The greatest integral value of m for which the point of intersection of `L_1 : 2x+y=50 a n d L_2 : y=mx+1` has integral coordinate, is `a. 5` b. `9` c. `47` d. `51""`

Write the integral values of m for which the x-coordinates of the point of intersectioin of the lines y=m x+1\ a n d\ 3x+4y=9 is an integer.

Square of the distance between the integral points of intersection of L_1 : 2x+y=50 a n dL_2 :y=mx+1 for the greatest and the least integral values of m is a. 5 b. 20 c. 25 d. 30""

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is 2 (b) 0 (c) 4 (d) 1

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is (a) -2 (b) 0 (c) 4 (d) 1

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is (a) 2 (b) 0 (c) 4 (d) 1

The least integral value of ' a ' for which the graphs y=2a x+1 and y=(a-6)x^2-2 do not intersect: (a) -6 (b) -5 (c) 3 (d) 2

If the straight lines joining the origin and the points of intersection of y=mx+1 and x^2+y^2=1 are perpendicular to each other, then find the value of m .

The lines joining the origin to the point of intersection of The lines joining the origin to the point of intersection of 3x^2+m x y=4x+1=0 and 2x+y-1=0 are at right angles. Then which of the following is not a possible value of m ? -4 (b) 4 (c) 7 (d) 3

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . Locus of T is a circle having centre at (A) (a, b) (B) (a, b/2) (C) (a/2, b) (D) (a/2, b/4)