CSIR NET Maths previous year question papers

Single choice · Rings and Fields

1. A

   I = (x, y)

2. B

   I = (x + y)

3. C

   $I = (x^{2} + y^{2})$

4. D

   I = (xy − 1)

Multi-select · full marks only for the exact set · Rings and Fields

1. A

   S is a cyclic group.

2. B

   S has $\varphi(2025)$ elements, where $\varphi$ denotes the Euler $\varphi-$function.

3. C

   S has $\varphi(2025)$ generators, where $\varphi$ denotes the Euler $\varphi-$function.

4. D

   S has 81 elements.

Multi-select · full marks only for the exact set · Analytic Functions

1. A

   f(z̄) is an entire function.

2. B

   conj(f(z)) is an entire function.

3. C

   conj(f(z̄)) is an entire function.

4. D

   conj(f(z̄)) + f(z̄) is an entire function.

Multi-select · full marks only for the exact set · Rings and Fields

1. A

   For all prime numbers p, f(X) mod p is irreducible in $(\mathbb{Z}/p\mathbb{Z})[X]$.

2. B

   There exists a prime number p such that g(X) mod p is irreducible in $(\mathbb{Z}/p\mathbb{Z})[X]$.

3. C

   g(X) is irreducible in $\mathbb{Q}[X]$.

4. D

   f(X) is irreducible in $\mathbb{Q}[X]$.