CSIR NET Maths previous year question papers

Single choice · Cauchy Theory

1. A

   The function zf(1/z) → 0 as |z| $\to \infty$.

2. B

   The function f is constant.

3. C

   c = 0.

4. D

   c > 0.

Single choice · Cauchy Theory

1. A

   |f(z)| $\to \infty$ as |z| $\to \infty$.

2. B

   f(z)/z → 0 as |z| $\to \infty$.

3. C

   zf(z) → 0 as |z| $\to \infty$.

4. D

   f(z) → 0 as |z| $\to \infty$.

Multi-select · full marks only for the exact set · Cauchy Theory

1. A

   f has a pole at z = 0.

2. B

   There is an entire function g such that f = g on $\mathbb{C}$ \ {0}.

3. C

   f is a polynomial of degree at most 2.

4. D

   f has an essential singularity at z = 0.

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

1. A

   The power series converges for every $z \in \mathbb{C}$

2. B

   The power series converges for every $z \in \mathbb{R}$

3. C

   The power series converges for every z ∈ {$2^{n} : n \in \mathbb{N}$}

4. D

   The power series converges for every z ∈ {$1/5^{n} : n \in \mathbb{N}$}