Chapter Exam

Chapter-9 Straight Lines — Online MCQ Test

Q: What is the slope of a line passing through points (2, 3) and (5, 9)?

Answer: A. 2 — Slope m = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(5 - 2) = 6/3 = 2.

Q: What is the y-intercept of the line 3x + 2y = 6?

Answer: B. 3 — Setting x = 0: 2y = 6, so y = 3. The y-intercept is 3.

Q: The equation of a line in slope-intercept form is y = mx + c. Here 'c' represents:

Answer: B. y-intercept — 'c' is the constant term that represents the y-intercept (where the line crosses the y-axis).

Q: Which of the following lines are parallel?

Answer: A. y = 2x + 3 and y = 2x - 5 — Parallel lines have equal slopes. Both lines have slope m = 2.

Q: Find the equation of a line passing through (2, 3) with slope 2 using point-slope form.

Answer: A. y - 3 = 2(x - 2) — Using point-slope form: y - y₁ = m(x - x₁), we get y - 3 = 2(x - 2).

Q: What is the angle of inclination of the line with slope √3?

Answer: C. 60° — Slope m = tan(θ). Here √3 = tan(60°), so angle of inclination is 60°.

Q: The line passing through (2, 3) perpendicular to the line 4x + 3y = 7 has slope:

Answer: A. 3/4 — Slope of 4x + 3y = 7 is -4/3. Perpendicular slope = -1/(-4/3) = 3/4.

Q: Find the distance between parallel lines 2x + 3y - 5 = 0 and 2x + 3y + 7 = 0.

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.

Q: Three points P(h, 0), Q(0, k), and R(1, 1) are collinear. Which relation must hold?

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.

MATHS · Grade 11 · CBSE(NCERT)

Practice Chapter-9 Straight Lines with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 11 MATHS. 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.

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Chapter-9 Straight Lines — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 11 MATHS — Chapter-9 Straight Lines, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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).

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.

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).

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°.

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.

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.

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.

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.

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