If a system of three linear equations x + 4ay + a = 0, x + 3by + b = 0, and x + 2cy + c = 0 is consistent, then prove that a,b,c are in H.P.

If the equations 2x + 3y + 1 = 0,3x + y - 2 = 0 , and ax + 2y-b = 0 are consistent then prove that a - b = 2 .

If c lt 1 and the system of equations x + y - 1 = 0, 2x - y - c = 0 and -bx + 3by - c = 0 is consistent, then the possible real values of b are a) b in (-3,(3)/(4)) b) b in (-(3)/(2),4) c) b in (-(3)/(4),3) d)None of these

If the system of equations x - 2y +z = a , 2x + y - 2z = b, x +3y - 3z = c, has at least one solution, then a) a + b + c = 0 b) a - b + c = 0 c) -a + b + c = 0 d) a + b - c = 0

If pqrne0 and the system of equations (p + a) x + by + cz = 0 , ax + (q + b)y + cz = 0 ,ax + by + (r + c) z =0 has a non-trivial solution, then value of (a)/(p) + (b)/(q) + (c )/(r ) is a)-1 b)0 c)1 d)2

If the three linear equations x+4ay+az=0 x+3by+bz=0 x+2cy+cz=0 have a non trivial solution, where a ne 0, b ne 0 ,c ne 0 then ab+bc is equal to a)2ab b) -ac c)ac d) 2ac

Solve the following system of linear equations. x+y+z=3 , y-z=0 , 2x-y=1

If the roots of the equation x ^(2) + 2 bx + c =0 are alpha and beta, then b ^(2) - c is equal to

If the roots of the equation a(b-c)x^(2) + b(c-a) x+c(a-b)=0 are equal, then prove that a, b, c are in H.P

The values of lambda for which the system of equations x + y - 3 = 0 (1+lambda)x+(2+lambda)y-8=0 x-(1 +lambda) y + (2 + lambda) = 0 is consistent are a) -5//3,1 b) 2//3,-3 c) -1//3,-3 d)0,1