Let `M= [(0,-alpha),(alpha,0)]`, where `alpha` is a non-zero real number an `N = Sigma_(k=1)^(49) M^(2k)`. If `(I- M^(2))N= -2I`, then the positive integral value of `alpha` is ____

Let alpha and beta be two real roots of the equation x^(2)-ax+a-4=0 if alpha 2 then number of positive integral values of 'a' is/are

If M& alpha are twin prime & alpha+M=7 then the greatest integral value of N is

The value of alpha^(-n)+alpha^(-2n), n in N and alpha is a non-real cube root of unity, is

If alpha,beta(alpha

Let A = [{:(cos alpha,- sin alpha ), ( sin alpha , cos alpha ):}], (a in R) such that A ^(32) = [{:(0,-1), (1, 0):}] is the value of alpha is (pi)/(2^(k)), then the value of k is

Consider I(alpha)=int_(alpha)^(alpha^(2))(dx)/(x) (where alpha gt 0 ), then the value of Sigma_(r=2)^(5)I(r )+Sigma_(k=2)^(5)I((1)/(k)) is

Let A be a nxxn matrix such that A ^(n) = alpha A, where alpha is a real number different from 1 and - 1. The matrix A + I_(n) is

Let log_(3)N=alpha_(1)+beta_(1) log_(5)N=alpha_(2)+beta_(2) log_(7)N=alpha_(3)+beta_(3) where alpha_(1), alpha_(2) and alpha_(3) are integers and beta_(1), beta_(2), beta_(3) in [0,1) . Q. Number of integral values of N if alpha_(1)=4 and alpha_(2)=2 :

Let log_(3)N=alpha_(1)+beta_(1) log_(5)N=alpha_(2)+beta_(2) log_(7)N=alpha_(3)+beta_(3) where alpha_(1), alpha_(2) and alpha_(3) are integers and beta_(1), beta_(2), beta_(3) in [0,1) . Q. Largest integral value of N if alpha_(1)=5, alpha_(2)=3 and alpha_(3)=2 .