JEE ADVANCED TYPE 1

1. 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:

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

3. 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:

4. Select all correct statements about organic reactions:

5. Select all correct statements about integration:

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

7. Select all correct statements about modern physics:

8. 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:

9. Select all correct statements in mechanics:

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

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

12. Select all correct statements about electrostatics:

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).

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

15. 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:

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

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

18. Select all correct statements about electromagnetic induction:

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

20. Hybridization of the central atom in SF6 is:

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

22. Compute S = 1^3 + 2^3 + … + 20^3.

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

24. Select all correct statements about acids and bases:

25. 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:

26. Which of the following is aromatic?

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

28. 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:

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

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

31. 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):

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

33. Which has the highest first ionization enthalpy?

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

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

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

37. 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).

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

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

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

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

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

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

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

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

46. 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:

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

48. 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:

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

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

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

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

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

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

55. Compute |(1,2,2) × (2,0,1)|.

56. Value of Σ_{k=0}^{6} C(6,k)^2 is:

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

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

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

60. 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:

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

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

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

64. 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).

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

66. Select all correct statements about coordination compounds:

67. 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

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

69. 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:

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

71. 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:

72. Select all correct statements about determinants:

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

74. Select all correct statements about chemical equilibrium:

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

76. 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:

77. Select all correct statements about current electricity:

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

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

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

81. 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:

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

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

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

85. Select all correct statements regarding periodic trends:

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

87. Select all correct statements about chemical kinetics:

88. Evaluate ∫₀¹ x e^x dx.

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

90. 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:

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

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

93. Select all correct statements about electrochemistry:

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

95. 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:

96. Select all correct statements about conics:

97. Evaluate ∫₀¹ 1/(1+√x) dx.

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

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

100. 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:

101. Select all correct statements about complex numbers:

102. Select all correct statements:

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

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

105. The geometry of [Ni(CN)4]2− is:

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

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

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