The product of any $r$ consecutive natural numbers is always divisible by

Let $A$ and $B$ be two sets containing $4$ and $2$ elements respectively. Then the number of subsets of the set $A \times B$,each having at least $3$ elements is:

The number of numbers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) which are multiples of $3$ is?

If $110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear,then the value of $n$ is:

In how many ways can the letters of the word '$NUTAN$' be arranged when consonants occupy odd places and vowels come on even places?

How many $4$-digit numbers,divisible by $5$,can be formed using the digits $0, 3, 5, 7,$ and $9$ if repetition of digits is not allowed?