Class 11 Mathematics Straight Lines MCQs Set 22

Question. If the slope of a line is \( -\frac{1}{\sqrt{3}} \) then its inclination is
(a) \( \frac{\pi}{3} \)
(b) \( \frac{5\pi}{6} \)
(c) \( \frac{2\pi}{3} \)
(d) \( \frac{3\pi}{4} \)
Answer: (b) \( \frac{5\pi}{6} \)

Question. If the straight line \( (3x+4y+5)+k(x+2y-3)=0 \) is parallel to x-axis then the value of k is
(a) 1
(b) -3
(c) 4
(d) 2
Answer: (b) -3

Question. Number of straight lines passing through (1, 3), (7, -3), (5, -1), (6, -2) is
(a) 2
(b) \( 4C_2 \)
(c) \( 4P_2 \)
(d) \( 4C_4 \)
Answer: (d) \( 4C_4 \)

SLOPE-INTERCEPT FORM, SLOPE POINT FORM AND TWO-POINT FORM

Question. The equation of the horizontal line passing through the point (4,-7) is
(a) y-7=0
(b) y+7=0
(c) y-4=0
(d) y+4=0
Answer: (b) y+7=0

Question. The equation of the straight line making an intercept of 3 units on the y-axis and inclined at \( 45^\circ \) to the x-axis is
(a) y = x-1
(b) y = x+3
(c) y = 45x + 3
(d) y = x+45
Answer: (b) y = x+3

INTERCEPTS AND INTERCEPT FORM

Question. Equation of the line having intercepts a,b on the axes such that a+b=5 and \( ab = \frac{21}{4} \) is
(a) 3x+2y=6
(b) 2x+3y=6
(c) 14x+6y=21
(d) x+4y=4
Answer: (c) 14x+6y=21

Question. x intercept of the line parallel to 4x+7y=9 and passing through (2,3) is
(a) \( \frac{25}{4} \)
(b) \( \frac{17}{4} \)
(c) \( \frac{29}{4} \)
(d) \( \frac{29}{7} \)
Answer: (c) \( \frac{29}{4} \)

Question. A straight line meet the axes in A and B such that the centroid of triangle OAB is (a,a). Then the equation of the line AB is
(a) x+y=a
(b) x-y=3a
(c) x+y=2a
(d) x+y=3a
Answer: (d) x+y=3a

NORMAL FORM AND SYMMETRIC FORM

Question. Equation of the line on which the length of the perpendicular from origin is 5 and the angle which this perpendicular makes with the x axis is \( 60^\circ \)
(a) \( x + \sqrt{3}y = 12 \)
(b) \( \sqrt{3}x + y = 10 \)
(c) \( x + \sqrt{3}y = 8 \)
(d) \( x + \sqrt{3}y = 10 \)
Answer: (d) \( x + \sqrt{3}y = 10 \)

Question. A point on line x - y + 1 = 0 at a distance \( 2\sqrt{2} \) from the point (1, 2) is
(a) (3,4)
(b) (3,0)
(c) (-1,4)
(d) (0,1)
Answer: (a) (3,4)

PROBLEMS ON DISTANCES

Question. The perpendicular distance from (1,2) to the straight line 12x+5y=7 is
(a) 15/13
(b) 12/13
(c) 5/13
(d) 7/13
Answer: (a) 15/13

Question. The vertices of a triangle are A(5,6) B(1, -4) C(-4,0) then the length of the altitude through the vertex A is
(a) \( \frac{66}{\sqrt{41}} \)
(b) \( \frac{55}{\sqrt{41}} \)
(c) \( \frac{17}{5} \)
(d) \( \frac{19}{5} \)
Answer: (a) \( \frac{66}{\sqrt{41}} \)

Question. The distance between the parallel lines 8x+6y+5=0 and 4x+3y-25=0 is
(a) \( \frac{7}{2} \)
(b) \( \frac{9}{2} \)
(c) \( \frac{11}{2} \)
(d) \( \frac{5}{4} \)
Answer: (c) \( \frac{11}{2} \)

Question. The equation of the line which is parallel to 5x+12y+1=0 and 5x+12y+7=0 and lying midway between them is
(a) 5x+12y+13=0
(b) 5x+12y-4=0
(c) 5x+12y+4=0
(d) 5x+12y-6=0
Answer: (c) 5x+12y+4=0

