Find the angle between the vector 

Find the distance of a point (2, 5, −3) from the plane 

Find the differential equation of the family of lines passing through the origin. 

Find the integrating factor for the following differential equation:

Evaluate: 

Evaluate 

17.

Evaluate:

In a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides

How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?

Find x such that the four points A(4, 1, 2), B(5, x, 6) , C(5, 1, -1) and D(7, 4, 0) are coplanar.