The number of divisors of $9600$ including $1$ and $9600$ are

The greatest value of $x$ satisfying $21 \equiv 385 \pmod{x}$ and $587 \equiv 167 \pmod{x}$ is

Consider the following statements:
$I$: The number of non-trivial even divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $(\alpha_1+2\alpha_3+\alpha_5)(\alpha_2+\alpha_5+1)(\alpha_4+1)-1$.
$II$: The number of non-trivial odd divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $\alpha_2+\alpha_4+\alpha_5+\alpha_2\alpha_4+\alpha_4\alpha_5$. Then:

The coefficient of $x^7$ in $(1-x+2x^3)^{10}$ is $........$.

The number $111...1$ ($91$ times) is

The number of positive divisors of $252$ is