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TIFR-2019-Maths-A: 16

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The number of ring homomorphisms from $\mathbb{Z}\left [ x,y \right ]$ to $\mathbb{F}_{2}\left [ x \right ]/\left ( x^{3}+x^{2}+x+1 \right )$ equals 

  1. $2^{6}$
  2. $2^{18}$
  3. $1$
  4. $2^{9}$
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