If `(alpha, beta)` be the circumcentre of the triangle whose sides are `3x-y=5, x+3y=4 and 5x+3y+1=0`, then (A) `11alpha - 21beta = 0` (B) `11alpha + 21beta = 0` (C) `alpha +2beta=0` (D) none of these

If the tangent to the curve y= (x)/(x^(2) - 3), x in r ( xne pm sqrt3) , at a point (alpha, beta ) ne (0, 0) on it is parallel to the line 2x + 6y -11 =0 , then (A) |6alpha + 2beta|=19 (B) |6alpha + 2 beta|=9 (C) |2 alpha + 6 beta |= 19 (D) | 2 alpha + 6 beta| = 11

If the function f(x)=x^(3)+alpha x^(2)+beta x+1 has maximum value at x=0 and minimum value at x=1, then (i)alpha=(2)/(3),beta=0 (ii) alpha=-(3)/(2),beta=0(iii)alpha=0,beta=(3)/(2)(iv) none of these

If alpha,beta are the roots of 3x^(2)-5x+7=0 then alpha^(3)+beta^(3)=

Through the point P(alpha,beta), where alpha beta>0 , the straight line (x)/(a)+(y)/(b)=1 is drawn so as to form a triangle of area S with the axes.If ab>0, then the least value of S is alpha beta(b)2 alpha beta (c) 3 alpha beta(d) none

The graph of the equations 5x- 2y + 1 = 0 and 4y- 3x +5 =0, intersect at the point P(alpha,beta) . What is the value of (2 alpha- 3 beta) ?

The graphs of the equations 3x + y- 5 = 0 and 2x - y - 5 = 0 intersect at the point P(alpha,beta) . What is the value of (3 alpha+ beta) ?

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