$A$ boy added all natural numbers from $1$ to $12,$ however he added one number twice due to which the sum became $80.$ What is the number which he added twice?

What is the smallest $6$-digit number that is completely divisible by $108$?

$n$ is a whole number which when divided by $4$ gives the remainder $3$. The remainder when $2n$ is divided by $4$ is

The numerator and denominator of a fraction are in the ratio of $2:3$. If $6$ is subtracted from the numerator,the result is a fraction that has a value $\frac{2}{3}$ of the original fraction. The numerator of the original fraction is

What least number must be subtracted from $1294$ so that the remainder when divided by $9, 11, 13$ will leave in each case the same remainder $6$?

The value of $(1001)^3$ is