If `P(alpha,beta),alpha in Z,beta in Z` lies on or inside the quadrilateral formed by `xy(x-y+1)(5x-2y-10)=0` then the number of points `P` is

If the point (alpha, alpha^(4)) lies on or inside the triangle formed by lines x^(2)y+xy^(2)-2xy=0 , then the largest value of alpha is .

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

P(alpha,beta) lies on the line y=6x-1 and Q(beta,alpha) lies on the line 2x-5y=5 then the equation of line PQ is

If x = sin alpha, y = sin beta, z = sin (alpha + beta) then cos (alpha + beta) =

The points (2 ,1)(3 ,-2) and (alpha ,beta) form a triangle of area 4 square units.If the point (alpha, beta) lies on the line y=x+3 then the value of alpha+beta is (are)

The points (2, 1), (3, -2) and (alpha, beta) form a triangle of area 4 square units. If the point (alpha, beta) lies on the line y=x+3 then the value of alpha+beta is (are)

The points (2, 1), (3, -2) and (alpha, beta) form a triangle of area 4 square units. If the point (alpha, beta) lies on the line y=x+3, then the value of alpha+beta is (are)

The points (2, 1), (3, -2) and ( alpha, beta ) form a triangle of area 4 square units.If the point ( alpha,beta ) lies on the line y=x+3 then the value of alpha +beta is (are)

I If a point (alpha,beta) lies on the circle x^(2)+y^(2)=1 then the locus of the point (3 alpha.+2,beta), is

Let alpha, beta and gamma be real numbers such that the system of linear equations x + 2y + 3z = alpha 4x + 5y + 6z = beta 7x + 8y + 9z = gamma-1 Let P be the plane containing all those (alpha, beta, gamma) for which the above system of linear equations is consistent, and D be the square of the distance of the point (0,1,0) from the plane P. The value of absM is ______