CSIR NET Maths previous year question papers

Single choice · Continuity and Differentiation

1. A

   For every bounded subset $A \subseteq \mathbb{R}, f$⁻$^{1}(A)$ is a bounded subset of $\mathbb{R}$.

2. B

   For every Cauchy sequence $(x_{n})_{n}\ge_{1}$ in $\mathbb{R}, (f(x_{n}))_{n}\ge_{1}$ is a Cauchy sequence in $\mathbb{R}$.

3. C

   There exists $x \in \mathbb{R}$ such that f(x) = x.

4. D

   There exists $x \in \mathbb{R}$ such that f(x) = 0.

Single choice · Inner Product Spaces and Forms

1. A

   {$(-1/\sqrt{2}, 0, 0, -1/\sqrt{2}), (-1/\sqrt{6}, \sqrt{2}/\sqrt{3}, 0, 1/\sqrt{6}), (0, 0, 1, 0)$}

2. B

   {$(1/\sqrt{2}, 0, 0, 1/\sqrt{2}), (-1/\sqrt{6}, \sqrt{2}/\sqrt{3}, 0, 1/\sqrt{6}), (0, 0, 1, 0)$}

3. C

   {$(1/\sqrt{2}, 0, 0, 1/\sqrt{2}), (-1/\sqrt{6}, \sqrt{2}/\sqrt{3}, 0, -1/\sqrt{6}), (0, 0, 1, 0)$}

4. D

   {$(1/\sqrt{2}, 0, 0, 1/\sqrt{2}), (1/\sqrt{6}, -\sqrt{2}/\sqrt{3}, 0, -1/\sqrt{6}), (0, 0, 1, 0)$}

Single choice · Inner Product Spaces and Forms

1. A

   A is invertible

2. B

   There exist non-zero vectors v, w such that ⟨v, w⟩ = 0

3. C

   ⟨u, v⟩ ≠ ⟨u, w⟩ for all non-zero vectors u, v, w with v ≠ w

4. D

   Every eigenvalue of $A^{2}$ is positive

Single choice · The Real Line

1. A

   The series is divergent.

2. B

   The series is convergent.

3. C

   The series is conditionally convergent.

4. D

   The series is absolutely convergent.