2nd PUC Mathematics Series 7

61. If the points (a₁, b₁), (a₂, b₂) and(a₁ + a₂, b₁ + b₂) are collinear, then

62. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.

63. Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).

64. The derivative of f(tan x) w.r.t. g(sec x) at x = π/4, where f'(1) = 2 and g'(√2) = 4, is

65. If x² + y² = 1, then

66. The value of c in Rolle’s theorem for the function, f(x) = sin 2x in [0, π/2] is

67. The value of c in mean value theorem for the function f(x) = (x – 3)(x – 6)(x – 9) in [3, 5] is

68. The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is

69. The number of discontinuous functions y(x) on [-2, 2] satisfying x² + y² = 4 is

70. If y = (1 + x)(1 + x²)(1 + x⁴)…..(1 + x²ⁿ), then the value of dy/dx at x = 0 is