If the lines `ax+by+c=0, bx+cy+a=0 and cx+ay+b=0 (a, b,c` being distinct) are concurrent, then

If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b and c being distinct and different from 1) are concurrent the value of 1/(a-1)+1/(b-1)+1/(c-1) is

If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurrent, then a , b , c are in a. H.P. b. G.P. c. A.P. d. none of these

If the lines ax+12y+1=0, bx+13y+1=0 and cx+14y+1=0 are concurrent, then a,b,c are in:

If the straight lines. ax + amy + 1 = 0, bx + (m + 1)by + 1=0 and cx + (m +2)cy + 1=0, m!=0 are concurrent then a,b.c are in: (A) A.P. only for m = 1 (B) A.P. for all m (C) G.P. for all m (D) H.P. for all m

The three striaght lines ax+by=c, bx+cy=a and cx+ay=b are collinear if:

If a gt b gt c and the system of equtions ax +by +cz =0 , bx +cy+az=0 , cx+ay+bz=0 has a non-trivial solution then both the roots of the quadratic equation at^(2)+bt+c are

If the straight lines a x + m ay + 1 =0 b x + ( m +1) by + 1 =0 cx + (m+2) cy +1 =0, m ne0 are concurrent, then a, b, c are in :

If the straight lines x+y-2=0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

If the lines : x+2ay+a=0, x+3by+b=0 and x+4cy+c=0 are concurrent, where a,b,c are non-zero real numbers, then :

If alpha and beta are the roots of the equation ax^2 + bx +c =0 (a != 0; a, b,c being different), then (1+ alpha + alpha^2) (1+ beta+ beta^2) =