Class 11 Mathematics Straight Lines MCQs Set B

Question: If the coordinates of the points A and B be (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is
a) 5/4
b) √10/4
c) √13/3
d) None of the options
Answer: a

Question: A triangle ABC is right angled at A has points A and B as (2, 3) and (0, –1) respectively. If BC = 5, then point C may be
a) (– 4, 2)
b) (4, – 2)
c) (0, 4)
d) (0, – 4)
Answer: c

Question: The distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0 is a/b . Value of a + b is
a) 2
b) 5
c) 7
d) 3
Answer: c

Question: Equation of the straight line making equal intercepts on theaxes and passing through the point (2, 4) is :
a) 4x – y – 4 = 0
b) 2x + y – 8 = 0
c) x + y – 6 = 0
d) x + 2y – 10 = 0
Answer: c

Question: The equation of the line which bisects the obtuse angle between the lines x – 2y + 4 = 0 and 4x – 3y + 2 = 0, is
a) (4 – √5)x – (3 – 2√5)y + (2 – 4√5) = 0
b) (4 + √5)x – (3 + 2√5)y + (2 + 4√5) = 0
c) (4 + √5)x + (3 + 2√5)y + (2 + 4√5) = 0
d) None of the options
Answer: a

Question: The distance of the line 2x + y = 3 from the point (–1, 3) in the direction whose slope is 1, is
a) 2/3
b) √2/3
c) 2√2/3
d) 2√5/3
Answer: c

Question: If p be the length of the perpendicular from the origin on the straight line ax + by = p and b = √3/2 , then what is the angle between the perpendicular and the positive direction of x-axis?
a) 30°
b) 45°
c) 60°
d) 90°
Answer: c

Question: The line joining (–1, 1) and (5, 7) is divided by the line x + y = 4 in the ratio 1 : k. The value of ‘k’ is
a) 2
b) 4
c) 3
d) 1
Answer: a

Question: A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y – intercept is:
a) 1/3
b) 2/3
c) 1
d) 4/3
Answer: d

Question: Which one of the following is the nearest point on the line 3x– 4y = 25 from the origin?
a) ( –1, –7)
b) (3, –4)
c) ( –5, –8)
d) (3, 4)
Answer: b

Question: The distance of the point (–1, 1) from the line 12(x + 6) = 5 (y – 2) is
a) 2
b) 3
c) 4
d) 5
Answer: d

Question: The line (3x – y + 5) + λ(2x – 3y – 4) = 0 will be parallel to y-axis, if λ =
a) 1/3
b) –1/3
c) 3/2
d) –3/2
Answer: b

Question: The intercept cut off by a line from y-axis twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is
a) 2x + y = 4
b) 2x + y + 4 = 0
c) 2x – y = 4
d) 2x – y + 4 = 0
Answer: a

Question: If three points (h, 0), (a, b) and (0, k) lies on a line, then the value of a/h + b/k
a) 0
b) 1
c) 2
d) 3
Answer: b

Question: The equation of a line through the point of intersection of the lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and whose distance from the origin is 5 is
a) 2x + y – 5 =0
b) x – 3y + 6 = 0
c) x + 2y – 7 = 0
d) x + 3y + 8 = 0
Answer: a

Question: If the coordinates of the points A, B, C be (–1, 5), (0, 0) and (2, 2) respectively and D be the middle point of BC, then the equation of the perpendicular drawn from B to the line AD is
a) x + 2y = 0
b) 2x + y = 0
c) x – 2y = 0
d) 2x – y = 0
Answer: c

Question: What is the image of the point (2, 3) in the line y = – x ?
a) (–3, –2)
b) (– 3, 2)
c) (–2, –3)
d) (3, 2)
Answer: a

Question: Equation of angle bisector between the lines 3x + 4y – 7 = 0 and 12x + 5y + 17 = 0 are
a) 3x + 4y – 7/√25 = ± 12x + 5y + 17/√169
b) 3x + 4y + 7/√25 = 12x + 5y + 17/√169
c) 3x + 4y + 7/√25 = ± 12x + 5y + 17/√169
d) None of the options
Answer: a

Question: The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are
a) (–6, 5)
b) (5, 6)
c) (–5, 6)
d) (6, 5)
Answer: b

Question: The line L has intercepts a and b on the coordinate axes. When keeping the origin fixed, the coordinate axes are rotated through a fixed angle, then same line has intercepts p and q on the rotated axes, then
a) a² + b² = p² + q²
b) 1/a² + 1/b² = 1/p² + 1/q²
c) a² +β² = b² + q²
d) b² + q² = 1/b² + 1/q²
Answer: b

Question: Distance between the parallel lines
Ax + By + C₁ = 0 and Ax + By + C₂ = 0, is given by:

Answer: c

Question: The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is –1 is

Answer: a

ASSERTION – REASON TYPE QUESTIONS

a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
c) Assertion is correct, reason is incorrect
d) Assertion is incorrect, reason is correct.

Question:
Assertion: If A (– 2, –1), B (4, 0), C (3, 3) and D (–3, 2) are the vertices of a parallelogram, then mid-point of AC = Mid-point of BD
Reason: The points A, B and C are collinear ⇔ Area of ΔABC = 0.
Answer: b

Question:
Assertion: The distance between the parallel lines 3x – 4y + 9 = 0 and 6x – 8y – 15 = 0 is 33/10 .
Reason: Distance between the parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0, is given by d = |C₁ − C₂ |/√A² + B²
Answer: a

Question:
Assertion: The inclination of the line l may be acute or obtuse.
Reason: Slope of x-axis is zero and slope of y-axis is not defined.
Answer: b

Question:
Assertion: If the lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, are parallel, then a₁/a₂ = b₁/b₂.
Reason: If the lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are perpendicular, then a₁a₂ – b₁b₂ = 0.
Answer: c

Question:
Assertion: The equation of a line parallel to the line ax + by + c = 0 is ax – by – λ = 0, where λ is a constant.
Reason: The equation of a line perpendicular to the line ax + by + c = 0 is bx – ay + λ = 0, where λ is a constant.
Answer: d

Question:
Assertion: Slope of the line passing through the points (3, –2) and (3, 4) is 0.
Reason: If two lines having the same slope pass through a common point, then these lines will coincide.
Answer: c

Question:
Assertion: Equation of the horizontal line having distance ‘a’ from the x-axis is either y = a or y = –a.
Reason: Equation of the vertical line having distance b from the y-axis is either x = b or x = –b.
Answer: b

Question:
Assertion: The equation of the line making intercepts a and b on x and y-axis respectively is x/a + y/b = 1
Reason: The slope of the line ax + by + c = 0 is b/a .
Answer: c

Question:
Assertion: Pair of lines x + 2y – 3 = 0 and – 3x – 6y + 9 = 0 are coincident.
Reason: Two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are coincident if a₁/a₂ = b₁/b₂ = c₁/c₂ .
Answer: a

Question:
Assertion: If Θ is the inclination of a line l, then the slope or gradient of the line l is tan Θ.
Reason: The slope of a line whose inclination is 90°, is not defined.
Answer: b