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If u (x, y, z, t) = f(x + iβy - vt) + g(x - iβy - vt), where f and g are arbitrary and twice differentiable functions, is a solution of the wave equation $$\frac{{\partial {u^2}}}{{\partial {x^2}}} = \frac{{{\partial ^2}u}}{{\partial {y^2}}} = \frac{1}{{{c^2}}}\frac{{{\partial ^2}u}}{{\partial {t^2}}}$$     then β is
The highest pressure gas of a mixture has partial pressure p, the partial pressure of other gases decreases by factor of 2n-1, the partial pressure of second gases decreases by a factor of 2, partial pressure of third gas increases by 4, and so on, if the total pressure of gas mixture is 31p/16, how many gases are present in the mixture?
The equation relating E, P, V and T which is true for all substanes under all conditions is given by $${\left( {\frac{{\partial {\text{E}}}}{{\partial {\text{V}}}}} \right)_{\text{T}}} = {\text{T}} \cdot {\left( {\frac{{\partial {\text{P}}}}{{\partial {\text{T}}}}} \right)_{\text{H}}} - {\text{P}}{\text{.}}$$      This equation is called the
On a P-V diagram of an ideal gas, suppose a reversible adiabatic line intersects a reversible isothermal line at point A. Then at a point A, the slope of the reversible adiabatic line $${\left( {\frac{{\partial {\text{P}}}}{{\partial {\text{V}}}}} \right)_{\text{S}}}$$  and the slope of the reversible isothermal line $${\left( {\frac{{\partial {\text{P}}}}{{\partial {\text{V}}}}} \right)_{\text{T}}}$$  are related as (where, $${\text{y}} = \frac{{{{\text{C}}_{\text{p}}}}}{{{{\text{C}}_{\text{v}}}}}$$  )
Maxwell equation $${\left( {\frac{{\partial P}}{{\partial T}}} \right)_V} = {\left( {\frac{{\partial S}}{{\partial V}}} \right)_T}$$     is produced from which of the following equation
The solution of initial value problem; $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = 2\frac{{\partial {\text{u}}}}{{\partial {\text{t}}}} + {\text{u,}}$$   where u(x, 0) = 6e-3x is
Let $${\text{f}}\left( {{\text{x, y}}} \right) = \frac{{{\text{a}}{{\text{x}}^2} + {\text{b}}{{\text{y}}^2}}}{{{\text{xy}}}},$$     where a and b are constants. If $$\frac{{\partial {\text{f}}}}{{\partial {\text{x}}}} = \frac{{\partial {\text{f}}}}{{\partial {\text{y}}}}$$   at x = 1 and y = 2, then the relation between a and b is
The average weight of 20 contestants in a fashion show increased by 5.75 kg when one of the contestants left the show but when a new contestant joined the show then the average weight decreased by 2.75 kg. What is the difference between the weight of the new contestant who joined the show and the contestant who left the show?
Which of the following commands will display the current IP addressing and the layer 1 and 2 status of an interface?
1. show version
2. show protocols
3. show interfaces
4. show controllers
5. show ip interface
The two types of of auxiliary verbs are primary auxiliary verbs and modal auxiliary verbs. What is the third type?