CSIR NET Maths previous year question papers

Single choice · Sequences and Series of Functions

1. A

   $(f_{n})_{n}\ge_{1}$ converges uniformly on [0, 1] to a continuous function f.

2. B

   $(f_{n})_{n}\ge_{1}$ converges pointwise on [0, 1] to a discontinuous function f.

3. C

   $(f_{n})_{n}\ge_{1}$ converges pointwise on [0, 1] to a continuous function f.

4. D

   $(f_{n})_{n}\ge_{1}$ does not converge pointwise on [0, 1].

Single choice · Continuity and Differentiation

1. A

   f∘g is uniformly continuous, but g∘f is not uniformly continuous.

2. B

   g∘f is uniformly continuous, but f∘g is not uniformly continuous.

3. C

   Neither f∘g nor g∘f is uniformly continuous.

4. D

   Both f∘g and g∘f are uniformly continuous.

Single choice · Sequences and Series of Functions

1. A

   $\sum(n\ge1) f_{n}$ and $\sum(n\ge1) g_{n}$ are uniformly convergent on the interval [−1, 1].

2. B

   $\sum(n\ge1) f_{n}$ is uniformly convergent on the interval [−1, 1], but $\sum(n\ge1) g_{n}$ is not.

3. C

   $\sum(n\ge1) g_{n}$ is uniformly convergent on the interval [−1, 1], but $\sum(n\ge1) f_{n}$ is not.

4. D

   Neither $\sum(n\ge1) f_{n}$ nor $\sum(n\ge1) g_{n}$ is uniformly convergent on the interval [−1, 1].

Single choice · Sequences and Series of Functions

1. A

   The series is neither absolutely convergent nor uniformly convergent.

2. B

   The series is both absolutely convergent and uniformly convergent.

3. C

   The series is absolutely convergent but not uniformly convergent.

4. D

   The series is uniformly convergent but not absolutely convergent.

Single choice · Continuity and Differentiation

1. A

   f(x) = sin(1/x)

2. B

   f(x) = $e^{-1/x^{2}}$

3. C

   f(x) = eˣ cos(1/x)

4. D

   $f(x) = \cos x \cdot \cos(\pi/x)$