If `alpha_r=(cos2rpi+isin2rpi)^(1/10)`, then `|(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|=` (A) `alpha_5` (B) `alpha_7` (C) `0 (D) none of these

If alpha = cos((8pi)/11)+i sin ((8pi)/11) then Re(alpha + alpha^2+alpha^3+alpha^4+alpha^5) is

If alpha=cos ((2pi)/5)+isin((2pi)/5) , then find the value of alpha+alpha^2+alpha^3+alpha^4

Suppose a sample space S consists of 4 elements, i.e., S={alpha_1, alpha_2, alpha_3, alpha_4} " where " alpha_1, alpha_2, alpha_3, alpha_4 are pair wise mutually exclusive. Which function defines a probability function on S? (1) P(alpha_1)=1/2, P(alpha_2)=1/3, P(alpha_3)=1/4, P(alpha_4)=1/4 (2) P(alpha_1)=1/4, P(alpha_2)=-1/2, P(alpha_3)=7/9, P(alpha_4)=1/3 (3) P(alpha_1)=1/2, P(alpha_2)=1/4, P(alpha_3)=1/8, P(alpha_4)=1/8 (4) P(alpha_1)=1/2, P(alpha_2)=1/4, P(alpha_3)=1/8, P(alpha_4)=0

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

If the roots of equation x^3+a x^2+b=0a r ealpha_1,alpha_2 and alpha_3(a ,b!=0) , then find the equation whose roots are (alpha_1alpha_2+alpha_2alpha_3)/(alpha_1alpha_2alpha_3),(alpha_2alpha_3+alpha_3alpha_1)/(alpha_1alpha_2alpha_3),(alpha_1alpha_3+alpha_1alpha_2)/(alpha_1alpha_2alpha_3)

if sqrt(alpha_(1)-1)+2sqrt(alpha_(2)-4)+3sqrt(alpha_(3)-9)+4sqrt(alpha_(4)-16)=(alpha_(1)+alpha_(2)+alpha_(3)+alpha_(4))/(2) where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are all real. Then

If alpha is root of equation f(x)=0 then the value of (alpha+ 1/alpha)^2+(alpha^2+ 1/alpha^2)^2+(alpha^3+1/alpha^3)+………+(alpha^6+ 1/alpha^6)^2 is (A) 18 (B) 54 (C) 6 (D) 12

If alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_1-alpha_2)(alpha_1-alpha_3)(alpha_1-alpha_n)=n(alpha_1^ n-1+a)

If a variable takes the discrete values alpha+4 , alpha -(7)/(2), alpha-(5)/(2), alpha-2,alpha-3,alpha+(1)/(2), alpha-(1)/(2), alpha+5(alpha gt 0) , then the median is

If sqrt(alpha_1-1)+2sqrt(alpha_2-4)+3sqrt(alpha_3-9)+4sqrt(alpha_4-16)=(alpha_1+alpha_2+alpha_3+alpha_4)/2w h e r ealpha_1,alpha_2,alpha_3,alpha_4 are all real. Thena. alpha_1+alpha_2=10 b. alpha_2+alpha_3=26 c. alpha_4-alpha_3=12 d. alpha_4-alpha_2-alpha_1=22