cmi-entrance 2019 Q6

cmi-entrance · India · pgmath 4 marks Groups Ring and Field Structure

Let $K$ be the smallest subfield of $\mathbb{C}$ containing all the roots of unity. Choose the correct statement(s) from below:
(A) $\mathbb{C}$ is algebraic over $K$;
(B) $K$ has countably many elements;
(C) Irreducible polynomials in $K[X]$ do not have multiple roots;
(D) The characteristic of $K$ is zero.

Let $K$ be the smallest subfield of $\mathbb{C}$ containing all the roots of unity. Choose the correct statement(s) from below:\\
(A) $\mathbb{C}$ is algebraic over $K$;\\
(B) $K$ has countably many elements;\\
(C) Irreducible polynomials in $K[X]$ do not have multiple roots;\\
(D) The characteristic of $K$ is zero.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17* Q18* Q19* Q20*