41. If p is the perpendicular distance from the origin to the line whose intercepts on the axes are a and b, then
Answer: 1/p² = 1/a² + 1/b²
42. The equation of the line that divides the line segment joining the points (-4, 6) and (8, 8) into two equal parts is
Answer: 6x + y – 19 = 0
43. The general solution of tan2θ tanθ = 1, where n ∈ Z is
Answer: (2n+1)π/4
44. The slope of the tangent to the curve x = 3t² + 1, y = t³ – 1 at x = 1 is
Answer: 0
45. ∫eˣ(1+sinx)/(1+cosx) dx =
Answer: eˣ tanx/2 + c
46. If the distance between the foci is 16 and the eccentricity is 1/2, then the length of the major axis of the ellipse is
Answer: 32
47. For the function f(x) = 2x³ – 15x² + 36x + 4, the value of x at which the function is maximum is
Answer: 3
48. The value of ∫1/(x-5)² dx is
Answer: -1/(x-5) + c
49. The value of ∫2dx/√(1-4x²) is
Answer: tan⁻¹(2x) + c
50. The point on the curve y = 2x² – x + 1 where the tangent is parallel to the line y = 3x + 9 is
Answer: (1, 2)
51. An algebraic expression which has only one term is called
Answer: Monomial
52. The pair of equations x + 2y − 5 = 0 and −4x − 8y + 20 = 0 has
Answer: Infinitely many solutions
53. If the lines 3x + 2ky − 2 = 0 and 2x + 5y + 1 = 0 are parallel, what is the value of k?
Answer: 4/15
54. If one of the equations of a pair of dependent linear equations is −3x + 5y − 2 = 0, the other equation will be
Answer: −6x + 10y − 4 = 0
55. Which algebraic method(s) is/are used to solve a pair of linear equations?
Answer: All of the above
56. The zeros of the quadratic polynomial x² + 99x + 127 are
Answer: Both negative
57. The distance of point P(2, 3) from the x-axis is
Answer: 3
58. The fourth vertex D of a parallelogram ABCD, given that three vertices are A(-2, 3), B(6, 7), and C(8, 3), is
Answer: (0, -1)
59. The point located on the perpendicular bisector of the line segment joining points A(-2, -5) and B(2, 5) is
Answer: (0, 0)
60. If the points A(1, 2), O(0, 0), and C(a, b) are collinear, then
Answer: a = 2b