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

Multi-select · full marks only for the exact set · Ordinary Differential Equations

1. A

   $\varphi_{1}(x + 2\pi)$ is also a solution of ODE

2. B

   $\varphi_{2}(x + 4\pi)$ is also a solution of ODE

3. C

   There are NO constants a, b such that $\varphi_{2}(x + 4\pi) = a\varphi_{1}(x) + b\varphi_{2}(x)$

4. D

   There exist $a, b \in \mathbb{R}$ such that $\varphi_{1}(x + 2\pi) = a\varphi_{1}(x) + b\varphi_{2}(x)$

Multi-select · full marks only for the exact set · Ordinary Differential Equations

1. A

   There exists a q such that cos(x) and e^x cos(x) are solutions of ODE

2. B

   There exists a q such that sin(x) and cos(x) are solutions of ODE

3. C

   There exists a q such that e^x sin(x) and e^x cos(2x) are solutions of ODE

4. D

   There exists a q such that xe^x and x(x − 1)e^x are solutions of ODE

Multi-select · full marks only for the exact set · Classical Mechanics

1. A

   $\partial/\partial{}t [f, g] = [\partial{}f/\partial{}t, g] + [f, \partial{}g/\partial{}t]$

2. B

   If f is a constant of motion, and f is independent of t, then [H, f] is a constant of motion

3. C

   [[H, f], g] + [[g, H], f] + [[f, g], H] = 0

4. D

   If f and g are constants of motion, then [f, g] is a constant of motion

Multi-select · full marks only for the exact set · Linear Integral Equations

1. A

   R(0,1,1/3) = 3/2

2. B

   R(1/2,1/2,1/3) = 2/3

3. C

   y(1) = 3e+1

4. D

   y(1) = e+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⁻$^{1}$

Multi-select · full marks only for the exact set · Linear Integral Equations

1. A

   R(x, t) = 1

2. B

   R(x, t) = e^(t−x)

3. C

   u(ln 8) = 10

4. D

   u(ln 7) = 9