Class 11 Mathematics Straight Lines MCQs Set C

Question: Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x-2y=3
(a) 3x+y+7=0 
(b) 3x-y-7=0 
(c) 3x+2y-7=0
(d) None of these
Answer: b

Question: Let PS be the median of the triangle with vertices P(2,2)Q(6,-1 ) and R (7,3 ).The equation of the line passing through (1,-1 ) and parallel to PS is
(a) 2x-9y-7=0
(b) 2x -9y-11=0 
(c) 2x+9y-11=0 
(d) 2x+9y+7=0 
Answer: d

Question: One diagonal of a square is along the line 8x- 15y= 0 and one of its vertex is (1,2). Then, the equations of the sides of the square passing through this vertex are
(a) 23x+7y=9,7x+23y=53 
(b) 23x-7y+9=0,7x+23y+53=0 
(c) 23x-7y-9=0,7x+23y-53=0
(d) None of the above 
Answer: c

Question: The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point whose coordinates are
(a) (1,1)
(b) (2,2)
(c) (3,3)
(d) (4,4)
Answer: b

Question: Find the equation of the line passing through the point of intersection of 2x+y=5 and x+3y+8=0 and parallel to the line 3x+4y =7
(a) 4x -3y +3 =0 
(b) 3x +4y +3=0 
(c) 4x + 3y -3=0 
(d) 3x -4y -3= 0
Answer: b

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

Question: If the line x/a +y/b = 1 passes through the points (2, –3) and (4, –5), then (a,b) is
(a) (1, 1)
(b) (–1, 1)
(c) (1, –1)
(d) (–1, –1)
Answer: d

Question: For specifying a straight line, how many geometrical parameters should be known?
(a) 1
(b) 2
(c) 4
(d) 3 
Answer: b

Question: Find the equations of the lines through the point of intersection of the lines x- y +1=0 and 2x - 3y +5 = 0 and whose distance from the point (3,2) is 7/5.
(a) 3x- 4y +6 =0 and 4x -3y + 1= 0
(b) 3x+4y +6 =0 and 4x +3y +1=0 
(c) 3x -4 - 6= 0 and 4x +3y +1=0
(d) None of the above
Answer: a

Question: Equation of a line, which is intersecting the X-axis Bat a distance of 3 units to the left of origin with slope –2, is 
(a) 2x+y+6=0
(b) 2x -y+6 =0 
(c) 2x -y- 6 =0 
(d) None of these
Answer: a

Question: A ray of light passing through the point (1, 2) reflects on the X-axis at point A and the reflected ray passes through the point (5, 3). Find coordinates of A.
(a) (13/5,0) 
(b) (−13/5,0),
(c) (0,13/5)
(d) None of these
Answer: a

Question: Consider the straight lines x+ 2y+4 = 0 and 4x+2y-1=0. The line 6x+6y+7=0 is
(a) bisector of the angle including origin
(b) bisector of acute angle
(c) bisector of obtuse angle
(d) None of the above 
Answer: a,b

Question: If bx+ cy= a, where a, b, c are of the same sign, be a line such that the area enclosed by the line and the axes of reference is 1/8 sq unit, then
(a) b, a, c are in GP
(b) b,2a, c, are in GP
(c) b, a/2,c are in AP
(d) b,-2a, c, are in Gp 
Answer: b,d

Question: Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, –1).
(a) x- 4y +3=0
(b) x + 4y −3 =0
(c) x-4y-3=0 
(d) None of these
Answer: a

Question: If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.
(a) 8 x- 5y+ 60=0
(b) 8x − 6y+60=0
(c) 8x +5y +60=0
(d) None of these
Answer: a

Question: Find the equations of the lines, which cut off intercepts on the axes whose sum and product are 1 and – 6, respectively. 
(a) 2x + 3y+ =0 or 3x-2y+6=0 
(b) 2x -3y -6=0 or 3x- 2y+6=0 
(c) 2x -3y -6=0 or 3x+2y+6=0 
(d) None of the above
Answer: b

Question: Find equation of the line passing through the point (2, 2) and cutting off intercepts the axes whose sum is 9. 
(a) x+ 2y = 6
(b) 2x +y =8
(c) 2x +y =5
(d) 2x -y =6 
Answer: a

Question: If non-zero numbers a ,b, c are in HP, then the straight line x/a+ y/b + 1/c =0 always passes through a fixed point. That point is
(a) (1,-1/2)
(b) (1,-2)
(c) (-1,-2)
(d) (-2,2)
Answer: b

Question: If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be
(a) 2x +3y =12
(b) 3x +y =12 
(c) 4x-3y=16 
(d) 5x-2y =10 
Answer: a

Question: Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x+4y=4 and the opposite vertex of the hypotenuse is (2, 2).
(a) x-7y+12=0,7x+y-16=0
(b) x-7y+16=0,7x+y-16=0
(c) x-7y+12=0,7x+y+16=0
(d) None of the above
Answer: a

Question: If the distance of any point ( x,y )from the origin is defined as d(x,y) max{|x|,|y}, d (x,y) =a, non-zero constant, then the locus is a
(a) circle
(b) straight line
(c) square
(d) triangle 
Answer: b

Question: Slope of a line which cuts of intercepts of equal lengths on the axes is
(a) –1
(b) –0
(c) 2
(d) 3
Answer: a

