JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q3

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MathematicsSingle correct+4 / -1Question 3 of 90

For $n\in\mathbf N$ , let $S_n=\left\{z\in\mathbf C:|z-3+2i|=\dfrac n4\right\}$ and $T_n=\left\{z\in\mathbf C:|z-2+3i|=\dfrac1n\right\}$ . Then the number of elements in the set $\{n\in\mathbf N:S_n\cap T_n=\phi\}$ is :

Answer and worked solution

Official answer: Dropped: full marks to everyone

This question was dropped in NTA's final key.

Why. The centres are $\sqrt2$ apart. The circles meet only when $\left|\frac n4-\frac1n\right|\le\sqrt2\le\frac n4+\frac1n$ , which holds for $n=5,6$ only; for every other natural $n$ they are disjoint, so the set is infinite and no option fits.

Topics:Geometry in the complex plane Equation of a circle

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JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 3