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Class 11 Maths Chapter 9: Straight Lines MCQs with answers

10 multiple-choice questions on Straight Lines, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
The slope of a line whose inclination with the positive direction of the x-axis is 150° is
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Answer: (c) −1/√3

m = tan 150° = tan (180° − 30°) = −tan 30° = −1/√3.

Question 2
Which of the following lines has a slope that is not defined?
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Answer: (a) x = −3

x = −3 is a vertical line: its inclination is 90°, and tan 90° is not defined. y = 4 has slope 0; y = x has slope 1; x + y = 0 has slope −1.

Question 3
The slope of the line through A(2, 5) and B(6, k) is −32. The value of k is
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Answer: (d) −1

(k − 5)/(6 − 2) = −3/2 gives k − 5 = −6, so k = −1.

Question 4
The points (1, 4), (3, p) and (6, −6) are collinear. The value of p is
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Answer: (b) 0

For collinear points the slopes are equal: slope through (1, 4) and (6, −6) is −10/5 = −2, so (p − 4)/(3 − 1) = −2 and p = 0.

Question 5
The line through (2, −1) and (5, a) is parallel to the line 2x − 3y + 7 = 0. The value of a is
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Answer: (b) 1

2x − 3y + 7 = 0 has slope −A/B = 2/3. Parallel lines have equal slopes: (a + 1)/(5 − 2) = 2/3, so a + 1 = 2 and a = 1.

Question 6
The lines 3x + ky = 7 and 2x − 5y + 1 = 0 are perpendicular. The value of k is
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Answer: (d) 65

Slopes are −3/k and 2/5. Perpendicular: (−3/k)(2/5) = −1, so 6 = 5k and k = 6/5. (k = −15/2 would make the lines parallel.)

Question 7
The acute angle between the lines y = 3x + 1 and y = −2x + 4 is
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Answer: (a) 45°

m₁ = 3, m₂ = −2: tan θ = |(−2 − 3)/(1 + (3)(−2))| = |−5/−5| = 1, so θ = 45°. 135° is the obtuse angle.

Question 8
The obtuse angle between the lines x − y + 3 = 0 and x = 7 is
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Answer: (c) 135°

x − y + 3 = 0 has slope 1, inclination 45°; x = 7 is vertical, inclination 90°. The formula for tan θ cannot be used (x = 7 has no slope); the angles between the lines are 90° − 45° = 45° and 180° − 45° = 135°.

Question 9
The equation of the line through (−3, 1) whose inclination is 45° is
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Answer: (c) x − y + 4 = 0

m = tan 45° = 1. Point-slope form: y − 1 = 1(x + 3), i.e. x − y + 4 = 0. x + y + 2 = 0 passes through (−3, 1) but has inclination 135°.

Question 10
The y-intercept of the line through (2, 3) and (−4, 6) is
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Answer: (b) 4

Slope = (6 − 3)/(−4 − 2) = −1/2. y − 3 = −(1/2)(x − 2); at x = 0, y = 3 + 1 = 4. (8 is the x-intercept.)

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