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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
To constitute a matter of res judicata which of the following conditions must concur?
1. The matter directly and substantially in issue in the subsequent suit or issue must be the same matter which was directly and substantially in issue either actually (section 11, explanation III) or constructively (section 11, explanation IV) in the former suit
2. The former suit must have been a suit between the same parties under whom they or any of them claim. Explanation VI of Section 11 must be read with this condition
3. The parties as aforesaid must have litigated under the same title in the former suit
4. The court which decided the former suit must have been a court competent to try the subsequent suit of the suit in which such issue has been subsequently raised. Explanation II of section 11 is to be read with condition
5. The matter directly and substantially in issue in the subsequent suit must have been heard and finally decided by the court in the first suit. Explanation V of section 11 is to be read with this condition
The condition that a second order partial differential equation should satisfy to be parabolic is b2-ac=0.
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
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?
Heat Equation is an example of elliptical partial differential equation.
Wave equation is a linear elliptical partial differential equation.
The figure shows the plot of y as a function of x
Differential Equations mcq question image
The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is
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, $${\text{y}} = \frac{{{{\text{C}}_{\text{p}}}}}{{{{\text{C}}_{\text{v}}}}}$$  )