`a in N, a <=100}`, and `[tan^2 x] -tan x- a=0` has a real roots (where, [ ] denotes function), then number of elements in the set S is

P={n^(3)+(n+1)^(3)+(n+2)^(3);n in N} and Q={8n:n in N} then

If n in N, n > 1 , then value of E= a - ""^(n)C_(1) (a-1) + ""^(n)C_(2) (a -2)+ ... + (- 1)^(n) (a-n) (""^(n)C_(n)) is

If N_a =[an : n in N], " then " N_5 nn N_7 is equal to : a) N_7 b)N c) N_(35) d) N_5

If u_(n)=sin(n theta) sec^(n) theta, v_(n)=cos(n theta) sec^(n) theta , n in N, n ne 1," then " (v_(n)-v_(n-1))/(u_(n-1))+(1)/(n)(u_(n))/(v_(n)) =

if A= {5^(n)-4n-1: n in N} and B={16(n-1):n in N} then

A = {8^(n) - 7n - 1 : n in N}, B = {49(n-1) : n in N } then

Show that the function f:N rarr N, given by f(n)=n- (-1)^(n), AA n in N is a bijection.

If A={4^(n)-3n-1:n in N) and B={9(n-1):n in N} then