Home
Class 12
MATHS
Two consecutive number p,p + 1 are remov...

Two consecutive number p,p + 1 are removed from natural numbers. 1,2,3, 4……….., `n-1,` n such that arithmetic mean of these number reduces by 1, then (n-p) is equal to.

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
A
`A.M`. of `1,2,3,4,…….,n`
`((n(n+1))/(2))/(n) = (n+1)/(2)`
If `p,p+1` are removed then
`A.M.=((n(n+1))/(2)-(2p+1))/(n-2)`
` therefore 1=((n+1)/(2))-((n(n+1)-2(2p+1))/(2.(n-2)))`
`implies(n-p)=1`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    ALLEN|Exercise part-2 Mathematics|18 Videos

  • TEST PAPERS

    ALLEN|Exercise part-2 Mathematic|18 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|3 Videos

Similar Questions

Explore conceptually related problems

Two consecutive number from n natural numbers 1,2,3,……, n are removed. Arithmetic mean of the remaining numbers is (105)/(4). The value of n is:

Two consecutive numbers from 1, 2, 3, ..., n are removed, then arithmetic mean of the remaining numbers is 105/4 then n/10 must be equal to

Two consecutive number from n natural numbers 1,2,3,……, n are removed. Arithmetic mean of the remaining numbers is (105)/(4). The G.M. of the removed numbers is :

Two consecutive number from n natural numbers 1,2,3,……, n are removed. Arithmetic mean of the remaining numbers is (105)/(4). Let removed numbers are x _(1), x _(2) then x _(1)+ x _(2) + n=

The arithmetic mean of first n natural numbers, is

If the arithmetic mean of the first n natural numbers is 15 , then n is "__________" .

The arithmetic mean of first n odd natural numbers, is

The arithmetic mean of the squares of first n natural numbers is

Two consecutive numbers from 1,2,3 …., n are removed .The arithmetic mean of the remaining numbers is 105/4 The sum of all numbers

Two consecutive numbers from 1,2,3 …., n are removed.The arithmetic mean of the remaining numbers is 105/4 . The removed numbers