If $a$ is the number of all even divisors and $b$ is the number of all odd divisors of the number $10800$,then $2a+3b=$

Let $n$ be a non-negative integer. Then the number of divisors of the form $4n+1$ of the number $(10)^{10} \cdot (11)^{11} \cdot (13)^{13}$ is equal to $....$

The number of terms in the expansion of $(x+y+z)^{10}$ is

The digit in the unit place of the number $843^{843} + 492^{295}$ 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:

Let $d(n)$ denote the number of divisors of $n$ including $1$ and itself. Then, $d(225)$, $d(1125)$, and $d(640)$ are