Discussion Forum



1)

Two sets A and B are as  under A= { (a,b)} $\in$ RxR: $\mid a-5\mid<1$ and $\mid b-5\mid<1$;  B={(a,b) $\in$ RxR:

 $4(a-6)^{2}+9(b-5)^{2}\leq 36$ } , Then



A) $B\subset A$

B) $A\subset B$

C) $A\cap B =\phi $ (an empty set)

D) neither $A\subset B $ nor $B\subset A $

Answer:

Option B

Explanation:

We have

$\mid a-5\mid<1$ and $\mid b-5\mid<1$

$\therefore$    -1 < a - 5< 1 and -1 < b-5 < 1   

$\Rightarrow$      4<a<6 and 4<b<6

  Now ,  $4(a-6)^{2}+9(b-5)^{2}\leq 36$

$\Rightarrow$   $\frac{(a-6)^{2}}{9}+\frac{(b-5)^{2}}{4}\leq1$

   Taking axes as a-axis and b-axis

1082019157_axis.JPG

The set A represents square PQRS inside set B representing ellipse and hence $A\subset B$