93. A buffer contains acetic acid and sodium acetate such that [CH3COO−]/[CH3COOH] = 3. Given pKa = 4.76, the pH is:

1) 5.24

2) 5.54

3) 4.94

4) 4.76

94 / 108

94. Select all correct values of θ in [0,2π) satisfying sinθ = 1/2:

1) θ=5π/6

2) θ=π/6

3) θ=11π/6

4) θ=7π/6

95 / 108

95. A loop is in uniform magnetic field 0.2 T perpendicular to its plane. Its area increases at 0.05 m²/s. Magnitude of induced emf (V) is:

96 / 108

96. Select all correct statements about determinants:

1) If two rows are identical, determinant is 1.

2) det(A^T)=det(A).

3) Swapping two rows changes the sign of determinant.

4) Adding a multiple of one row to another row leaves determinant unchanged.

97 / 108

97. Number of stereoisomers of 2,3-dichlorobutane is:

1) 1

2) 3

3) 2

4) 4

98 / 108

98. A simple pendulum is taken from Earth (g=9.8 m/s²) to a planet where g=4.9 m/s². The ratio of its time period (planet/Earth) is:

1) 1.91

2) 0.71

3) 1.41

4) 1.99

99 / 108

99. Match the trigonometric expression (List-I) with its identity (List-II).

1. sin²x+cos²x

2. 1+tan²x

3. 1+cot²x

100 / 108

100. For matrix A = [[2,1],[1,2]], the larger eigenvalue is:

1) 4

2) 1

3) 3

4) 2

101 / 108

101. General solution of dy/dx = (y/x) + x (x>0) is:

1) y = x + Cx²

2) y = Cx

3) y = x² + C/x

4) y = x² + Cx

102 / 108

102. Select all correct statements about integration:

1) ∫_{a}^{b} f(x) dx = ∫_{a}^{c} f(x) dx + ∫_{c}^{b} f(x) dx for any c in [a,b].

2) ∫ f'(x) dx = f(x) + C.

3) If f is odd, then ∫_{−a}^{a} f(x) dx = 0.

4) If f(x)≥0 on [a,b], then ∫_{a}^{b} f(x) dx ≥ 0.

103 / 108

103. Number of permutations of digits 1,2,3,4,5 in which 1 and 2 are not adjacent is:

1) 48

2) 72

3) 48

4) 60

104 / 108

104. Number of moles of an ideal gas at P=2 atm, V=5 L and T=500 K (R=0.0821 L·atm·mol⁻¹·K⁻¹) is:

105 / 108

105. Match the quantum number set (List-I) with a possible orbital type (List-II).

1. (n=3, l=2)

2. (n=2, l=1)

3. (n=4, l=0)

106 / 108

106. Compute determinant of matrix [[1,1,1],[1,2,3],[1,3,6]].

107 / 108

107. Select all correct statements about current electricity:

1) Drift velocity of electrons is proportional to electric field.

2) Kirchhoff’s loop law follows from conservation of charge.

3) Resistance of a metallic conductor increases with temperature.

4) Wheatstone bridge can be used to measure unknown resistance accurately.

108 / 108

108. Select all correct statements about coordination compounds:

1) [NiCl4]2− is square planar and diamagnetic.

2) [CoF6]3− is paramagnetic.

3) In [Fe(CN)6]4−, Fe(II) forms a low-spin complex.

4) [Ni(CN)4]2− is diamagnetic.

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