Prove. If `cosalpha +isinalpha` is the solution of the equatioin `x^n +p_1x^(n-1) +p_2 x^(n-2) +…+p_n =0` where `p_1,p_2,p_3,…p_n` are real then the value of `p_1 sinalpha+p_2 sin2alpha+p_3sin3alpha+…+p_nsin nalpha=0`

If p^(2)-p+1=0 , then the value of p^(3n) can be

If n is a natural number such that n=P_1^(a_1)P_2^(a_2)P_3^(a_3)...P_k^(a_k) where p_1,p_2,...p_k are distinct primes then minimum value of log n is:

Find n if : "" ^(2n)P_(n+1) : ""^(2n-2) P_n = 56 : 3

If the line x cosalpha + y sin alpha = P touches the curve 4x^3=27ay^2 , then P/a=

Find n if : ""^(2n+1) P_(n-1) : ""^(2n-1) P_n = 3: 5

If alpha,beta roots of x^(2)-6p_(1)x+2=0,beta,gamma are roots of x^(2)-6p_(2)x+3=0and gamma,alpha are roots of equation x^(2)-6p_(3)x+6=0 where p_(1),p_(2),p_(3) are positive then The values of p_(1),p_(2),p_(3) respectively are

If e^(ax) +e^(-bx) = p_0 +p_1x +p_2x^2 + ....oo then (p_0 , p_1,p_2) =

If the coefficients of (p+1) th and (P+3) th terms in the expansion of (1+x)^(2n) are equal then prove that n=p+1

If a variable takes values 0, 1, 2,…,n with frequencies q^(n), (n)/(1)q^(n-1)p, (n(n-1))/(1.2)q^(n-2)p^(2),…,p^(n) where p+q = 1, then the mean is

For a binomial variate X , if n = 3 and P(X =1) = 12 P(X =3) , then the value of p is