CSIR NET Maths previous year question papers

Single choice · Linear Integral Equations

1. A

   y(0) + y(1) = 1/2

2. B

   y(−1) + y(1) = 1

3. C

   y′(0) + y′(1) = 3/2

4. D

   y′(−1) + y′(1) = 3

Single choice · Ordinary Differential Equations

1. A

   $d^{2}u/$dx$^{2} + \lambda{}u = 0, u(0) = 0 = u(1)$

2. B

   $d^{2}u/$dx$^{2} - \lambda{}u = 0, u(0) = 0 = u(1)$

3. C

   du/dx $+ \lambda{}u = 0, u(0) = 0 = u(1)$

4. D

   du/dx $- \lambda{}u = 0, u(0) = 0 = u(1)$

Single choice · Partial Differential Equations

1. A

   u(1, 0) = 0

2. B

   $u(x_{1}, y_{1}) = u(x_{2}, y_{2})$ whenever $x_{1}^{2} + y_{1}^{2} = x_{2}^{2} + y_{2}^{2}$

3. C

   $u(1, y) = \sqrt{2}$ for all $y \in \mathbb{R}$

4. D

   $u(x_{1}, y_{1}) = u(x_{2}, y_{2})$ whenever $x_{1} + y_{1} = x_{2} + y_{2}$

Single choice · Partial Differential Equations

1. A

   $u(\pi/8, 1) + u(-\pi/8, 1) = 2$

2. B

   $u(\pi/8, 1) = u(-\pi/8, 1)$

3. C

   $u(\pi/8, 1) + 2u(-\pi/8, 1) = 2$

4. D

   $u(\pi/8, 1) = -u(-\pi/8, 1)$

Single choice · Linear Integral Equations

1. A

   0

2. B

   1

3. C

   2

4. D

   2e⁻$^{1}$