The product of consecutive positive integers is divisible by a.`r !` b. `r !+1` c. `(r+1)!` d. none of these

Prove that the product of two consecutive positive integers is divisible by 2.

Prove that the product of three consecutive positive integers is divisible by 6 .

Property:Product of r consecutive number is divisible by r!

True or false: The product of any r consecutive natural numbers is always divisible by r!

If r, s, and t are consecutive positive positive multiples of 3, is rst divisible by 27, 54, or both?

Statement-1: The smallest positive integer n such that n! can be expressed as a product of n-3 consecutive integers, is 6. Statement-2: Product of three consecutive integers is divisible by 6.

In an equilateral triangle, the inradius and the circumradius are connected by r=4R b. r=R//2 c. r=R//3 d. none of these

If N denotes the number of ways of selecting r objects of out of n distinct objects (rgeqn) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .^(r-1)C_(r-n) b. .^(r-1)C_n c. .^(r-1)C_(n-1) d. none of these

The greatest integer by which 1+sum_(r=1)^(30)rxxr ! is divisible is a. composite number b. odd number c. divisible by 3 d. none of these

The roots of the equation a x^2+b x+c=0, a in R^+, are two consecutive odd positive (A) |b|lt=4a (B) |b|geq4a (C) |b|geq2a (D) none of these