KVPY SA Exam 2018 Question Paper

${15}^2\times 5^{18}$
$=9\times 5^{20}$
$\left[{\log }_{10}\left(9\times 5^{20}\right)\right]=\left[2{\log }_{10}^3+20{\log }_{10}5\right]$
= $\left[2\times 4771+20\left(1-0.3010\right)\right]$
= 14 {characteristic}
Hence the number have 15 digits
At worst all digit can have value 9
Hence sum should less then 135
And the last digit should be 5 Hence
Sum should greater than Or equal to 6