Arun Sharma Solutions for Exercise 2: Level of Difficulty

$K$ is a three-digit number such that the ratio of the number to the sum of its digits is least. What can be said about the difference between the tens and the units digit?

$K$ is a three-digit number such that the ratio of the number to the sum of its digits is least. For how many values of K will the ratio be the highest?

A triangular number is defined as a number which has the property of being expressed as a sum of consecutive natural numbers starting with $1$. How many triangular numbers less than $1000$, have the property that they are the difference of squares of two consecutive natural numbers?

$x$ and $y$ are two positive integers. Then what will be the sum of the coefficients of the expansion of the expression ${(x+y)}^{44}$?

What is the remainder when $9+9^2+9^3+....+9^{2n+1}$ is divided by $6$?

The remainder when the number $123456789101112........484950$ is divided by $16$ is _____.

What is the highest power of $3$ available in the expression $\left(58!-38!\right)$?

Find the remainder when the number represented by $22334$ raised to the power $(1^2+2^2+3^2+....+{66}^2)$ is divided by $5$.