[" Let "2" be the sat of all integers and "],[A=[12,y/x^(4)-y^(4)=175,x,y in Z]],[B=[1z,yti,x>y,x,y in Z}],[" Then,mus number of elements in "A nn B" is "]

Let Z be the set of all integers and A={(x,y);x^(4)-y^(4)=175,x,y in Z},B={(,),x>y,x,y in Z} Then,the number of elements in A nn B is

Let R be the relation on the set Z of all integers defined by R={(x, y) : x,y in Z,x-y is divisible by n}.Prove that i) (x, x) in R for all x in , Z ii) (x, y) in R implies that (y, x) in R for all x, y in Z iii) (x, y) in R and (y, z) in R implies that (x, z) in R for all x, y, z in Z

If x, y and z are integers then (x^(+) ____)+z=____+(y+____)

Let x,y,z be real numbers satisfying x+y+z=3,x^(2)+y^(2)+z^(2)=5 and x^(3)+y^(3)+z^(3)=7 then the value of x^(4)+y^(4)+z^(4) is

Let S be the set of all column matrices [b_1b_2b_3] such that b_1,b_2, b_3 in R and the system of equations (in real variable) -x+2y+5z=b_1 2x-4y+3z=b_2 x-2y+2z=b_3 has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each [b_1b_2b_3] in S? (a) x+2y+3z=b_1, 4y+5z=b_2 and x+2y+6z=b_3 (b) x+y+3z=b_1, 5x+2y+6z=b_2 and -2x-y-3z=b_3 (c) -x+2y-5z=b_1, 2x-4y+10 z=b_2 and x-2y+5z=b_3 (d) x+2y+5z=b_1, 2x+3z=b_2 and x+4y-5z=b_3

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

The values of x, y, z for the equations x-y+z=1, 2x-y=1, 3x+3y-4z=2 are

Let x,y,z be positive real numbers such that x+y+z=12 and x^(3)y^(4)z^(5)=(0.1)(600)^(3) Then x^(3)+y^(3)+z^(3) is

If x+a=y+b+1=z+c then the value of [[x, (a+y), (a+x)], [y, (b+y), (b+y)], [z, (c+y), (c+z)]] is