Question. The point on the line x + y = 4 that lies at a unit distance from the line 4x + 3y - 10 = 0 is
(a) (1,3)
(b) (-7,11)
(c) (11,-7)
(d) (2,2)
Answer: (b) (-7,11)

POSITION OF A POINT (S) W.R.T. LINE (S)

Question. The ratio in which the line 3x+4y-7=0 divides the line joining the points (1,2) (2,3) is
(a) 4:11 Internally
(b) 4:11 Externally
(c) 7:11 Internally
(d) 7:11 Externally
Answer: (b) 4:11 Externally

Question. The line segment joining the points (1,2) and (k,1) is divides by the line \( 3x + 4y - 7 = 0 \) in the ratio 4:9 then k is
(a) 2
(b) -2
(c) 3
(d) -3
Answer: (b) -2

POINT OF INTERSECTION OF LINES AND CONCURRENCY OF LINES

Question. If the point of intersection of kx+4y+2=0, x-3y+5=0 lies on 2x+7y-3=0 then k=
(a) 2
(b) 3
(c) -2
(d) -3
Answer: (b) 3

Question. The lines \( px + qy + r = 0 \), \( qx + ry + p = 0 \), \( rx + py + q = 0 \), are concurrent then
(a) \( p + q + r = 0 \)
(b) \( p^3 + q^3 + r^3 = 3pqr \)
(c) \( p^2 + q^2 + r^2 - pq - qr - rp = 0 \)
(d) All of the options
Answer: (d) All of the options

Question. The point of concurrence of the lines \( \frac{x}{3} + \frac{y}{4} = 1 \), \( \frac{x}{4} + \frac{y}{3} = 1 \), x = y is
(a) \( (\frac{4}{3}, \frac{4}{3}) \)
(b) \( (\frac{2}{7}, \frac{2}{7}) \)
(c) \( (\frac{12}{7}, \frac{12}{7}) \)
(d) \( (\frac{7}{12}, \frac{7}{12}) \)
Answer: (c) \( (\frac{12}{7}, \frac{12}{7}) \)

Question. If 4a+5b+6c=0 then the set of lines ax+by+c=0 are concurrent at the point
(a) \( (\frac{2}{3}, \frac{5}{6}) \)
(b) \( (\frac{1}{3}, \frac{1}{2}) \)
(c) \( (\frac{1}{2}, \frac{4}{3}) \)
(d) \( (\frac{1}{3}, \frac{7}{3}) \)
Answer: (a) \( (\frac{2}{3}, \frac{5}{6}) \)

Question. Let a and b be nonzero reals. Then the equation of the line passing through the origin and the point of intersection of x/a + y/b = 1 and x/b + y/a = 1 is
(a) ax+by=0
(b) bx+ay=0
(c) y-x=0
(d) x+y=0
Answer: (c) y-x=0

Question. The line which is concurrent with the lines 2x + 3y = 7, 2x = 3y + 1 and passing through the origin is
(a) x + 2y = 0
(b) x - 2y = 0
(c) 2x + y = 0
(d) 2x - y = 0
Answer: (b) x - 2y = 0

ANGLE BETWEEN LINES

Question. If \( \theta \) is an acute angle between the lines y=2x+3, y=x+1 then the value of \( \tan \theta = \)
(a) 2/3
(b) 1/3
(c) 3/4
(d) 1/2
Answer: (b) 1/3

Question. The angle between the lines kx+y+9=0, y-3x=4 is \( 45^\circ \) then the value of k is
(a) 2 or 1/2
(b) 2 or -1/2
(c) -2 or 1/2
(d) -2 or -1/2
Answer: (b) 2 or -1/2

TRIANGLES AND AREA OF THE TRIANGLE

Question. The straight lines x + y = 0, 3x + y - 4 = 0 and x + 3y - 4 = 0 form a triangle which is
(a) isosceles
(b) right angled
(c) equilateral
(d) right angled isosceles triangle
Answer: (c) equilateral

Question. If a, c, b are three terms of a G.P., then the line ax + by + c = 0
(a) has a fixed direction
(b) always passes through a fixed point
(c) forms a triangle with the axes whose area is constant
(d) always cuts intercepts on the axes such that their sum is zero
Answer: (c) forms a triangle with the axes whose area is constant

Question. Area enclosed by the co-ordinate axes and the line passing through the points (8,-3), (-4,12) is
(a) 98/5
(b) 49/5
(c) 24/25
(d) 17/8
Answer: (a) 98/5

