CSIR NET Maths previous year question papers

Single choice · Partial Differential Equations

1. A

   $lim_{t\to\infty}$ u(5, t) = 1

2. B

   $lim_{t\to\infty}$ u(5, t) = 2

3. C

   $lim_{t\to\infty}$ u(5, t) = 1/2

4. D

   $lim_{t\to\infty}$ u(5, t) = 0

Multi-select · full marks only for the exact set · The Real Line

1. A

   The subsequences {$x_{2n}$₊$_{1}$}, {$x_{2n}$} and {$x_{3n}$} are convergent and have the same limit.

2. B

   The subsequences {$x_{2n}$₊$_{1}$}, {$x_{2n}$} and {$x_{3n}$} are convergent.

3. C

   The subsequences {$x_{kn}$}$_{n}$ are convergent for every k ≥ 2.

4. D

   lim |$x_{n}$₊$_{1} - x_{n}$| = 0.

Multi-select · full marks only for the exact set · The Real Line

1. A

   If a = 0, then the sequence {$x_{n}$} converges to 1/2.

2. B

   If a = 0, then the sequence {$x_{n}$} converges to −1/2.

3. C

   The sequence {$x_{n}$} converges for every a ∈ (−1/2, 3/2), and it converges to 1/2.

4. D

   If a = 0, then the sequence {$x_{n}$} does not converge.

Multi-select · full marks only for the exact set · The Real Line

1. A

   There exists an integer n ≥ 1 such that $n^{2} \sin(1/n) \ge x$.

2. B

   There exists an integer n ≥ 1 such that n cos(1/n) ≥ x.

3. C

   There exists an integer n ≥ 1 such that n $e^{-n}$ ≥ x.

4. D

   There exists an integer n ≥ 2 such that n (log $n)^{-1}$ ≥ x.