Let  and  denotes null set. If  denotes cartesian product of the sets A and B ; then  is

If  , then  is equal to

For any two sets A and B,  equals

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets , A x B and B x A are

For any two sets A and B, if  and  for some set X , then

If  is a set with 10 elements and , then the number of elements in A is

Let A and B be two sets, then  is equal to

If  is equal to

If  has a derivative at  is equal to

The value of  is

The derivative of  with respect to log  is

The derivative of  with respect to  is

The rate of change of  with respect to  at  is

If  then    is

If a₁, a₂, a₃, ........., a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + a₃ + .... + a_{n – 1} + 2a_n is

In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.

The domain of the function is