If x,y,z is integer and `xge0,yge1,zge2,x+y+z=15` then the number of values of the ordered triplet (x,y,z) is

If x, y, z are integers such that x >=0, y >=1, z >=2 and x + y + z = 15 , then the number of values of ordered triplets (x,y,z) are

If xyz = 1 and x, y, z gt 0 then the minimum value of the expression (x+2y)(y+2z)(z+2x) is

The equation "cosec " x/2 + " cosec " y/2 + " cosec " z/2=6 , where 0 lt x, y,z lt pi/2 and x+y+z=pi , have i) Three Ordered triplet (x,y,z)solutions ii) Two ordered triplet (x,y,z) solutions. iii) Just one ordered triplet (x,y,z) solution iv) No ordered triplet (x,y,z) solution

If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x , y , z) that satisfy the equation is 0 (b) 1 (c) 2 (d) Infinite solutions

If x,y,z are positive integers, then the value of the expression (x+y)(y+z)(z+x) is

If 9(27)^(x^2+y+z)+9(27)^(x+y+z^2)+9(27)^(x+y^2+z)=11 then find the number of possible triplet (x ,y ,z)dot

If x > 0, y > 0, z>0 and x + y + z = 1 then the minimum value of x/(2-x)+y/(2-y)+z/(2-z) is:

If x,y and z are positive integers such that x < y < z and x + y + z = 6 , then what is the value of z?

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

If x, y, z are distinct positive numbers such that x+(1)/(y)=y+(1)/(z)=z+(1)/(x) , then the value of xyz is __________