JEE Main 2022 · 29 Jul · Shift 2 · Mathematics Q30

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MathematicsInteger+4 / -1Question 30 of 90

Let $S=\left\{(x,y)\in\mathbb N\times\mathbb N:9(x-3)^2+16(y-4)^2\le144\right\}$ and $T=\left\{(x,y)\in\mathbb R\times\mathbb R:(x-7)^2+(y-4)^2\le36\right\}$ . Then $n(S\cap T)$ is equal to _______.

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Answer and worked solution

Official answer: 27

S is the lattice points with $x,y\ge1$ inside the ellipse $\frac{(x-3)^2}{16}+\frac{(y-4)^2}9\le1$ ; T is the disc of radius 6 about (7, 4).

Row by row (points of S also in T): y = 1: x = 3; y = 2: 2 to 5; y = 3: 2 to 6; y = 4: 1 to 7; y = 5: 2 to 6; y = 6: 2 to 5; y = 7: x = 3. That is 1 + 4 + 5 + 7 + 5 + 4 + 1 = 27.

Answer: 27

Topics:Ellipse Equation of a circle

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JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 30