. Consider the set A, of points (x, y) such that 0 Sxsn, Osy sn where n, x, y are integers. Let S be the set of all lines passing through at least two distinct points form A. Suppose we choose a line l at random from S Let P, be the probability that l is tangent to the circle x2 + y2 = . Then the limit him in is n-> (a) o (b) 1 SP

Consider the set A_(n) of point (x,y) such that 0 le x le n, 0 le y le n where n,x,y are integers. Let S_(n) be the set of all lines passing through at least two distinct points from A_(n) . Suppose we choose a line l at random from S_(n) . Let P_(n) be the probability that l is tangent to the circle x^(2)+y^(2)=n^(2)(1+(1-(1)/(sqrt(n)))^(2)) . Then the limit lim_(n to oo)P_(n) is

Let l be the line through (0,0) an tangent to the curve y = x^(3)+x+16. Then the slope of l equal to :

Let l be the line through (0,0) an tangent to the curve y = x^(3)+x+16. Then the slope of l equal to :

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let (x,y) be any point on the parabola y^(2)=4x. Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :