If `tantheta=sqrt n`, where `n in N, >= 2`, then `sec2theta` is always (a) a rational number (b) an irrational number (c) a positive integer (d) a negative integer

The 10th term of (3-sqrt((17)/4+3sqrt(2)))^(20) is (a)a irrational number (b)a rational number (c)a positive integer (d)a negative integer

If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers

The product of n positive numbers is 1, then their sum is a positive integer, that is

Prove that (n !)^2 < n^n n! < (2n)! , for all positive integers n.

If x_1 , x_2, ..., x_n are any real numbers and n is anypositive integer, then

Prove that n^(2)-n divisible by 2 for every positive integer n.

If A is a square matrix that |A|= 2, than for any positive integer n , |A^(n)|=