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TIFR ECE 2023 | Question: 5

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Let $\mathrm{B}$ denote the unit ball in $\mathbb{R}^{2}$, and $\mathrm{Q}$ a square of side length $2$. Let $\mathrm{K}$ be the set of all vectors $z$ such that for some $x \in \mathrm{B}$ and some $y \in \mathrm{Q}, z=x+y$. The area of $\mathrm{K}$ is

  1. $4+\pi$
  2. $6+\pi$
  3. $8+\pi$
  4. $10+\pi$
  5. $12+\pi$

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