JEE MAINS TYPE 2

1. Distance of point (3,4) from line 3x+4y-10=0 is:

2. Determinant of the matrix [[2,1,3],[1,0,2],[4,1,5]] is:

3. If a=(1,2,2) and b=(2,1,-2), then a·b equals:

4. For first order reaction, if t1/2 = 10 min, rate constant k (in min^-1) is approximately 0.693/10. Round to 2 decimals and then as integer of hundredths (e.g., 0.07→7).

5. If the mean of numbers 2, 5, x, 11, 17 is 9, find x.

6. A physical quantity has dimensions [M^0 L^1 T^-2]. It corresponds to:

7. Value of ∫_0^1 (1/(1+x^2)) dx is:

8. A particle starts from rest and moves with constant acceleration a. Its displacement in time t is:

9. A fair die is thrown twice. Probability that the sum is 9 is:

10. If f(x)=x^3-3x, then the number of real roots of f(x)=0 is:

11. Which reagent converts an aldehyde to primary alcohol?

12. For SHM x=A sin(ωt), the maximum acceleration is:

13. Which compound shows geometrical isomerism?

14. In a stationary wave on a string, the distance between two consecutive nodes is:

15. Oxidation state of Mn in KMnO4 is:

16. If 0.5 mol of ideal gas is present at 300 K and R=0.082 L·atm·mol^-1·K^-1, pressure when volume is 12.3 L is (atm). Round to nearest integer.

17. If sinθ = 3/5 and θ is acute, then tanθ equals:

18. Induced emf in a coil is given by:

19. A block of mass m is on a rough horizontal surface (coefficient of friction μ). The minimum horizontal force required to just start motion is:

20. Two trains move in the same direction with speeds 54 km/h and 36 km/h. Time taken by the faster train (length 180 m) to completely pass a 120 m long slower train is:

21. Number of 5-digit numbers formed using digits 1,2,3,4,5,6 without repetition and divisible by 5 is:

22. Two capacitors C and 2C are connected in series. Equivalent capacitance is:

23. The minimum value of x^2 + 4/x for x>0 is:

24. Work done by centripetal force in uniform circular motion over one complete revolution is:

25. Hybridization of central atom in SF6 is:

26. IUPAC name of CH3-CH2-CHO is:

27. A perfectly elastic head-on collision occurs between two equal masses, one moving with speed u and the other at rest. After collision, the speed of the initially moving mass becomes:

28. If α and β are roots of x^2 – 6x + k = 0 and α^2 + β^2 = 20, then k is:

29. If 7C2 = nC2, find n.

30. Benzene undergoes nitration in presence of:

31. Root mean square speed of molecules of an ideal gas is proportional to:

32. A cell of emf E and internal resistance r is connected to external resistance R. The current is:

33. A body moves with acceleration 2 m/s^2 for 5 s starting from rest. Find its final speed (m/s).

34. Energy stored (in joule) in a 2 μF capacitor charged to 100 V is (use 1 μF = 10^-6 F). Give answer as integer in mJ.

35. Force on a charge q moving with velocity v perpendicular to uniform magnetic field B is:

36. If f(x)=|x-2|, then f is NOT differentiable at:

37. Which of the following has highest boiling point?

38. For ideal gas, compressibility factor Z equals:

39. General solution of dy/dx = y is:

40. Calculate molar mass of CaCO3 (Ca=40, C=12, O=16).

41. Number of neutrons in 35Cl (atomic number 17) is:

42. Equation of circle with diameter endpoints (0,0) and (4,6) is:

43. A 6 Ω resistor and 3 Ω resistor are connected in parallel. Equivalent resistance (Ω) is:

44. In electrochemical cell, the unit of cell constant is:

45. Number of significant figures in 0.004050 is:

46. For a convex lens, if object is placed at 2f, the image is formed at:

47. Distance between points (1,2,3) and (4,6,3) is:

48. Which of the following is a reducing sugar?

49. If z = (1+i)/(1-i), then |z| equals:

50. Moment of inertia of a thin ring of mass M and radius R about its diameter is:

51. If the sum of first n terms of an AP is S_n = 3n^2 + 2n, then the 10th term is:

52. Escape speed from the surface of a planet of mass M and radius R is:

53. Let A={1,2,3,4,5}. Number of non-empty subsets of A having an odd sum is:

54. Rate law: rate = k[A]^2[B]. The overall order of reaction is:

55. Which of the following has maximum first ionization enthalpy?

56. pOH of 1×10^-3 M NaOH solution is:

57. pH of 0.01 M HCl solution (at 25°C) is:

58. For an ideal gas in an isothermal process, the change in internal energy ΔU is:

59. Evaluate the determinant | 1 2 3; 0 1 4; 5 6 0 | (nearest integer).

60. The monomer unit of PVC is:

61. For a streamline flow of incompressible fluid, if area of cross-section halves, the speed becomes:

62. For reaction N2(g)+3H2(g)⇌2NH3(g), decreasing volume at constant temperature shifts equilibrium:

63. The coordination number of Fe in [Fe(CN)6]4- is:

64. In photoelectric effect, stopping potential depends on:

65. Electric field at the centre of a uniformly charged ring is:

66. Which of the following is amphoteric oxide?

67. A convex lens forms an image of an object at a distance 30 cm on the other side when the object is 15 cm in front. Find focal length (cm).

68. ∫ (2x)/(x^2+1) dx equals:

69. For parabola y^2=8x, the length of latus rectum is:

70. Coefficient of x^5 in (1+2x)^8 is:

71. Limit as x→0 of (sin 5x)/(x) is:

72. Solve for x>0: log_2(x) + log_2(x/8) = 5. (Answer as integer)

73. Among the following, strongest intermolecular hydrogen bonding is in:

74. A 2 kg block is lifted vertically by 5 m. Take g=10 m/s^2. Work done against gravity (J) is:

75. The major product of dehydration of 2-butanol is: