Unique Academic Board Solutions for Exercise 1: Practice Exercise

If the number $357*25*$ is divisible by both $3$ and $5$, then the missing digits in the unit's place and the thousandth place respectively are;

In a three-digit number, the digit at the hundred's place is three times the digit at the unit'splace and the sum of the digits is $28$. If the digits are reversed. The number is reduced by $995$. The difference of hundred's and ten's digit of the number is:

The difference between the squares of two consecutive odd integers is always divisible by :

The largest number that exactly divides each number of the sequence $\left(1^5-1\right)$, $\left(2^5-2\right)$, $\left(3^5-3\right)$,  $\left(n^5-n\right)$ is:

The number of prime factors in $9^{222}\times 6^{333}\times 5^{111}$ is:

When the sum of two numbers is multiplied by $5$, the product is divisible by $15$. Which one of the following pairs of numbers satisfies the above condition ?

A number when divided by the sum of $555$ and $445$ gives two times their difference as quotient and $30$ as the remainder. The number is:

A number when divided by $114$ leaves the remainder $21$. If the same number is divided by $19$, then the remainder will be: