Consider the cartesian plane `R^2` and let X denote the subset of points for which both coordinates are integers. A coin of diameter `1/2` is tossed randomly onto the plane. Find probability p that the coin covers a point of X.

A bag contains (2n + 1) coins. It is known that n of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is (31)/(42) , then determine the value of n.

Consider the random experiment of tossing dice. If number obtained on it is multiple of 3 then toss dice again, and if any other number is obtained toss a coin. Find probability of an event that coin shows tail given that at least once number 2 comes up.

Plot the points T(4,-2) and V(-2,4) on a cartesian plane. Whether these two coordinates locate the same point?

Find the coordinates of the point P on AD such that AP : PD = 2 : 1.

Let P be a point whose coordinates differ by unity and the point does not lie on any of the axes of reference. If the parabola y^2=4x+1 passes through P , then the ordinate of P may be

Consider the parabola y^2 = 8x. Let Delta_1 be the area of the triangle formed by the end points of its latus rectum and the point P( 1/2 ,2) on the parabola and Delta_2 be the area of the triangle formed by drawing tangents at P and at the end points of latus rectum. Delta_1/Delta_2 is :

Find the equation of the plane passing through the point (2,3,1) having (5,3,2) as the direction ratio is of the normal to the plane.

Find the coordinates of a points A, where AB is the diameter of circle whose centre is (2,-3) and B is (1, 4)

A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q(8, 0, 10). Find the coordinates of the point R.

Consider three vectors p=i+j+k, q=2i+4j-k and r=i+j+3k . If p, q and r denotes the position vector of three non-collinear points, then the equation of the plane containing these points is