# Class 11 Mathematics Straight Lines MCQs

## Straight Lines Class 11 MCQ

Class 11 Mathematics students should refer to the following multiple-choice questions with answers for Straight Lines in standard 11. These MCQ questions with answers for Grade 11 Mathematics will come in exams and help you to score good marks

### Class 11 Straight Lines MCQ Questions with Answers

Question. The equation of a straight line which cuts off an intercept of 5 units on negative direction of y-axis and makes an angle of 120º with the positive direction of x-axis is
(a) 3x + y + 5 = 0
(b) 3x + y - 5 = 0
(c) 3x - y - 5 = 0
(d) 3x - y + 5 = 0

Question. The equation of the straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0 is
(a) 2x + 3y + 6 = 0
(b) 2x – 3y – 6 = 0
(c) 2x – 3y + 6 = 0
(d) 2x + 3y – 6 = 0

Question. A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is
(a) 3x2 + 4y2 = 192
(b) 4x2 + 3y2 = 192
(c) x2 + y2 = 192
(d) None of these

Question. If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through
(a) (1, – 2)
(b) (1, 2)
(c) (– 1, 2)
(d) (– 1, – 2)

Question. If the points (5, –1, 1), (–1, –3, 4) and (1, –6, 10) are the three vertices of a rhombus taken in order, then which one of the following is the fourth vertex?
(a) (7, – 4, 11)
(b) (3, 7/2,11/2)
(c) (7, – 4, 7)
(d) (7, 4, 11)

Question. What is the area of the triangle whose vertices are (0,0,0) (3, 4, 0) and (3, 4, 6) ?
(a) 12 square units
(b) 15 square units
(c) 30 square units
(d) 36 square units

Question. The points (1,3) and (5,1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c, then one of the remaining vertices is
(a) (4, 4)
(b) (2, 2)
(c) (0, 2)
(d) (4, 2)

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

Question. If the mid point of the section of a straight line intercepted between the axes is (1, 1), then what is the equation of this line?
(a) 2x + y = 3
(b) 2x – y = 1
(c) x – y = 0
(d) x + y = 2

Question. What is the equation of the line which passes through (4, – 5) and is parallel to the line 3x + 4y +5 = 0 ?
(a) 3x – 4y – 32 = 0
(b) 3x + 4y + 8 = 0
(c) 4x – 3y – 31 = 0
(d) 3x + 4y – 8 = 0

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 – x)
(b) m(y – x)
(c) m(y – x)
(d) m(x – y)

Question. The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if :
(a) y = mx + c
(b) x = my + c
(c) y = mc + y
(d) x = mc + y

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

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

Question. One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is
(a) (–1, –1)
(b) (2, 2)
(c) (–2, – 2)
(d) (2, –2)

Question. What is the angle between the two straight lines y = (2 - 3)x + 5 and y = (2 + 3) x - 7?
(a) 60°
(b) 45°
(c) 30°
(d) 15°

Question. The middle point of A (1, 2) and B (x, y) is C (2, 4).If BD is perpendicular to AB such that CD = 3 unit, then what is the length BD ?
(a) 2 2 unit
(b) 2 unit
(c) 3 unit
(d) 3 2 unit

Question. If A (2, 3), B (1, 4), C (0 – 2) and D (x, y) are the vertices of a parallelogram, then what is the value of (x, y) ?
(a) (1, – 3)
(b) (2, 4)
(c) (1, 1)
(d) (0, 0)

Question. If (a, b), (c, d) and (a – c, b – d) are collinear, then which one of the following is correct ?
(a) bc – ad = 0
(b) ab – cd = 0
(c) bc + ad = 0
(d) ab + cd = 0

Question. One of the equations of the lines passing through the point (3, – 2) and inclined at 60° to the line 3x+y = 1:
(a) x – y = 3
(b) x + 2 = 0
(c) x + y = 0
(d) y + 2 = 0

Question. The straight lines x + 2y – 9 = 0, 3x + 5y – 5 = 0 and ax + by = 1 are concurrent if the straight line 35x – 22y + 1 = 0 passes through :
(a) (a, b)
(b) (b, a)
(c) (a, – b)
(d) (– a, b)

Question. Let A (1, k), B(1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse.
If the area of the triangle is 1square unit, then the set of values which 'k' can take is given by
(a) {–1, 3}
(b) {–3, –2}
(c) {1, 3}
(d) {0, 2}

Question. P(3, 1), Q (6, 5) and R (x, y) are three points such that the angle RPQ is a right angle and the area of DRQP = 7, then the number of such points R is
(a) 0
(b) 1
(c) 2
(d) 4

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)

Question. The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is
(a) (–1, –14)
(b) (3, 4)
(c) (0, 0)
(d) (1, 2)

Question. Locus of the mid-points of the portion of the line x sin q + y cos q = p intercepted between the axis is
(a) 4xy = p2(x2 + y2)
(b) 4x2y2 = p2(x2 + y2)
(c) 4x2y2 = p(x + y)
(d) 4xy = p(x + y)

Question. What is the locus of a moving point equidistant from the straight lines x + y = 0 and x – y = 0 ?
(a) xy = 0
(b) xy = constant
(c) x = 0
(d) y = 0

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)

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°

Question. The coordinates of P and Q are (–3, 4) and (2, 1), respectively. If PQ is extended to R such that PR = 2QR, then what are the coordinates of R ?
(a) (3, 7)
(b) (2, 4)
(c) (1/2, 5/2)
(d) (7, – 2)

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

Question. The coordinates of three points O, A and B are (0,0), (0, 4) and (6, 0), respectively. If a point P movesso that the area of D POA is always twice the area of D POB, then P lies on
(a) 3x – y = 0
(b) x + y = 0
(c) x – 3y = 0
(d) x + 3y = 0

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