Number of ways in which three numbers in A.P. can be selected from `1,2,3,..., n` is a. `((n-1)/2)^2` if `n` is even b. `n(n-2)/4` if `n` is even c. `(n-1)^2/4` if `n` is odd d. none of these

Given that n is odd, number of ways in which three numbers in AP can be selected from 1, 2, 3,……., n, is

Show that the number of ways in which three numbers in arithmetical progresssion can be selected from 1,2,3,……..n is 1/4(n-1)^(2) or 1/4n(n-2) according as n is odd or even.

lim_(n->oo)(-3n+(-1)^n)/(4n-(-1)^n) is equal to a. -3/4 b. 0 if n is even c. -3/4 if n is odd d. none of these

The arithmetic mean of 1,2,3,...n is (a) (n+1)/2 (b) (n-1)/2 (c) n/2 (d) n/2+1

The arithmetic mean of 1,2,3,...n is (a) (n+1)/2 (b) (n-1)/2 (c) n/2 (d) n/2+1

The sum of first n odd natural numbers is 2n-1 (b) 2n+1 (c) n^2 (d) n^2-1

If f:{1,2,3....}->{0,+-1,+-2...} is defined by f(n)={n/2, if n is even , -((n-1)/2) if n is odd } then f^(-1)(-100) is

The total number of ways in which 2n persons can be divided into n couples is a. (2n !)/(n ! n !) b. (2n !)/((2!)^3) c. (2n !)/(n !(2!)^n) d. none of these

The total number of ways in which 2n persons can be divided into n couples is a. (2n !)/(n ! n !) b. (2n !)/((2!)^3) c. (2n !)/(n !(2!)^n) d. none of these

In a sequence of (4n+1) terms, the first (2n+1) terms are n A.P. whose common difference is 2, and the last (2n+1) terms are in G.P. whose common ratio is 0.5 if the middle terms of the A.P. and LG.P. are equal ,then the middle terms of the sequence is (n .2 n+1)/(2^(2n)-1) b. (n .2 n+1)/(2^n-1) c. n .2^n d. none of these