Q171 / 270 · NDA 2022 (Phase 1) · Mathematics

What is the maximum value of $n$ such that $5^n$ divides (30! +35 !), where $n$ is a natural number?

  • A
    4
  • B
    6
  • Correct answer
    C
    7
  • D
    8

Solution

$\begin{aligned} & 30!+35!=30!+35.34 .33 .32 .31 .30! \\ & 30!(1+35.34 .33 .32 .31) \\ & 1+35!.34 .33 .32 .31 \text { is not divisible by } 5\end{aligned}$ So, maximum value of $n$ such that $5^n$ divides 30 ! $\begin{aligned} & =\left[\frac{30}{5}\right]+\left[\frac{30}{5^2}\right]+\left[\frac{30}{5^3}\right]+\ldots \\ & =6+1+0+0 \ldots=7\end{aligned}$

Hence, the correct answer is option: 'C'.

More Permutation Combination Questions