# Given a wave with the dispersion relation ω = ck + m for k > 0 and m > 0, which of the following is true?

1. Group velocity is greater than the phase velocity
2. Phase velocity is greater than the group velocity
3. Group velocity and the phase velocity are equal
4. There is no definite relation between the group velocity and phase velocity

# Which of the following Maxwells equations implies the absence of magnetic monopoles?

1. $\bigtriangledown&space;.&space;\vec{E}&space;=&space;\frac{\pi&space;}{\epsilon_{0}&space;}$
2. $\bigtriangledown&space;.&space;\vec{B}&space;=&space;0$
3. $\bigtriangledown&space;\times&space;\vec{B}&space;=&space;-&space;\frac{\partial&space;\vec{B}}{\partial&space;t}$
4. $\bigtriangledown&space;\times&space;\vec{B}&space;=&space;\frac{1}{c^{2}}\frac{\partial&space;\vec{B}}{\partial&space;t}&space;+&space;\mu_{0}\hat{j}$

1. One
2. Two
3. Three
4. Four

# Consider a transformation from one set of generalized coordinates and momentum (q, p) to another set (Q, P) denoted by

Q = pqs;     P = qr

where s and r are constants. The transformation is canonical if

1. s = 0 and r = 1
2. s = 2 and r = -1
3. r = -1 and s = 0
4. s = 2 and r = 1
5. None of these

# Constraints that can be expressed as equations of coordinates and time

i-e by an expression of the form of $f(\vec{r_{1}},\vec{r_{2}},\vec{r_{3}},&space;...,\vec{r_{n}},t)&space;=&space;0$ is said to be

1. Holonomic
2. Non-Holonomic
3. Scleronomous
4. Hieronymus

1. $\mathbf{E&space;=&space;pc&space;+&space;m_{0}c^{2}}$
2. $\mathbf{E&space;=&space;pc&space;-&space;m_{0}c^{2}}$
3. $\mathbf{E^{2}&space;=&space;p^{2}c^{2}&space;+&space;m_{0}^{2}c^{4}}$
4. $\mathbf{E&space;=&space;p^{2}c^{2}&space;-&space;m_{0}^{2}c^{4}}$