A : x 2 + y 2 = 25... ( i ) \mathrm{A}: \mathrm{x}^2+\mathrm{y}^2=25...(i) A : x 2 + y 2 = 25... ( i )
B : x 2 144 + y 2 16 = 1... ( i i ) \frac{x^2}{144}+\frac{y^2}{16}=1...(ii) 144 x 2 + 16 y 2 = 1... ( ii )
C: x 2 + y 2 ≤ 4... ( i i i ) x^2+y^2 \leq 4...(iii) x 2 + y 2 ≤ 4... ( iii )
Solve (1) & (2)
$\begin{aligned}
By ( 1 ) ⇒ y = ± 25 − x 2 \operatorname{By}(1) \Rightarrow y= \pm \sqrt{25-x^2} By ( 1 ) ⇒ y = ± 25 − x 2
= ± 25 − 81 8 = ± 119 2 2 = \pm \sqrt{25-\frac{81}{8}}= \pm \frac{\sqrt{119}}{2 \sqrt{2}} = ± 25 − 8 81 = ± 2 2 119
∴ D = A ∩ B = \therefore \mathrm{D}=\mathrm{A} \cap \mathrm{~B}= ∴ D = A ∩ B =
{ ( 9 2 2 , 119 2 2 ) , ( 9 2 2 , − 119 2 2 ) , ( − 9 2 2 , 119 2 2 ) , ( − 9 2 2 , − 119 2 2 ) } \left\{\left(\frac{9}{2 \sqrt{2}}, \frac{\sqrt{119}}{2 \sqrt{2}}\right),\left(\frac{9}{2 \sqrt{2}},-\frac{\sqrt{119}}{2 \sqrt{2}}\right),\left(\frac{-9}{2 \sqrt{2}}, \frac{\sqrt{119}}{2 \sqrt{2}}\right),\left(\frac{-9}{2 \sqrt{2}}, \frac{-\sqrt{119}}{2 \sqrt{2}}\right)\right\} { ( 2 2 9 , 2 2 119 ) , ( 2 2 9 , − 2 2 119 ) , ( 2 2 − 9 , 2 2 119 ) , ( 2 2 − 9 , 2 2 − 119 ) }
No. of elements in set D = 4 D=4 D = 4
$\begin{aligned}
No. of elements in set C = 13 \mathrm{C}=13 C = 13
Total no. of one-one function from
Set D D D sec C ⇒ 13 × 12 × 11 × 10 = 17160 \sec C \Rightarrow 13 \times 12 \times 11 \times 10=17160 sec C ⇒ 13 × 12 × 11 × 10 = 17160