 Question: The ratio in which the line 3x+ 4y+2=0 divides the distance between the lines 3x +4y +5 =0 and 3x +4y +5 =0 is
(a) 1 : 2
(b) 3 : 7
(c) 2 : 3
(d) 2 : 5
Answer: b

Question: Equation to the straight line cutting off an intercept 2 from the negative direction of the axis of y and inclined at 30° to the positive direction of x-axis, is
(a) y x + −√3 =0
(b) y−x+2=0
(c) y−√3x-2=0
(d) √3y-x+2√3=0
Answer: d

Question: The straight lines 4ax+3by+c=0, where a+b+c =0 are concurrent at the point
(a) (4, 3)
(b) (1/4, 1/3)
(c) (1/2, 1/3)
(d) None of these 
Answer: c

 Question: The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line √3x+y=1 is
(a) y += 2 =0,√3x -y-2 -3√3=0
(b) x − 2= 0√3x-y+2+3√3 =0
(c) √3x-y-2-3√=0
(d) None of the above
Answer: a

Question: If the straight line ax by +c=0 always passes through ( 1,2), then a, b, c are in 
(a) AP
(b) HP
(c) GP
(d) None of these
Answer: a

Let L be the line belonging to the family of the straight lines (a+2b)x+(a-3b)y+a-8b=0, a b ∈ R,which is farthest from the point (2, 2).

Question: Area formed by the line L with coordinate axis is
(a) 4/3 sq units
(b) 9/2 sq units
(c) 49/8 sq units
(d) None of these 
Answer: c

Question: The equation of line L is
(a) x +4y +7=0
(b) 2x +3y+4=0 
(c) 4x-y-6=0 
(d) None of these
Answer: a

Question: If L is concurrent with the lines x- 2y+1 = 0 and 3x - 4y+ λ =0, lthen the value of λ is
(a) 2
(b) 1
(c) –4
(d) 5
Answer: d

Assertion and Reason
 Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c), (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question: Statement I Each point on the line y- x+12= 0 is equidistant from the lines 4y+3x-12=0,3y+ 4x -24 =0 .
Statement II The locus of a point which is equidistant from two given lines is the angular bisector of the two lines. 
Answer: a

Question: Statement I If the points (1, 2) and (3, 4) be on the same side of the line 3x -5y+λ = 0, then λ < 7 or λ > 11
Statement II If the points (x₁,y₁) 1 1 and (x₂,y2) be on the same side of the line f (x,y) ≡ ax+by+c=0, then f(x₁,y₁)/f (x₂,y₂)<0 
Answer: c

Question: Consider a, b c , and are variables.
Statement I Such that 3a+2b+4c=0, then the family of lines given by ax+ by+c = 0pass through a fixed point (3, 2).
Statement II The equation ax+ by+ c = 0 will represent a family of straight line passing through a fixed point if there exists a linear relation between a b c , and . 
Answer: d

Question: The line L given by x/5+y/b=1 passes through the point (13,32). The line K is parallel to L and has the equation x/c +y/3=1. Then, the distance between L and K is 
(a) 23/√15
(b) √17
(c) 17/√15
(d) 23/√17
Answer: d

Question: A straight line through the point A(3,4) is such that is intercept between the axis is bisected at A. Its equation is 
(a) 4x +3y=24
(b) 3x+4y=25 
(c) x+ y = 7
(d) 3x- 4y +7=0 
Answer: a

Question: The lines x+ y + =|a| and ax-y = 1 intersect each other in the first quadrant. Then, the set of all possible values of a in the interval 
(a) (–1, 1]
(b) (0 ,∞)
(c) [1,∞)
(d) (-1,∞) 
Answer: c

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

Question: If (a,a²) falls inside the angle made by the lines, y=x/2,x>0 and y=3x,x>0, then a ∈
(a) (1/2,3)
(b)(-3,-1/2)
(c) (0,1/2)
(d) (3, ∞) 
Answer: a

Question: Let P=(1,0),Q=(0,0) and R = (3,3√3) three points. The equation of the bisector of the ∠PQR is
(a) √3/2x+y=0
(b) x+√3y+=0
(c) √3x+ y=0
(d) x+√3/ y =0
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 values of p 
Answer: a

Question: If non-zero numbers a, b c and are in HP, then the straight line x/a+y/b+1/c=0 always passes through a fixed point. That point is 
(a) (1,1/2)
(b) (1, –2
(c) (–1,–2)
(d) (–1, 2) 
Answer: b

Question: The equation of the bisector of the actue angles between the lines 3x-4y+7=0 and 12x+5y-2=0 = is 
(a) 99x- 27y -81 =0
(b) 11x-3y+9 =0
(c) 21x+ 77y-101=0 
(d) 21x+77y+101=0 
Answer: c

Question: Let A(2, 3) and B( -2,1,) be vertices of a ∆ABC. If the centroid of this triangle moves on the line 2x+3y=1, then the locus of the vertex C is the line
(a) 2x+3y=9
(b) 2x-3y=7 
(c) 3x-2y=5 
(d) 3x-2y=3 
Answer: a

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

Question: The equation of the straight line joining the origin to the point of intersection of y -x + 7=0 and y+2x -2 = 0 is
(a) 3x + 4y= 0
(b) 3x - 4y= 0 
(c) 4x - 3y= 0 
(d) 4x +3y =0 
Answer: d