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 the odd the number of ways in which three numbers in A.P. can be selected from {1,2,3,4….,n} is

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

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

If the numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n.

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

The total number of ways in which n^2 number of identical balls can be put in n numbered boxes (1,2,3,.......... n) such that ith box contains at least i number of balls is a. .^(n^2)C_(n-1) b. .^(n^2-1)C_(n-1) c. .^((n^2+n-2)/2)C_(n-1) d. none of these

If n is a even number, find the sum of the series upto n terms 1^2-2^2+3^2-4^2+5^2-......

Find the sequence of the numbers defined by a_n={1/n , when n is odd -1/n , when n is even

If composite function f_1(f_2(f_3((f_n(x))))n timesis an decreasing function and if 'r' functions out of total 'n' functions are decreasing function while rest are increasing, then the maximum value of r(n-r) is (a) (n^2-4)/4 , when n is of the form 4k (b) (n^2)/4, when n is an even number (c) (n^2-1)/4, when n is an odd number (d) (n^2)/4, when n is of the form 4k+2