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

The image of the point A (1,2) by the line mirror y=x is the point B and the image of B by the line mirror y=0 is the point (alpha,beta) , then a. alpha=1,beta=-2 b. alpha = 0,beta=0 c. alpha=2,beta=-1 d. none of these

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

IF alpha , beta are the roots of x^2 - ax +b=0 , then the whose roots are (alpha + beta ) /( alpha ) , (alpha + beta)/( beta) is

If alpha and beta ( alpha'<'beta') are the roots of the equation x^2+b x+c=0, where c<0

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