Which of the following can not be valid assignment of probabilitiesfor outcomes of sample Space S = `{omega_1,omega_2,omega_3,omega_4,omega_5,omega_6,omega_7}`

Which of the following can not valid assignments for outcomes of sample space, S={omega_(1), omega_(2), omega_(3), omega_(4), omega_(5), omega_(6), omega_(7)}

Define the following terms : Mass percentage (w/w)

If omega = (-1+sqrt3i)/2 , find the value of |(1, omega, omega^2),(omega, omega^2, 1),(omega^2, 1 , omega)|

If omega is cube root of unity, then a root of the equation |(x + 1,omega, omega^2),(omega, x + omega , 1),(omega^2 , 1, x + omega)| = 0 is

Let a sample space be : S={omega_(1),omega_(2),.........,omega_(n)} . Which of the following assignments of probabilities to each outcome are valid ?

If 1,alpha_1,alpha_2,alpha_3,alpha_4 be the roots x^5-1=0 , then value of [omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4] is (where omega is imaginary cube root of unity)

Out of the followingg functions representing motion of a particle which represent SHM? y=sin omegat-cos omega t y=sin^2 omega t y=5cos((3pi)/4 - 3 omega t) y=1 + omega t+ omega^2 t^2 .

If omega^(3)=1 and omega ne1 , then (1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(5)) is equal to

If omega ne 1 and omega^3=1 , then : (a omega+b+c omega^2)/(a omega^2+b omega+c) + (a omega^2+b+c omega)/(a+b omega+c omega^2) is equal to :