CSIR NET Maths previous year question papers

Single choice · Continuity and Differentiation

1. A

   If f is continuous on the set S, then f is continuous on the set $\mathbb{R}$ \ S

2. B

   If g is continuous, then f is continuous on the set S

3. C

   If g is identically 0 and f is continuous on the set $\mathbb{R}$ \ S, then f is identically 0

4. D

   If g is identically 0 and f is continuous on the set S, then f is identically 0

Single choice · Groups

1. A

   If |G| $= p^{6}$, then G has a subgroup of index $p^{2}$.

2. B

   If |G| $= p^{6}$, then G has at least five normal subgroups.

3. C

   Center of G can be infinite.

4. D

   There exists G with |G| $= p^{6}$ such that G has exactly six normal subgroups.

Single choice · Groups

1. A

   G is a union of proper subgroups.

2. B

   G is a union of proper subgroups if |G| has at least two distinct prime divisors.

3. C

   If G is abelian, then G is a union of proper subgroups.

4. D

   G is a union of proper subgroups if and only if G is not cyclic.