Number roots of equation `g\'(x)` between `(beta+gamma)/2 and (2beta+gamma)/3` is a then the value of the determinant of order 3 having all its elements 1 and a is (A) 1 (B) -1 (C) `a+1` (D) none of these

If alpha+beta+gamma =2 and veca=alphahati+betahatj+gammahatk, hatkxx (hatkxxveca)=vec0 ,then gamma = (A) 1 (B) -1 (C) 2 (D) none of these

If alpha+beta+gamma =2 and veca=alphahati+betahatj+gammahatk, hatkxx (hatkxxveca)=vec0 then gamma= (A) 1 (B) -1 (C) 2 (D) none of these

Let alpha be the A.M. and beta , gamma be two G.M.\'s between two positive numbes then the value of (beta^3+gamma^3)/(alphabetagamma) is (A) 1 (B) 2 (C) 0 (D) 3

If alpha,beta are the roots of the equation x^2+p x+1=0;gamma,delta the roots of the equation x^2+q x+1=0 , then (alpha-gamma)(alpha+delta)(beta-gamma)(beta+delta)= (a) q^2-p^2 (b) p^2-q^2 (c) p^2=q^2 (d) none of these

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

If alpha, beta, gamma are the roots of the equation x^(3) + x + 1 = 0 , then the value of alpha^(3) + beta^(3) + gamma^(3) , is

If alpha,beta, gamma re the roots of the equations x^3+px^2+2x+p=0 then the general value of tan^-1 alpha+tan^-1 beta+tan^-1 gamma is (A) npi (B) (npi)/2 (C) (2n+1) pi/2 (D) dependent upon the value of p.

If alpha , beta , gamma are the roots of the equation x^3 +4x^2 -5x +3=0 then sum (1)/( alpha^2 beta^2)=

If alpha,\ beta,\ gamma are the zeros of the polynomial f(x)=a x^3+b x^2+c x+d , then 1/alpha+1/beta+1/gamma= (a) b/d (b) c/d (c) -c/d (d) c/a

If alpha , beta , gamma are the roots of the equation x^3 + qx +r=0 find the value of ( beta - gamma )^2 +( gamma - alpha)^2 +(alpha - beta)^2