If find

Evaluate :

A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B. If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.

OR

An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.

Find the distance between the point
(-1, -5, -10) and the point of intersection of the line and the plane x – y + z = 5.

If sin [cot^-1 (x + 1)] = cos (tan^-1 x), then find x.

OR

If then find x.