Let `n_1

Let nge1, n in Z . The real number a in 0,1 that minimizes the integral int_(0)^(1)|x^(n)-a^(n)|dx is

Let A_1 , G_1, H_1 denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For n >2, let A_(n-1),G_(n-1) and H_(n-1) has arithmetic, geometric and harmonic means as A_n, G_N, H_N, respectively.

Let A=Z , the set of integers. Let R_(1)={(m,n)epsilonZxxZ:(m+4n) is divisible by 5 in Z} . Let R_(2)={(m,n)epsilonZxxZ:(m+9n) is divisible by 5 in Z} . Which one of the following is correct?

Let A_0,A_1,.......,A_(n-1) be a n-sided polygon with vertices as 1,omega,omega^2,.......,omega^(n-1) Let B_1, B_1,..... B_(n -1) be another polygon with vertices 1 , 1 + omega, 1 +omega^2,........,1+omega^(n-1)[omega=cos((2pi )/n)+i sin n((2pi)/n)] for n=4,(A rdot(A_0, A_1, A_2, A_3))/(A r*(B_0, B_1, , B_3)) is lambda then

Let A_0,A_1,.......,A_(n-1) be a n-sided polygon with vertices as 1,omega,omega^2,.......,omega^(n-1) Let B_1, B_1,..... B_(n -1) be another polygon with vertices 1 , 1 + omega, 1 +omega^2,........,1+omega^(n-1)[omega=cos((2pi )/n)+i sin n((2pi)/n)] for n=4,(A rdot(A_0, A_1, A_2, A_3))/(A r*(B_0, B_1, , B_3)) is lambda then

Let z_1a n dz_2 be two complex numbers such that ( z )_1+i( z )_2=0 and arg(z_1z_2)=pidot Then, find a r g(z_1)dot

An unbiased normal coin is tossed n times. Let E_1: event that both heads and tails are present in n tosses. E_2: event that the coin shows up heads at most once. The value of n for which E_1a n dE_2 are independent is _________.

An unbiased normal coin is tossed n times. Let E_1: event that both heads and tails are present n tosses. E_2: event that the coin shows up heads at most once. The value of n for which E_1a n dE_2 are independent is _________.

An unbiased normal coin is tossed n times. Let E_(1): event that both heads and tails are present in n tosses. E_(2): event that the coin shows up heads at most once. The value of n for which E_(1) and E_(2) are independent is ______.

An unbiased normal coin is tossed n times. Let E_(1): event that both heads and tails are present in n tosses. E_(2): event that the coin shows up heads at most once. The value of n for which E_(1) and E_(2) are independent is ______.