Question

Let $Z$ be the set of all integers,
$ A =\left\{( x , y ) \in Z \times Z :( x -2)^{2}+ y ^{2} \leq 4\right\} $
$ B =\left\{( x , y ) \in Z \times Z : x ^{2}+ y ^{2} \leq 4\right\}$ and
$ C =\left\{( x , y ) \in Z \times Z :( x -2)^{2}+( y -2)^{2} \leq 4\right\}$
If the total number of relation from $A \cap B$ to $A \cap C$ is $2^{ p }$, then the value of $p$ is :

• A. 16
• B. 25
• C. 49
• D. 9

Answer 1

Answer: (B)

$(x-2)^{2}+y^{2} \leq 4 $
$x^{2}+y^{2} \leq 4$
No. of points common in $C _{1} \& C _{2}$ is 5 .
$(0,0),(1,0),(2,0),(1,1),(1,-1)$
Similarly in $C _{2} \& C _{3}$ is 5 .
No. of relations $=2^{5 \times 5}=2^{25}$.