x + y = 4 divides join of ( - 1 , 1 ) & ( 5,7 ) in (a) 2 : 1 (b) 1 : 2 (c) – 1 : 2 (d) N/T
Line segment joining points (-3,-4) & (1, -2) is divided by y – axis in ratio (a) 1 : 3 (b) 2 : 3 (c) 3 : 1 (d) N/T
No. of point on x – axis at a distance d ( d < 4 ) from ( 5,4 ) is (a) 1 (b) 2 (c) 3 (d) None
If ortho centre & centroid of  are (-3, 5) & (3, 3), its circumcentre is (a) (6, 2) (b) (3,-1) (c) (-3, 1) (d) N/T
sides of a  are x + y = 1, & x y = 0, then orthocentre of  is (a) ( 1/ 2 , 1 / 2) (b) ( 1/3 , 1/3 ) (c) ( 1/ 4 , 1 / 4 ) (d) N/T
Distance between 4x + 3y = 11 & 8x + 6y = 15

(a) 7/2 (b) 4 (c) 7/10 (d) N/T

Ratio in which 3x + 4y + 2 = 0 divides distance between 3x + 4y + 5 = 0 & 3x + 4y – 5 = 0 is (a) 7 : 3 (b) 3 : 7

If (-2,6) is image of (4, 2) w. r. t. line then equation of the line is (a) 3x - 2y + 5=0 (b) 3x – 2y + 10= (c) 2x + 3y -5=0 (d) 6x-4y =
Area of triangle whose sides are along x = 0 , y =0 & 4x+ 5y =20 is (a) 20 (b) 10 (c) 1/20 (d) 1/
Line which passes through (1, -2) & cuts off equal intercepts from axes will be (a) x + y = 1 (b) x – y = 1 (c) x + y + 1 = 0 (d) N/T
A line through (x 1 , y 1 ) & its segment between axis is bisected at this point then its equation

(a) 2 y

y x

x 1 1

  (b) 2(xy 1 + yx 1 ) = x 1 y 1

If straight lines xy – x – y +1=0 and line ax + 2y – 3 = 0 are concurrent , then a is (a) -1 (b) 0 (c) 3 (d) 1
Equation of straight line passing through intersection of lines x – 2y = 1 & 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) N/T
x + 2y = 3, 2x + y = 3 & line ‘L’ ( thro’ origin ) are concurrent then equation of ‘L’ is (a) x = y (b) x = - y

ASSIGNMENT- STRAIGHT LINES

Nishant Gupta, D-122, Prashant vihar, Rohini, Delhi-

If a, b, c are in A.P; then ax + by + c = 0 represents (a) Straight line (b) family of concurrent lines (c) family of parallel lines (d) N/T
Nearest point on line 3x - 4y = 25 from origin

(a) (-4,5) (b)(3,-4) (c) (3, 4) (d) N/T

(a) (3, -1) (b) (1, -3) (c) (-1, -1) (d) N/T

If 3 sides of a  are x + y = 1, 3x + 5y = 2 & x – y = 0, then orthocentre of  lies on line (a) 5x – 3y = 2 (b) 3x – 5y + 1 = (c) 2x – 3y = 1 (d) N/T
If algebric sum of distance from pts. (2, 0), (0, 2) & (1, 1) to a variable straight line is 0, then line passes through point (a) (-1, 1) (b) (1, 1) (c) (1, -1) (d) N/T
If algebric sum of distance of pts. (2, 1), (3,
1. & (-4, 7) from straight line y = mx + c is 0, then line passes through point (a) (1, 3) (b) (1, 10) (c) (1, 6) (d) (1, 10 / 3)
If a line joining A(2, 0) & B (3, 1) is rotated about A in clockwise direction through an  15 o, then line in new position is

(a) 3 x y 2 3 (b) 3 x y 2 3 (c) √3 y = x-2 (d) N/T

(a) x = -2y (b) 2x = y (c) x = 2y (d) None

Then equation of bisector of PQR is

(a) x y 0 2

  (b) x  3 y= 0

A line passing through ( 2,2 ) cuts a triangle of area 9 sq. units from first quadrant then possible sum of slopes is (a) - 2. 5 (b) - 2 (c) - 1. 5 (d) -
A straight line meets axes at A & B such that centroid of triangle OAB is ( a,a ) then equation of AB is (a) x - y = a (b) x + y = a (c) x + y =2 a (d) x + y =3 a
Distance of ( 3,5 ) from 2x + 3y = 14 measured parallel to x – 2y = 1 is

(a) 5

(b) 13

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) -
Point ( 2 , 1 ) is shifted by 3√2 || to x+ y = 1, in the direction of increasing ordinates , to reach Q. The image of Q by x + y = 1 is (a) (-1, 4) (b) (-1, -2) (c) (5, 4) (d) ( -3 , 2 )
(2,0) & ( 0,2) are base of an isosceles ∆ are. If one of sides is x=2 then other side is (a) x- y =2 (b) x - y = - 2 (c) y = 2 (d) 2x + y = 2
A variable line passing through ( 1,3 ) meets x-axis at A & y- axis at B .If rectangle OAPB is completed then locus P is ( O being origin ) (a) 1/y + 3/x = 1 (b) x + 3y = 1 (c) 1/x + 3 / y = 1 (d) 3x + y = 1
If ( a, a^2 ) lies inside the angle formed by y = x/2 & y= 3x , x > 0 then a lies in (a) ( 0 , 1/2) (b) (3, ∞) (c) ( 1/2 , 3 ) (d) ( -3 , - 1/2 )
x1, x 2 , x 3 & y 1 , y 2 , y 3 are in G.P. with same common ratio, then (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ) (a) Collinear (b) lie on ellipse

The point A divides the joint of (–5, 1) and (3,
1. in the ratio K : 1. The difference of the two values of K for which the area of the triangle ABC where B = (1, 5) and C = (7, 2) equals 2 units is : (a) 96/5 (b) 31/ (c) 32/9 (d) 35/
If ( α , α ) lies in between x + y = 2 & x + y = - 2 then

(a) | α | = 1 (b) | α | < 1 (c) | α | = 2 (d) | α | < 1/

The line ( k +1 ) 2 x + k y – 2 k 2 – 2 =0 passes through a point regardless the value of k. Which of the following is line of slope 2 & passing through the point (a) y = 2x – 8 (b) y = 2x – 5 (c) y = 2x – 4 (d) y = 2x + 8