An operation * on X. If (a*b)*c=a*(b*c) then it is

An operation * on X .If a*b=b*a then it is

An operation * on X .If a*b=b+a then it is

Let '**' be a binary operation defined on NxxN by : (a, b)**(c, d)=(a+c,b+d) . Find (1,2)**(2,3) .

Let '**' be a binary operation defined on NxxN by : (a, b)**(c, d)=(a+c,b+d) . Prove that '**' is commutative and associative.

If a + b + c = 0, then one of the solution of |(a-x,c,b),(c,b-x,a),(b,a,c-x)| = 0 is

If a, b, c are rational and no two of them are equal, then the equations (b-c)x^(2)+(c-a)x+(a-b)=0 and, a(b-c)x^(2)+ b(c-a)x+c(a-n)=0

Let alpha,beta be the roots of the equation (x-a)(x-b)=c,c!=0 Then the roots of the equation (x-alpha)(x-beta)+c=0 are a,c (b) b,ca,b(d)a+c,b+c

If a+b+c=0 the one root of |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}| =0 is