NET JRF PART - A : Questions and Solutions : NET DEC-2014

NET JRF PART - A : Questions and Solutions:

NET DEC-2014

1.) If n is a positive integer, then 

n ( n + 1 ) ( n + 2 ) ( n + 3 ) ( n + 4 ) ( n + 5 ) ( n + 6 )

 is divisible by 

(a) 3 but not 7 (b) 3 and 7 (c) 7 but not 3 (d) neither 3 nor 7 

Ans. : (b) 3 and 7 .

Solution: 

From the question, n is a positive integer.

( i.e., n = 1, 2, 3, 4, 5,.......)

Assume n = 1.

n ( n + 1 ) ( n + 2 ) ( n + 3 ) ( n + 4 ) ( n + 5 ) ( n + 6 ) = 1× 2 × 3 × 4 × 5 × 6 × 7 .

The answer which we get is divisible by 3 and 7 .

The product of n consecutive numbers is always divisible by n! .