Class 11 Mathematics Straight Lines MCQs Set E

Question. A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is
(a) (13/5 , 0)
(b) (5/13 , 0)
(c) (–7, 0)
(d) None of these
Answer: a

Question. The lines a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂ = 0 are perpendicular to each other
(a) a₁b₁ – b₁a₂ = 0
(b) a₁²b₂ + b₁²a₂ = 0
(c) a₁b₁ + a₂b₂ = 0
(d) a₁b₂ + b₁b₂ = 0
Answer: d

Question. The line parallel to the x-axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) ≠ (0, 0) is
(a) Above the x-axis at a distance of 3/2 from it
(b) Above the x-axis at a distance of 2/3 from it
(c) Below the x-axis at a distance of 3/2 from it
(d) Below the x-axis at a distance of 2/3 from it
Answer: c

Question. A line passes through P (1, 2) such that its intercept between the axes is bisected at P. The equation of the line is
(a) x + 2y = 5
(b) x – y + 1 = 0
(c) x + y – 3 = 0
(d) 2x + y – 4 = 0
Answer: d

Question. If two vertical poles 20 m and 80 m high stand apart on a hori ontal plane, then the height (in m) of the point of intersection of the lines oining the top of each pole to the foot of other is
(a) 16
(b) 18
(c) 50
(d) 15
Answer: a

Question. Suppose that the points (h, k), (1, 2) and (– 3, 4) lie on the line L₁. If a line L₂ passing through the points (h, k) and (4, 3) is perpendicular on L₁, then equals :
(a) 1/3
(b) 0
(c) 3
(d) – 1/7
Answer: a

Question. If the area of the triangle with vertices (x, 0), (1, 1) and (0, 2) is 4 square unit, then the value of x is :
(a) – 2
(b) – 4
(c) – 6
(d) 8
Answer: c

Question. Let the perpendiculars from any point on the line 7x + 56y = 0 upon 3x + 4y = 0 and 5x – 12y = 0 be p and p’, then
(a) 2p = p’
(b) p = 2p’
(c) p = p’
(d) None of these
Answer: c

Question. The lines p(p² +1) x – y + q = 0 and (p² + 1)²x + (p² + 1) y + 2q = 0 are perpendicular to a common line for
(a) exactly one value of p
(b) exactly two values of p
(c) more than two values of p
(d) no value of p
Answer: a

Question. Let θ₁ be the angle between two lines 2x + 3y + c₁ = 0 and – x + 5y + c₂ = 0 and θ₂ be the angle between two lines 2x + 3y + c₁ = 0 and – x + 5y + c₃ = 0, where c₁, c₂, c₃ are any real numbers :
Statement-1: If c₂ and c₃ are proportional, then θ₁ = θ₂.
Statement-2: θ₁ = θ₂ for all c₂ and c₃.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation of Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation of Statement-1.
(c) Statement-1 is false; Statement-2 is true.
(d) Statement-1 is true; Statement-2 is false.
Answer: a

Question. The point (x, y) lies on the line with slope m and through the fixed point (x₀, y₀) if and only if its coordinates satisfy the equation y – y₀ is equal to ……… .
(a) m(x – x₀)
(b) m(y – x₀)
(c) m(y – x)
(d) m(x – y₀)
Answer: a

Question. The perpendicular bisector of the line segment oining P (1, 4) and Q(k, 3) has y-intercept –4. Then a possible value of k is
(a) 1
(b) 2
(c) –2
(d) – 4
Answer: d

Question. If a, b, c ∈ R and 1 is a root of equation ax² + bx + c = 0, then the curve y = 4ax² + 3bx + 2c, a ≠ 0 intersect x-axis at
(a) two distinct points whose coordinates are always rational numbers
(b) no point
(c) exactly two distinct points
(d) exactly one point
Answer: d

Question. A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle α(o < α < π/4) with the positive direction of x-axis. The equation of its diagonal not passing through the origin is
(a) y(cos α + sin α) + x(cos α – sin α) = α
(b) y(cos α – sin α) – x(sin α – cos α) = α
(c) y(cos α + sin α) + x(sin α – cos α) = α
(d) y(cos α + sin α) + x(sin α + cos α) = α
Answer: a

