The number of lines that are parallel to 2x + 6y- 7= 0 and have an intercept 10 between the coordinate axes is : -

(a) 1 (b) 2 (c) 4 (d) infintely many

y = mx + c................1

2x + 6y - 7 = 0

m = -1/3 so the eq of line which is parallel to above line is

y = -x/3 + c        ................2

y intercept = (0,c)

x intercept = (3c,0)

y using distance formula , distance  bw these two points will be

d = (9c² + c²)^1/2 = (+ or - )(root10)c            (distance bw coordinate axis)

d = 10             (given) so

c = + or - (root10)

there are two possible values for c so total number of lines can be 2 ...