Chapter-9 Straight Lines — Online MCQ Test
MATHS · Grade 11 · CBSE(NCERT)
Practice Chapter-9 Straight Lines with a free chapter-wise online MCQ test.
This chapter covers: Slope of a line - Collinearity - Angle between two lines - Point-slope form - Slope-intercept form - Two-point form - Intercept form - General equation - Distance of a point from a....
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-9 Straight Lines — Important Questions & Answers
What is the slope of a line passing through points (2, 3) and (5, 9)?
- A. 2
- B. 3
- C. 1
- D. 4
Answer: A. 2
Slope m = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(5 - 2) = 6/3 = 2.
Slope m = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(5 - 2) = 6/3 = 2.
What is the y-intercept of the line 3x + 2y = 6?
- A. 2
- B. 3
- C. 6
- D. 1
Answer: B. 3
Setting x = 0: 2y = 6, so y = 3. The y-intercept is 3.
Setting x = 0: 2y = 6, so y = 3. The y-intercept is 3.
The equation of a line in slope-intercept form is y = mx + c. Here 'c' represents:
- A. Slope of the line
- B. y-intercept
- C. x-intercept
- D. Angle of inclination
Answer: B. y-intercept
'c' is the constant term that represents the y-intercept (where the line crosses the y-axis).
'c' is the constant term that represents the y-intercept (where the line crosses the y-axis).
Which of the following lines are parallel?
- A. y = 2x + 3 and y = 2x - 5
- B. y = 2x + 3 and y = -2x + 3
- C. y = 2x + 3 and y = 3x + 2
- D. y = 2x + 3 and y = 0.5x + 3
Answer: A. y = 2x + 3 and y = 2x - 5
Parallel lines have equal slopes. Both lines have slope m = 2.
Parallel lines have equal slopes. Both lines have slope m = 2.
Find the equation of a line passing through (2, 3) with slope 2 using point-slope form.
- A. y - 3 = 2(x - 2)
- B. y + 3 = 2(x + 2)
- C. y - 2 = 3(x - 3)
- D. 2y - 3 = x
Answer: A. y - 3 = 2(x - 2)
Using point-slope form: y - y₁ = m(x - x₁), we get y - 3 = 2(x - 2).
Using point-slope form: y - y₁ = m(x - x₁), we get y - 3 = 2(x - 2).
What is the angle of inclination of the line with slope √3?
- A. 30°
- B. 45°
- C. 60°
- D. 90°
Answer: C. 60°
Slope m = tan(θ). Here √3 = tan(60°), so angle of inclination is 60°.
Slope m = tan(θ). Here √3 = tan(60°), so angle of inclination is 60°.
The line passing through (2, 3) perpendicular to the line 4x + 3y = 7 has slope:
- A. 3/4
- B. -3/4
- C. 4/3
- D. -4/3
Answer: A. 3/4
Slope of 4x + 3y = 7 is -4/3. Perpendicular slope = -1/(-4/3) = 3/4.
Slope of 4x + 3y = 7 is -4/3. Perpendicular slope = -1/(-4/3) = 3/4.
Find the distance between parallel lines 2x + 3y - 5 = 0 and 2x + 3y + 7 = 0.
- A. 2/√13
- B. 12/√13
- C. 5/√13
- D. 3/√13
Answer: B. 12/√13
Distance between parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is |c₁ - c₂|/√(a² + b²) = |-5 - 7|/√(4 + 9) = 12/√13.
Distance between parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is |c₁ - c₂|/√(a² + b²) = |-5 - 7|/√(4 + 9) = 12/√13.
Three points P(h, 0), Q(0, k), and R(1, 1) are collinear. Which relation must hold?
- A. h + k = hk
- B. 1/h + 1/k = 1
- C. h - k = 0
- D. hk = 1
Answer: B. 1/h + 1/k = 1
For collinearity, slope PQ = slope QR. This gives: -k/h = (1 - k)/(1 - 0). Solving: -k(1) = h(1 - k) → -k = h - hk → h + k = hk. Rearranging: 1/h + 1/k = 1.
For collinearity, slope PQ = slope QR. This gives: -k/h = (1 - k)/(1 - 0). Solving: -k(1) = h(1 - k) → -k = h - hk → h + k = hk. Rearranging: 1/h + 1/k = 1.
A line L passes through (2, 1) and has a slope of m. Another line perpendicular to L passes through (1, 0). If both lines intersect at (2, 1), which of the following is true?
- A. m = 1 and the perpendicular line has slope -1
- B. m can be any value as long as the perpendicular slope is -1/m
- C. The lines must have slopes that satisfy m × (-1/m) = -1
- D. m = 2 is the only possible value
Answer: C. The lines must have slopes that satisfy m × (-1/m) = -1
For perpendicular lines with slopes m and m', the condition m × m' = -1 must hold. Since the perpendicular line has slope -1/m, the product equals -1, satisfying the perpendicularity condition.
For perpendicular lines with slopes m and m', the condition m × m' = -1 must hold. Since the perpendicular line has slope -1/m, the product equals -1, satisfying the perpendicularity condition.