Online Test — Straight Lines
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
medium
A road is represented by line y = 2x + 1. Another road parallel to it passes through (0,5). Its equation is:
y = 2x + 5
y = 5x + 2
y = −2x + 5
y = 2x − 5
Explanation: Parallel lines have same slope 2.
Question 2 of 10
medium
A line has an obtuse angle of inclination and a positive y-intercept. Which of the following MUST be true about its x-intercept?
It is negative
It is positive
It is zero
Cannot be determined
Explanation: Obtuse angle implies negative slope (m < 0). Positive y-intercept means c > 0. Equation: y = mx + c. X-intercept is x = −c/m. Since c>0 and m<0, −c/m is positive.
Question 3 of 10
easy
If the slope of a line is √3, its inclination is:
30°
45°
60°
90°
Explanation: tan θ = √3, therefore θ = 60°.
Question 4 of 10
easy
The lines L1: 2x − 3y = 0 and L2: 3x + 2y = 0 are:
Parallel
Perpendicular
Coincident
Intersecting but not perpendicular
Explanation: Slope of L1 is 2/3. Slope of L2 is −3/2. Since (2/3) × (−3/2) = −1, the lines are perpendicular.
Question 5 of 10
easy
The distance of point (3,4) from x-axis is:
3
4
5
7
Explanation: Distance from x-axis equals absolute y-coordinate.
Question 6 of 10
medium
If a line is equally inclined to both axes in first quadrant, its equation through origin is:
y = x
y = −x
x + y = 1
x = y + 1
Explanation: Equal inclination implies angle 45°, slope 1.
Question 7 of 10
medium
Find the slope of a line passing through the origin and the midpoint of the line segment joining (4, 4) and (8, 2).
1
1/2
2
−1/2
Explanation: Midpoint = ((4+8)/2, (4+2)/2) = (6, 3). Slope of line through (0,0) and (6,3) = (3−0)/(6−0) = 3/6 = 1/2.
Question 8 of 10
easy
The slope of the line passing through points (2, 3) and (6, 11) is:
2
1
3
4
Explanation: m = (11−3)/(6−2) = 8/4 = 2.
Question 9 of 10
easy
Find the angle of inclination of a line whose slope is 1/√3.
30°
45°
60°
90°
Explanation: Slope m = tan(θ) = 1/√3. Therefore, the inclination angle θ is 30°.
Question 10 of 10
easy
What is the condition for two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to be parallel?
a1a2 + b1b2 = 0
a1/a2 = b1/b2 ≠ c1/c2
a1b2 + a2b1 = 0
a1/b1 = a2/b2 = c1/c2
Explanation: Parallel lines have the same slope, so −a1/b1 = −a2/b2, which means a1/a2 = b1/b2. If they are distinct lines, the ratio must not equal c1/c2.