Notes
IIT Madras
Mathematics 🧮
Activity Questions 2.6

Activity Questions 2.6

Multiple Choice Questions (MCQ):

Question 1: If a line is perpendicular to the X-axis, then the slope of such line is _______

Options:

  • 0
  • Not defined
  • 1
  • -1

Solution

Question 2: If a line is parallel to a line which is perpendicular to the Y-axis, then the slope of the first line is _______

Options:

  • 0
  • Not defined
  • 1
  • -1

Solution

Question 3: The angle formed by the intersection of 2 lines with slopes 1 and -1 is _______

Options:

  • 0 degree
  • 45 degree
  • 90 degree
  • 180 degree

Solution

Multiple Select Questions (MSQ):

Question 4: If l₁ and l₂ are lines parallel to each other with slopes m₁ and m₂ and with inclinations α and β respectively, then which of the following is/are correct?

Options:

  • α = β and, tan α = tan β
  • α ≠ β and, tan α ≠ tan β
  • m₁ = m₂, always
  • m₁ × m₂ = -1

Solution

Question 5: Lines l₁ and l₂ are perpendicular to each other with slopes m₁ and m₂ and with inclinations α and β respectively. Then, which of the following is/are correct?

Options:

  • α = β and, tan α = tan β
  • β = 90 + α, and tan α = -cot β
  • β = 90 + α, and tan β = -cot α
  • m₂ = -1/m₁

Solution

Question 6: If two lines l₁ and l₂ with slopes m₁ and m₂ and inclinations α₁ and α₂ (α₂ > α₁) respectively intersect each other and make an acute angle θ and an obtuse angle φ, then which of the following is/are correct?

Note: θ = (α₂ - α₁)

Options:

  • tan θ = (tan α₂ - tan α₁)/(1 + tan α₁ × tan α₂) ≠ (m₁ - m₂)/(1 + m₁ × m₂)
  • m₁ × m₂ = (-1)
  • tan φ = (m₁ - m₂)/(1 + m₁ × m₂)
  • tan θ = tan (α₂ - α₁)

Solution

Solution

Solution

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