# Unseen Passage

For Class 4 to Class 12

# Straight Lines MCQ Class 11 Mathematics

Please refer to Chapter 10 Straight Lines MCQ Class 11 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 11 Mathematics. Students should refer to MCQ Questions for Class 11 Mathematics with Answers to score more marks in Grade 11 Mathematics exams. Students should read the chapter Straight Lines and then attempt the following objective questions.

## MCQ Questions Class 11 Mathematics Chapter 10 Straight Lines

The Straight Lines MCQ Class 11 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question: The equation of the straight line passing through the point (3, 2) and perpendicular to the line y x = is
(a) x- y = 5
(b) x+ y = 5
(c) x+ y = 1
(d) 2x -y =6

B

Question: A line AB makes zero intercepts on x-axis and y-axis and it is perpendicular to another line CD which is 3x+ 4y+ 6= 0. The equation of line AB is
(a) y = 4
(b) 4x -3y+8=0
(c) 4x -3y=0
(d) 4x -3y+6=0

C

Question: Equation of a line passing through the line of intersection of lines 2x-3y +4=0, 3x + 4y -5=0 and perpendicular to 6x -7y+ 3=0, is
(a) 119+ 102y+125 =0
(b) 119x+102y=125
(c) 119x +102y=125
(d) None of these

B

Question: A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio1 : n. Find the equation of the line.
(a) x (n+1)+3(n+1)y =n+11
(b) x(n +1)-3(n+1)y =n+11
(c) x(n+1)+3(n+1)y =n-11
(d) None of the above

A

Question: The equation of straight line through the intersection of the lines x- 2y = 1 and x+3y=2 and parallel to 3x+4y=0  is
(a) 3x+ 4y+ 5 =0
(b) 3x 4y-10= 0
(c) 3x+ 4y-5=0
(d) 3x+ 4y +6 =0

C

Question: The line x/a -y/b =1  cuts the x-axis at P. The equation of the line through P perpendicular to the given line is
(a) x+ y = ab
(b) x+ y = a+b
(c) ax+ by = a2
(d) bx+ ay= b2

C

Question: If the lines x= a+m, y =−2 and y= mx are concurrent, then least value of| |a is
(a) 0
(b) √2
(c) 2√2
(d) None of these

C

Question: The lines ax+ by+ c = 0, bx+ cy+ a = 0 and cx+ ay+ b= 0 (a≠b≠c)  are concurrent, if
(a) a3 +b3+ c3 +3abc=0
(b) a2+ b2+ c2- 3abc =0
(c) a+ b+ c = 0
(d) None of the above

C

Question: The value of λ for which the lines 3x+ 4y = 5, 5x+ 4y =  4 and λx+ 4y= 6 meet at a point is
(a) 2
(b) 1
(c) 4
(d) 3

B

Question: Find the values of θ and p, if the equation x cosθ+y sin θ =p is the normal form of the line √3x+y+2=0..
(a) 210°, 1
(b) 210°, 2
(c) 220°, 3
(d) None of these

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

D

Question: The line through the points (h ,3) and (4, 1) intersects the line 7x- 9y- 19= 0 at right angle. Find the value of h.
(a) −22/9
(b) 22/9
(c) 22/7
(d) 22/13

B

Question: The equation of the sides of a triangle are x -3y=0, 4x +3y =5 and 3x+y = 0. The line 3x- 4y=0, passes through the
(a) incentre
(b) centroid
(c) orthocentre
(d) circumcentre

C

Question: In what direction should a line be drawn through the point (1 2) so that its point of intersection with the line x+ y + = 4 is at a distance of √6/3 from the given point?
(a) 75°
(b) 60°
(c) 90°
(d) 45°

A

Question:

B

Question: The triangle formed by the lines x +y = 0, 3x+ y =4, x+ 3y = 4 is
(a) isosceles
(b) equilateral
(c) right angled
(d) None of these

A

Question: Find angles between the lines √3x+y=1 and x+√3y=1
(a) 35°
(b) 30°
(c) 45°
(d) 60°

B

Question: Two lines are drawn through (3, 4) each of which makes angle of 45° with line x- y = 2 , then area of the triangle formed by these lines is
(a) 9 sq units
(b) 9/2 sq units
(c) 2 sq units
(d) 2/9 sq unit

B

Question: Distance between the lines 5x+3y-7=0  and 15x 9y +14 = 0 is
(a) 35/√34
(b) 1/3√34
(c) 35/3√34
(d) 35/2√34

C

Question: The distance of the point of intersection of lines 2x- 3y +5= 0 and 3x +4y = 0 from the line 5x -2y = 0 is
(a) 130/17√29
(b) 13/7√ 9
(c) 130/7
(d) 13/7

A

Question: The inclination of the straight line passing through the point( − 3, 6) and the mid-point of the line joining the points (4 ,5)  and (2 ,9 ) is
(a) π/4
(b) π/6
(c) π/3
(d) 3π/4

D

Question: A point equidistant from the lines 4x +3y+10=0, 5x-12y+26=0 and 7x+24y-50=0  is
(a) (1, –1)
(b) (1, 1)
(c) (0, 0)
(d) (0, 1)

C

Question: The coordinates of the foot of perpendicular from the point (2, 3) on the line y = 3x +4 is given by

B

Question: The length of perpendicular from the point( a cos α,a sin α)  upon the straight line y = x tan α +c, c > 0, is
(a) c
(b) c sin2 α
(c) c cos α
(d) c sec2 α

C

Question: Equation of the line passing through (1, 2) and parallel to the line y= 3x -1 is
(a) y+2=x+1
(b) y+2=3(x+1)
(c) y-2=3(x-1)
(d) y -2=x-1

C

Question: The equation of bisectors of the angles between the lines |x|=|y|  are

C

Question: Equation of straight line belonging to families of straight lines (x+2y)+λ 3x+2y+1)=0 and (x+2y)+μ(x-y+1)=0
(a) 6x+5y=2
(b) 5x-6y+4=0 6
(c) 5x+ 6y=4
(d) None of these

B

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

C

Question: Lines 2x+y =1 and 2x+y=7 are
(a) on the same side of a point(0,1/2)
(b) on the opposite side of a point (0,1/2)
(c) same lines
(d) perpendicular lines

A

Question: Locus of the image of the point (2,3) in the line (x+2y+3)+λ(2x-3y+4)=0is (λ∈R)
(a) x2+y2-3x-4y-4=0
(b) 2x2+3y2+2x+4y-7=0
(c) x2+ y2-4y+4=0
(d) None of the above

C

Question: Equations of diagonals of the square formed by the lin  es x=0,y=0,x=1 and y =1 are
(a) y= x, y +x=1
(b) y = x, x +y=2
(c) 2y= x, y+ x=1/3
(d) y=2x,y+2x=1

A

Question: A square of area 25 sq units is formed by taking two sides as 3x+4y=k1 and x+4y=k2, ,then|k1-k2| is
(a) 5 units
(b) 1 unit
(c) 25 units
(d) None of these

C

Question: Orthocentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is
(a) (3, 5/4)
(b) (3, 12)
(c) (3, 3/4)
(d) (3, 9)

C

Question: Two vertices of a triangle are (5, 1)and(−2,3) . If the orthocentre of the triangle is the origin, then coordinates of third vertex are
(a) (4,7)
(b) (−4,−7)
(c) (-4,7)
(d) None of these

B

Question: Orthocentre of the triangle formed by the lines x+y = 1 and xy = 0 is
(a) (0, 0)
(b) (0 ,1)
(c) (1, 0)
(d) (−1,1)

A

Question: The point moves such that the area of the triangle formed by it with the points (1,5) and (3 ,7) is 21 sq units. The locus of the point is
(a) 6x+y-32=0
(b) 6x-y+32 =0
(c) x+6y-32=0 y
(d) 6x-y-32=0 32

A

Question: If t1 and t2 are roots of the equation t2+λt+1=0, where λ is an arbitrary constant. Then, the line joining the points (at12,2at1) (at22,2at2) always passes through a fixed point whose coordinates are
(a) (a,0)
(b) (-a,0)
(c) (0.-a)
(d) (0,-a)

B

Question: The number of points on the line 3x+ 4y=5, which are at a distance of sec2θ+2cosec2 θ, ∈ R, from the point (1, 3) is
(a) 1
(b) 2
(c) 3
(d) infinite

B

Question: The base BC of Δ ABC is bisected at (p,q) and equation of sides AB and AC  are px+ qy  = 1 and qx+ py = 1 respectively. Then, the equation of the median through A is

A

Question: A system of lines is given as y mi x+ci,, where mcan take any value out of 0, 1, − 1 and when mis positive, then ccan be 1 or − 1, when mi equal  to − 1, ci can take 0 or 2. Then, the area enclosed by all these straight line is
(a) 3/√2(√2-1) s q units
(b) 3/√2sq units
(c) 3/2sq units
(d) None of these

C

Question: If 5a+ 4b+ 20c= t, then the value of t for which the line ax +by+ c−1=0 always passes through a fixed point is
(a) 0
(b) 20
(c) 30
(d) None of these

B

Question: A beam of light is sent along the line x- y = 1. Which after refracting from the x-axis enters the opposite side by turning through 30° towards the normal at the point of incidence on the x-axis. Then, the equation of the refracted ray is
(a) (2-√3) x-y=2+√3
(b) (2+√3) x-y=2+√3
(c) (2-√3) x+y=2+√3
(d) None of these

D

Question: The straight line ax+ by+ c = 0 where abc ≠ 0 will pass through the first quadrant if
(a) ac>0,bc >0
(b) c >0 and bc <0
(c) bc >0 and/or ac >0
(d) ac < 0 and/or bc <0

D

Question: Consider the family of lines
(x+y-1)+ λ (2x+3y-5)=0  and 3x+2y-4)+µ (x+2y-6)=0, equation of a straight line that belongs to both the families is
(a) x − 2y-8=0
(b) x-2y+8=0
(c) 2x+y-8=0
(d) 2x-y-8=0

B

Question: The  of the point (3, 5) from the line 2x+3y-14= 0 measured parallel to line x-2y =1, is
(a) 7/√5distance
(b) 7/√13
(c) √5
(d) √13