Question. A straight line L is perpendicular to the line 4x-2y=1 and forms a triangle of area 4 sq.units with coordinate axes then, an equation of L is
(a) 2x+4y+8=0
(b) 2x-4y+8=0
(c) 2x+4y+7=0
(d) 4x-2y-7=0
Answer: (a) 2x+4y+8=0

QUADRILATERALS AND AREA OF THE QUADRILATERALS

Question. A square of area 25 sq.units is formed by taking two sides as \( 3x + 4y = k_1 \) and \( 3x + 4y = k_2 \) then \( |k_1 - k_2| = \)
(a) 5
(b) 1
(c) 25
(d) 125
Answer: (c) 25

Question. The equations of two sides of a square whose area is 25 sq.units are 3x-4y=0 and 4x+3y=0. The equation of other two sides of the square are
(a) \( 3x - 4y \pm 25 = 0, 4x + 3y \pm 25 = 0 \)
(b) \( 3x - 4y \pm 5 = 0, 4x + 3y \pm 5 = 0 \)
(c) \( 3x - 4y \pm 5 = 0, 4x + 3y \pm 25 = 0 \)
(d) 3x - 4y = 0, 4x + 3y = 0
Answer: (a) \( 3x - 4y \pm 25 = 0, 4x + 3y \pm 25 = 0 \)

Question. If 2x+3y=5 is the perpendicular bisector of the line segment joining the points \( A(1, \frac{1}{3}) \) and B then B=
(a) \( (\frac{21}{13}, \frac{49}{39}) \)
(b) \( (\frac{17}{13}, \frac{31}{39}) \)
(c) \( (\frac{7}{13}, \frac{49}{39}) \)
(d) \( (\frac{21}{13}, \frac{31}{39}) \)
Answer: (a) \( (\frac{21}{13}, \frac{49}{39}) \)

Question. If (2, -3) is the foot of the perpendicular from (-4, 5) on a line then its equation is
(a) 3x-4y+28=0
(b) 3x-4y-18=0
(c) 3x-4y+18=0
(d) 3x-4y-17=0
Answer: (b) 3x-4y-18=0

Question. If (-2, 6) is the image of the point (4,2) with respect to the line L=0, then L=
(a) 6x-4y-7=0
(b) 2x+3y-5=0
(c) 3x - 2y+5=0
(d) 3x-2y+10=0
Answer: (c) 3x - 2y+5=0

Question. One vertex of a square ABCD is A(-1,1) and the equation of one diagonal BD is 3x+y-8=0 then C=
(a) (-5,3)
(b) (5,3)
(c) (-5,-3)
(d) (2,5)
Answer: (b) (5,3)

Question. The reflection of the point (6,8) in the line x = y is
(a) (4,2)
(b) (-6,-8)
(c) (-8,-10)
(d) (8,6)
Answer: (d) (8,6)

CENTROID, CIRCUMCENTRE, ORTHOCENTRE AND INCENTRE

Question. The vertices of a triangle are (2,0) (0,2) (4,6) then the equation of the median through the vertex (2,0) is
(a) x+y-2=0
(b) x=2
(c) x+2y-2=0
(d) 2x+y-4=0
Answer: (b) x=2

Question. If the algebraic sum of the perpendicular distances from the points (2,0) (0,2) and (4,4) to a variable line is '0', then the line passes through the fixed point
(a) (1,1)
(b) (3,3)
(c) (2,2)
(d) (0,0)
Answer: (c) (2,2)

Question. If the equations of the three sides of a triangle are \( x + y = 1 \), \( 3x + 5y = 2 \) and \( x - y = 0 \) then the orthocentre of the triangle lies on the line
(a) 5x - 3y = 2
(b) 3x - 5y - 1 = 0
(c) 2x - 3y = 1
(d) 5x - 3y = 1
Answer: (d) 5x - 3y = 1

Question. Circum centre of the triangle formed by the lines x+y=0, 2x+y+5=0, x-y=2 is
(a) (-2, -1)
(b) (-3, 1)
(c) (-4, 3)
(d) (-1, -3)
Answer: (b) (-3, 1)

Question. The incentre of the triangle formed by the lines 3x + 4y = 10, 5x + 12y = 26, 7x + 24y = 50 is \( (\alpha, \beta) \) then \( \alpha + \beta = \)
(a) 0
(b) 1
(c) 2
(d) 4
Answer: (b) 1