Set Theory Test...

If $$X=\left\{ { 4 }^{ n }-3n-1;n\in R \right\} $$ and $$Y=\left\{ 9\left( n-1 \right) ;n\in N \right\} $$, then $$X\cap Y=$$

The number of binary operations on the set $$\{1, 2, 3\}$$ is _________.

Choose the correct answers from the alternatives given.
Directions for questions $$71$$ to $$75$$ : Study the pie chart carefully to answer the questions that follow.
Percentage distribution of students in different courses.
What is the value of half of the difference between the number of students in MBA and MBBS?
The Total number of student = $$6500$$

If $$a.N = \left\{ ax\thinspace :\thinspace x\in N \right\}$$ then $$3N\cap 7N=$$

The relation $$S=\{(3, 3), (4, 4)\}$$ on the set $$A=\{3, 4, 5\}$$ is __________.

A set of $$n$$ numbers has the sum $$s$$. Each number of the set is increased by $$20$$, then multiplied by $$5$$, and then decreased by $$20$$. The sum of the numbers in the new set thus obtained is:

If $$A= \{x:x$$ is a multiple of $$2\}, \,\,B= \{x:x$$ is a multiple of $$5\}$$ and $$C = \{x:x$$ is a multiple of 10$$\}$$, then $$ A\cap (B\cap C)$$ is equal to 

If $$M = \left\{ {x:x \geqslant 7\,\,{\text{and}}\,x \in N} \right\}$$ for universal set of natural numbers, then $$M'$$ is

In the equation $${ \left( x-m \right)  }^{ 2 }-{ \left( x-n \right)  }^{ 2 }={ \left( m-n \right)  }^{ 2 }$$, $$m$$ is a fixed positive number, and $$n$$ is a fixed negative number. The set of values $$x$$ satisfying the equation is:

Given : A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}
Find : $$(A \, \times \, B) \, \cap \, (B \, \times \, C)$$.