What is the Arithmetic mean of the first $n$ natural numbers?

Find the number which when multiplied by $15$ is increased by $196$.

Let $x$ be the smallest number,which when added to $2000$ makes the resulting number divisible by $12, 16, 18$ and $21$. The sum of the digits of $x$ is

$A$ number when divided by a certain divisor leaves a remainder of $241$. When twice the number is divided by the same divisor,the remainder is $112$. Find the divisor.

On dividing a number by $38$, we get $90$ as quotient and $19$ as remainder. What is the number?

The least value to be given to $*$ so that the number $5*3457$ is divisible by $11$ is