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

Find the distances of the point P(2, 3, 2) from the coordinate planes.

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) , determine the value of n .

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) , determine the value of n .

Let P\ a n d\ Q be any two points. Find the coordinates of the point R\ which divides P Q externally in the ratio 2:1 and verify that Q is the mid point of P R .

Set S is the set of all points (x, y) in the coordinate plane such that x and y both integers with absolute value less than 4. If one of these points is chosen at random, what is the probability that this point will be 2 units or less from the origin ?

If the perpendicular distance of a point A, other than the origin from the plane x + y + z = p is equal to the distance of the plane from the origin, then the coordinates of p are

A fair coin is tossed four times. Let X denote the number of heads occurring. Find the probability distribution, mean and variance of X.

Consider a plane x+y-z=1 and point A(1, 2, -3) . A line L has the equation x=1 + 3r, y =2 -r and z=3+4r . The coordinate of a point B of line L such that AB is parallel to the plane is

In the (x, y) coordinate plane, what is the radius of the circle having the point (2, -4) and (-4, 4) as endpoints of a diameter?

Consider the plane pi:x+y-2z=3 and two points P(2,1,6) and Q(6,5,-2) . Statement 1: PQ is parallel to the normal to the plane. Statement 2: Q is the image of point P in he plane pi