Number of natural numbers `n>=10` for which the expression `P(n)=^(n)C_(10)*^(n+1)C_(10)` is a perfect square of an integer?

The number of natural numbers n for which the equation (x-8)x=(n-10) has no real solutions equal to

10^(n)c_(2)=3^(n+1)c_(3), find n

Find the number of integers n for which (n)/(20-n) is the square of an integer.

If .^(n)C_(10) = .^(n)C_(15) , then evaluate .^(27)C_(n) .

The number of values of n in Z for which n^(2)+n+2 is a perfect square is

If n is an even natural number , then sum_(r=0)^(n) (( -1)^(r))/(""^(n)C_(r)) equals

The number formed from the last two digits (ones and tens) of the expression 2^(12n)-6^(4n) where n is any positive integer is 10(b)00(c)30 (d) 02

If m is the square of a natural number n, then n is