Question. If the line, 2x – y + 3 = 0 is at a distance 1/√5 and 2/√5 from the lines 4x – 2y + α = 0 and 6x – 3y + β = 0, respectively, then the sum of all possible value of α and β is ______.
Answer: 30

STATEMENT TYPE QUESTIONS 

Question. Slope of the lines passing through the points
I. (3, – 2) and (– 1, 4) is −3/2
II. (3, – 2) and (7, – 2) is 0.
III. (3, – 2) and (3, 4) is 1.
Choose the correct option.
(a) Only I and III are true
(b) Only I and II are true
(c) Only II and III are true
(d) None of these
Answer: b

Question. The distances of the point (1, 2, 3) from the coordinate axes are A, B and C respectively. Now consider the following equations:
I. A² = B² + C²
II. B² = 2C²
III. 2A²C² = 13 B²
Which of these hold(s) true?
(a) Only I
(b) I and III
(c) I and II
(d) II and III
Answer: d

Question. Equation of a line is 3x – 4y + 10 = 0
I. Slope of the given line is 3/4.
II. x-intercept of the given line is −10/3.
III. y-intercept of the given line is 5/2.
Choose the correct option.
(a) Only I and II are true
(b) Only II and III are true
(c) Only I and III are true
(d) All I, II and III are true
Answer: d

Question. Consider the following statements.
I. If (a, b), (c, d) and (a – c, b – d) are collinear, then bc – ad = 0
II. If the points A (1, 2), B (2, 4) and C (3, a) are collinear, then the length BC = 5 unit.
Choose the correct option.
(a) Only I is true
(b) Only II is true
(c) Both are true
(d) Both are false
Answer: a

Question. Consider the following statements.
The three given points A, B, C are collinear i.e., lie on the same straight line, if
I. area of ΔABC is zero.
II. slope of AB = Slope of BC.
III. any one of the three points lie on the straight line joining the other two points.
Choose the correct option
(a) Only I is true
(b) Only II is true
(c) Only III is true
(d) All are true
Answer: d

Question. Consider the following statements.
I. Let A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) be the vertices of a triangle then centroid is
(x₁ + x₂ + x₃/3, y₁ + y₂ + y₃/3)
II. If the point P(x , y) divides the line joining the points A(x₁, y₁) and B(x₂, y₂) in the ratio m : n (internally), then
x = mx₂ + nx₁/m + n , y = my₂ + ny₁/m + n
Choose the correct option.
(a) Only I is true
(b) Only II is true
(c) Both are true
(d) Both are false
Answer: c

Question. Consider the following statements about straight lines :
I. Slope of horizontal line is zero and slope of vertical line is undefined.
II. Two lines are parallel if and only if their slopes are equal.
III. Two lines are perpendicular if and only if product of their slope is – 1.
Which of the above statements are true ?
(a) Only I
(b) Only II
(c) Only III
(d) All the above
Answer: d

Question. Consider the straight lines
L₁ : x – y = 1
L₂ : x + y = 1
L₃ : 2x + 2y = 5
L₄ : 2x – 2y = 7
The correct statement is
(a) L₁ || L₄ , L₂ || L₃ , L₁ intersect L₄.
(a) L₁ ⊥ L₂ , L₁ || L₃ , L₁ intersect L₂.
(a) L₁ ⊥ L₂ , L₂ || L₃ , L₁ intersect L₄.
(a) L₁ ⊥ L₂ , L₁ ⊥ L₃ , L₂ intersect L₄.
Answer: d

Question. Let L be the line y = 2x, in the two dimensional plane.
Statement 1: The image of the point (0, 1) in L is the point (4/5, 3/5).
Statement 2: The points (0, 1) and (4/5, 3/5) lie on opposite sides of the line L and are at equal distance from it.
(a) Statement 1 is true, Statement 2 is false.
(b) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(c) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(d) Statement 1 is false, Statement 2 is true.
Answer: c