Three randomly chosen nonnegative integers `x , ya n dz` are found to satisfy the equation `x+y+z=10.` Then the probability that `z` is even, is: `5/(12)` (b) `1/2` (c) `6/(11)` (d) `(36)/(55)`

The number of nonnegative integer solutions of the equation x+y+z+5t=15 is

Given x,y,z are integers satisfying the equation x^(2)+y^(2)+z^(2)=2xyz, then find number of such triplets.

The values of x, y, z for the equations 5x-y+4z=5, 2x+3y+5z=2, 5x-2y+6z=1 are

The number of nonnegative integer solutions of x+y+2z=20 is (A) 76(B)84(C)112 (D) 121

Let a ,b ,a n dc be any three nonzero complex number. If |z|=1a n d' z ' satisfies the equation a z^2+b z+c=0, prove that a a =c c a n d|a||b|=sqrt(a c( b )^2)

Solve the system of equations in x,y and z satisfying the following equations x+[y]+{z}=3.1,y+[z]+{x}=4.3 and z+[x]+{y}=5.4

Consider the system of equation x+2y-3z=a , 2x+6y-11z=b , x-2y+7c then

The number of solutions of the system of equations: 2x+y-z=7,\ \ x-3y+2z=1,\ \ x+4y-3z=5 is (a) 3 (b) 2 (c) 1 (d) 0

x, y and z are distinct positive integers in which x and y are odd and z is even. Which of thefollowing can not be true ? (1) (x-z)^2 y is even (2) (x-z)^2y^2 is odd (3) (x-z)y is odd(4) (x-y)^2z is even

The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then x=y+z (b) 2x=y+z( c) x=2y+2z(d) None of these