The number of $3$-digit numbers that are divisible by $2$ and $3$,but not divisible by $4$ and $9$,is

It is given that the number $43361$ can be written as a product of $two$ distinct prime numbers $p_1$ and $p_2$. Further,assume that there are $42900$ numbers which are less than $43361$ and are coprime to it. Then,the value of $p_1+p_2$ is

The number of divisors of $7!$ is

If the constant term in the expansion of $\left(3 x^{3}-2 x^{2}+\frac{5}{x^{5}}\right)^{10}$ is $2^{k} \cdot l$,where $l$ is an odd integer,then the value of $k$ is equal to

The coefficient of $x^{10}$ in the expansion of $(1+x^2-x^3)^8$ is

If $n=(210)^2(360)(143)$,then the total number of non-trivial factors of $n$ is