If `alpha` an integer and `P (alpha, alpha^2)` is a point in the interior of the quadrilateral `x=0, y=0, 4x+y-21=0 and 3x+y-4=0, and (1+ax)^n = 1 + 8x+24x^2 + …,` then `alpha=` (A) `a` (B) `-a` (C) `a^2` (D) none of these

If point P(alpha,alpha^(2)-2) lies inside the triangle formed by the lines x+y=1,y=x+1 and y=-1 then alpha in

If the point (1,alpha) always remains in the interior of the triangle formed by the lines y=x,y=0 and x+y=4, then alpha lies in the interval

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 x=2alpha+1\ a n d\ y=alpha-1 is a solution of the equation 2x-3y+5=0 , find the value of alpha

The range of value of alpha such that (0,alpha) lies on or inside the triangle formed by the lines y+3x+2=0,3y-2x-5=0,4y+x-14=0 is

If f(x+y) = f(x).f(y) for all x and y. f(1)=2 , and alpha_n = f(n), n epsilon N , then equation of the circle having (alpha_1, alpha_2) and (alpha_3, alpha_4) as the ends of its one diameter is : (A) (x-2) (x-8) + (y-4) (y-16) = 0 (B) (x-4) (x-8) + (y-2) (y-16) = 0 (C) (x-4) (x-16) + (y-4) (y-8) = 0 (D) none of these

Find the values of alpha so that the point P(alpha^(2),alpha) lies inside or on the triangle formed by the lines x-5y+6=0,x-3+2=0 and x-2y-3=0

Statement 1: The value of alpha for which the point (alpha,alpha^(2)) lies inside the triangle formed by the lines x=0,x+y=2 and 3y=x is (0,1) .Statement 2: The parabola y=x^(2) meets the linex +y=2 at (0,1) .

interval of alpha for which (alpha,alpha^(2)) and (0,0) lies on same side of 3x+y-10=0 is

a in R and (alpha-2)x^(2)+8x+alpha+4<0,AA x in R, then alpha cannot be