The value of `i^(1+3+5++(2n+1))` is________.

Let f be a real-valued invertible function such that f((2x-3)/(x-2))=5x-2, x!=2. Then value of f^(-1)(13) is________

If 2tan^2x-5secx=1 is satisfied by exactly seven distinct values of x in [0,((2n+1)pi)/2],n in N , then the greatest value of n is________.

Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value of n is________

If f(x) is an odd function, f(1)=3,f(x+2)=f(x)+f(2), then the value of f(3) is________

If f(x) is an odd function, f(1)=3,f(x+2)=f(x)+f(2), then the value of f(3) is________

The value of sum_(i=1)^(13) (n^(n) + i^(n-1)) is

If U_n=int_0^1x^n(2-x)^ndxa n dV_n=int_0^1x^n(1-x)^n dx ,n in N , and if (V_n)/(U_n)=1024 , then the value of n is________

The value of (1 + i)( 1 + i^(2) ) (1 + i^(3)) (1 + i^(4)) is

Find the value of (I ) sin^(-1) ( sin ((2pi )/(3)) ) (ii ) sin^(-1) (sin ((5 pi )/(4)))

If m is the minimum value of f(x , y)=x^2-4x+y^2+6y when xa n dy are subjected to the restrictions 0lt=xlt=1a n d0lt=ylt=1, then the value of |m| is________