If `int4(3-2x)^(-2)((3-2x)/(3+2x))^((1)/(3))dx=(3)/(alpha)((3+2x)/(3-2x))^((beta)/(gamma))+c`
`(beta and gamma" are prime nos.")`, then

If int_(pi/6)^(pi/3) sqrt (1- sin 2x) dx = alpha beta sqrt 2 gamma sqrt 3 , where alpha, beta and gamma are rational numbers, then 3 alpha 4 beta-gamma is equal to _______.

The value of the determinant |(1,(alpha^(2x)-alpha^(-2x))^2,(alpha^(2x)+alpha^(-2x))^2),(1,(beta^(2x)-beta^(-2x))^2,(beta^(2x)+beta^(-2x))^2),(1,(gamma^(2x)-gamma^(-2x))^2,(gamma^(2x)+gamma^(-2x))^2)| is (a) 0 (b) (alphabeta gamma)^(2x) (c) (alpha beta gamma)^(-2x) (d) None of these

If alpha, beta ,gamma are the roots of the equation x ^(3) + 2x ^(2) - x+1 =0, then vlaue of ((2- alpha )(2-beta) (2-gamma))/((2+ alpha ) (2+ beta ) (2 + gamma)) is :

If alpha,beta,gamma,delta in R satisfy ((alpha+1)^(2)+(beta+1)^(2)+(gamma+1)^(2)+(delta+1)^(2))/(alpha+beta+gamma+delta)=4 If biquadratic equation a_(0)x^(4)+a_(1)x^(3)+a_(2)x^(2)+a_(3)x_(a-)-4=0 has (alpha+(1)/(beta)-1),(beta+(1)/(gamma)-1),(gamma+(1)/(delta)-1),(delta+(1)/(alpha)-1) then the value of (a_(2))/(a_(0)) is

If (alpha, beta, gamma) are roots of equation x^(3)-3x^(2)+1=0 then the value of [((alpha)/(1+alpha))^(3)+((beta)/(1+beta))^(3)+((gamma)/(1+gamma))^(3) is k then |k|=

|[x-3, x-4, x-alpha], [x-2, x-3, x-beta], [x-1, x-2, x-gamma]| =0,"where" alpha, beta, gamma "are in AP"

alpha,beta,gamma roots of 4x^(3)+8x^(2)-x-2=0 ,then value of (4(alpha+1)(beta+1)(gamma+1))/(alpha beta gamma) is