Let X = \{ (x, y) {Z} × {Z} : x²/8 + y²/20 [JEE Adv 2023 P1]

Correct Answer is : 7322073/22022073

Correct Answer is : 7322073/22022073

Test Index

Probability

Section: Mathematics

Question : 10 of 52

Marks: +1, -0

Let

X = \{ (x, y) \in \mathbb{Z} \times \mathbb{Z} : \frac{x^2}{8} + \frac{y^2}{20} < 1.

y^2 < 5 x \}

P, Q

R

X

P, Q

R

Solution:

The given region are as

The points inside region are

\{(2,1),(2,-1),(2,2),(2,-2),(2,3),(2,-3),(2,0),(1,1),(1,-1),(1,2),(1,-2)

(1,0)\}

Total number of ways to select three points

= {}^{12}C_3 = 220

Required number of triangle

= 4 \times {}^{7}C_1 + 9 \times {}^{5}C_1 = 73

Points are taken such a way that distance between two points are multiple of 2 .

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