Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=a+b\left(mod 7\right)$ on $\left\{0,1,2,3,4,5,6\right\}$

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=$min $\left\{a,b\right\}$ on $N$.

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=$GCD $\left\{a,b\right\}$  on $N$.

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=$LCM $\left\{a,b\right\}$  on $N$.

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=$LCM $\left\{a,b\right\}$  on $\left\{0,1,2,3,4,..........,10\right\}$.

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=\sqrt{a^2+b^2}$ on $Q$.

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=a\times b$(mod$5$) on $\left\{0,1,2,3,4\right\}$.

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=a^2+b^2$ on $N$.

Determine whether the following operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

$a*b=a+b-ab$ on $R-\left\{1\right\}$.