Arun Sharma Solutions for Exercise 2: Review Test 2

What power of $210$ will exactly divide $142!$

Find the total number between $122$ and $442$ that are divisible by $3$ but not by $9$.

If $146!$  is divisible by $6^n$, then find the maximum value of $n$.

If we add the square of the digit in the tens place of a positive two-digit number to the product of the digits of that number, we shall get $52$, and if we add the square of the digit in the units place to the same product of the digits, we shall get $117$. Find the two-digit number.

Find the smallest natural number $n$ such that $(n+1)n\left[\right(n-1)!]$ is divisible by $990$.

If $x$, $y$ and $z$ are odd, even and odd, respectively, then $(x^2-y{z}^2+y^3)$ and $(x^2+y^2+z^2)$ are respectively:

For what relations between $b$and$c$is the number$abc-acb$ Divisible by$7,$ if $b>c$ ?

What is remainder when $a^6$ is divided by $\left(a+1\right)?$