`I f(n !)/(2!(n-2)!)and(n !)/(4!(n-4)!)a r e i n t h e r a t i o2:1,` n!4!(n-4 are in the ratio 2:1, then nn!a) If 21(n -2)1 and

Evaluate (n!)/((n-r)!) when : (i) n=10,r=4 (ii) r = 1 (iii) r = 2.

If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2 .

If n = 12, r = 4 , then evaluate the following: (i) (n!)/(r!(n-r)!) (ii) (n!)/((n-r+2)!)

If n = 12, r = 4 , then evaluate the following: (i) (n!)/(r!(n-r)!) (ii) (n!)/((n-r+2)!)

If composite function f_1(f_2(f_3((f_n(x))))n timesis an decreasing function and if r of f_i ' s are decreasing function while rest are increasing, then the maximum value of r(n-r) is (n^2-1)/4 , when n is an even number (n^2)/4, when n is an odd number (n^2-1)/4, when n is an odd number (n^2)/4, when n is an even number

If composite function f_1(f_2(f_3((f_n(x))))n timesis an increasing function and if r of f_i ' s are decreasing function while rest are increasing, then the maximum value of r(n-r) is (n^2-1)/4 , when n is an even number (n^2)/4, when n is an odd number (n^2-1)/4, when n is an odd number (n^2)/4, when n is an even number

If n is any positive integer, then the value of frac{i^(4n+1)-i^(4n-1)}{2} equals

If n is any positive integer,write the value of (i^(4n+1)-i^(4n-1))/(2)