If the greatest divisor of `30.5^(2n)+4.2^(3n)` is `p AA n in N` and that of `2^(2n+1)-6n-2` is `q AA n in N` ,then p+q

The number of proper divisors of 2^(p)*6^(q)*21^(r),AA p,q,r in N , is

If f: N to N, and x_(2) gt x_(1) implies f(x_(2)) gt f(x) AA x_(1), x_(2) in N and f(f(n))=3n AA n in N," then " f(2)= _______.

The number of odd proper divisors of 3^(p)*6^(q)*15^(r),AA p,q,r, in N , is

n(n+1)(n+2) is divisible by k for AA n in N . The largest k is

If n lt p lt 2n and p is prime and N=.^(2n)C_(n) , then

In the expansion of (x+a)^n if the sum of odd terms is P and the sum of even terms is Q , then (a) P^2-Q^2=(x^2-a^2)^n (b) 4P Q=(x+a)^(2n)-(x-a)^(2n) (c) 2(P^2+Q^2)=(x+a)^(2n)+(x-a)^(2n) (d)none of these

Using binomial theorem prove that 6^(2n) - 35n - 1 is divisible by 1225, AA n in N

If P(n) stands for the statement n(n+1)(n+2) is divisible by 3, then what is P(4).

If the sum of n terms of an A.P. is (p n+q n^2) , where p and q are constants, find the common difference.

If the sum of n terms of an A.P. is (p n+q n^2) , where p and q are constants, find the common difference.