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MHT-CET Straight Lines — practice questions — page 2

Explore 77 free Straight Lines questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Straight Lines questions and exercises with answers

Showing questions 31–60 of 77.

The distance between Ax + By + C1 = 0 and Ax + By + C2 = 0 isRead the answer and worked solution →The acute angle θ between lines of slopes m1 and m2 satisfies tan θ =Read the answer and worked solution →Find the acute angle between the line y = x and the x-axis.Read the answer and worked solution →Two lines have slopes 1/2 and 1/3. The tangent of the acute angle between them isRead the answer and worked solution →Lines with slopes 2 and –1/2 meet at an angle ofRead the answer and worked solution →If the acute angle between two lines is 30°, the obtuse angle between them isRead the answer and worked solution →If (m2 – m1)/(1 + m1m2) is positive, the angle θ between the lines isRead the answer and worked solution →Two lines meet at 45° and one has slope 0. The other slope can beRead the answer and worked solution →Find the slope of the line from the origin to the mid-point of the segment joining (0, –4) and (8, 0).Read the answer and worked solution →A line makes 30° with the positive y-axis, measured anticlockwise. Its slope isRead the answer and worked solution →The line joining (3, –1) and (4, –2) makes what angle with the positive x-axis?Read the answer and worked solution →A line through (2, 3) cuts equal intercepts on both axes. Its equation isRead the answer and worked solution →In triangle PQR with P(2, 1), Q(–2, 3), R(4, 5), the median through R isRead the answer and worked solution →The points (3, 0), (–2, –2) and (8, 2) are collinear since the slopes of the segments from (3, 0) to the others are bothRead the answer and worked solution →L (cm) is linear in C: 124.942 at 20 and 125.134 at 110. L rises per degree byRead the answer and worked solution →Linear demand: 980 L at Rs 14 and 1220 L at Rs 16. Sales at Rs 17 areRead the answer and worked solution →The point on the x-axis equidistant from (7, 6) and (3, 4) isRead the answer and worked solution →An equilateral triangle has a base of length 4 on the y-axis centred at the origin. A third vertex isRead the answer and worked solution →A line perpendicular to the segment from the origin to (–2, 9) passes through (–2, 9). Its equation isRead the answer and worked solution →A segment between the axes has mid-point P(a, b). Its x-intercept isRead the answer and worked solution →R(h, k) divides the segment from (p, 0) to (0, q) in the ratio 1:2. Then p equalsRead the answer and worked solution →The line through (–2, 3) parallel to 3x – 4y + 2 = 0 isRead the answer and worked solution →A line through (1, 2) and (3, 8) is parallel to every line of slopeRead the answer and worked solution →The lines 2x – y + 1 = 0 and x + 2y – 3 = 0 areRead the answer and worked solution →A line has inclination 45 degrees. What is its slope?Read the answer and worked solution →What is the slope of a line whose inclination is 60 degrees?Read the answer and worked solution →What is the slope of the X-axis?Read the answer and worked solution →Non-vertical lines with slopes m1 and m2 are perpendicular whenRead the answer and worked solution →A line has slope 2. What is the slope of a line perpendicular to it?Read the answer and worked solution →The inclination θ of a line always satisfiesRead the answer and worked solution →

Worked practice questions

The distance between Ax + By + C1 = 0 and Ax + By + C2 = 0 is

  1. |C1 – C2|/√(A² + B²)
  2. |C1 – C2|/(A + B)
  3. |C1 – C2|/(A² + B²)
  4. |C1 + C2|/√(A² + B²)
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Correct answer: A. |C1 – C2|/√(A² + B²)

Parallel lines with the same A and B are separated by the difference of constants over √(A² + B²).

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The acute angle θ between lines of slopes m1 and m2 satisfies tan θ =

  1. |(m2 – m1)/(1 – m1m2)|
  2. |(m2 – m1)/(1 + m1m2)|
  3. |(m2 + m1)/(1 – m1m2)|
  4. |(m2 – m1)/(m1m2)|
Show answer and solution

Correct answer: B. |(m2 – m1)/(1 + m1m2)|

tan(α2 – α1) expands to (m2 – m1)/(1 + m1m2), taken in absolute value for the acute angle.

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Find the acute angle between the line y = x and the x-axis.

  1. 45°
  2. 90°
  3. 60°
  4. 30°
Show answer and solution

Correct answer: A. 45°

With slopes 1 and 0, tan θ = |(0 – 1)/(1 + 0)| = 1, so θ = 45°.

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