Set Theory Test...

{$$x \epsilon R : \dfrac{14x}{x+1} - \dfrac{9x-30}{x-4} <0$$ } is equal to

If  $$a * b = 2 ^ { a b }$$  on  $$N \cup \{ 0 \}$$  then  $$*$$  is

If $$A = \{ 2,3,4,5,7 \} , B = \{ 7,8,9 \}$$, then find $$n ( A \cup B ).$$

If $$A=\left\{x|x\in N\quad and\quad x < 6\dfrac{1}{4}\right\}$$ and $$B=\left\{x|x\in N\quad and\quad x^2\leq 5\right\}$$. Then the number of subsets of set $$A\times (A\cap B)$$ which contains exactly $$3$$ elements is?

Mark the correct alternative of the following.
The number of subsets of a set containing n elements is?

In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak atleast one of the two languages is 

Choose the correct answer from the given four options
Which of the following collection doesn't form a set

Find the correct option for the given question.
Which of the following collections is a set?

Which of the following statements is true (if N, W and I are sets of Natural, Whole and Integer numbers respectively ?