The value of the determinant `|alphabetalalphax nalphabetax|` is independent of `l` b. independent of `n` c.`alpha(x-l)(x-beta)` d. `alphabeta(x-l)(x-n)`

The root of the equation |(x,alpha,1),(beta,x,1),(beta,gamma,1)| = 0 are independent of :

The expression cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2 alpha*cos2 beta is (a)independent of alpha(b) independent of beta (c)independent of alpha and beta(d) dependent on alphaand beta

The roots of the equation |{:(x,alpha,1),(beta,x,1),(beta,gamma,1):}|=0 are independent of

The value of the determinant |a^(2)a1cos nx cos(n+1)x cos(n+2)x sin nx sin(n+1)x sin(n+2)x is independent of n(b)a(c)x(d) none of these

The expression (sin(alpha+theta)-sin(alpha-theta))/(cos(beta-theta)-cos(beta+theta)) is independent of alpha b.independent of beta c. independent of theta d .independent of alpha and beta

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

Given that (log)_p x=alpha\ a n d(log)_q x=beta,\ then value of equals- a. (alphabeta)/(beta-alpha) b. (beta-alpha)/(alphabeta) c. (alpha-beta)/(alphabeta) d. (alphabeta)/(alpha-beta)

If p(x), q(x), r(x) be polynomials of degree one and alpha, beta, gamma are real nubers then |(p(alpha), p(beta), p(gamma)),(q(alpha), q(beta), q(gamma)), (r(alpha), r(beta), r(gamma))| (A) independent of alpha (B) independent of beta (C) independent gamma (D) independent of all alpha,beta and gamma

If alpha and beta be the zeroes of the polynomial p(x)=x^(2)-5x+2 , find the value of (1)/(alpha)+(1)/(beta)-3alphabeta.