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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 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
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
Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?
Consider the following remarks pertaining to the irrotational flow: 1. The Laplace equation of stream function \(\frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {y^2}}} = 0\) must be satisfied for the flow to be potential. 2. The Laplace equation for the velocity potential \(\frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {y^2}}} = 0\) must be satisfied to fulfil the orate . of mass conservation i.e continuity equation.. Which of the above statements is/are correct?
Laplace transform of the function f(t) is given by $${\text{F}}\left( {\text{s}} \right) = {\text{L}}\left\{ {{\text{f}}\left( {\text{t}} \right)} \right\} = \int_0^\infty {{\text{f}}\left( {\text{t}} \right){{\text{e}}^{ - {\text{st}}}}{\text{dt}}{\text{.}}} $$       Laplace transform of the function shown below is given by
Transform Theory mcq question image
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?
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, $${\text{y}} = \frac{{{{\text{C}}_{\text{p}}}}}{{{{\text{C}}_{\text{v}}}}}$$  )
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