If the number of integral solutions of the equation  $2x+2y+z=20$ where  $x\ge 0,y\ge 0$  and  $z\ge 0$  is 11k then k=

$2x+2y=20-z\Rightarrow x+y=10-\frac{Z}{2}$

Coefficient of  $P^{10-\frac{z}{2}}$  in  ${(1+P+P^2\mathrm{....})}^2=11-\frac{Z}{2}$
                     Patting $z = 0,2,4,6,8,10,12,14,16,18,20$

$\Rightarrow \text{ The number of integral solution }=11+10+9+8+7+6+5+4+3+2+1=$
                      The no. of integral solutions $= 66$