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Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?
Study the following statements.i) The displacement method is more useful when degree of kinematic indeterminacy is greater than the degree of static indeterminacy.ii) The displacement method is more useful when degree of kinematic indeterminacy is less than the degree of static indeterminacy.iii) The force method is more useful when degree of static indeterminacy is greater than the degree of kinematic indeterminacy.iv) The force method is more useful when degree of static indeterminacy is less than the degree of kinematic indeterminacy.The correct answer is
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
The rear window of an automobile is made of thick glass i.e. AB = 5 mm and thermal conductivity is 0.8 W/m degree. To defrost this window, a thin transparent film type heating element has been fixed to its inner surface. For the conditions given below, determine the electric power that must be provided per unit area of window if a temperature 5 degree Celsius is maintained at its outer surface. Interior air temperature and the corresponding surface coefficient are 20 degree Celsius and 12 W/m2 degree. Surrounding air temperature and the corresponding surface coefficient are – 15 degree Celsius and 70 W/m2 degree. Electric heater provides uniform heat flux
During heat treatment, cylindrical pieces of 25 mm diameter, 30 mm height and at 30 degree Celsius are placed in a furnace at 750 degree Celsius with convective coefficient 80 W/m2 degree. Calculate the time required to heat the pieces to 600 degree Celsius. Assume the following property values Density = 7850 kg /m3 Specific heat = 480 J/kg K Conductivity = 40 W/m degree
A water line is buried underground in dry soil that has an assumed initial temperature of 4.5 degree Celsius. The pipe may have no flow through it for long period of time, yet it will not be drained in order that no freezing occurs, the pipe must be kept at a temperature not lower than 0 degree Celsius. The pipe is to be designed for a 30 hour period at the beginning of which the soil surface temperature suddenly drops to – 17 degree Celsius. Workout the minimum earth covering needed above the water pipe so as to prevent the possibility of freezing during 36 hour cold spell. The soil in which the pipe is buried has the following properties Density = 640 kg/m3 Specific heat = 1843J/kg degree Thermal conductivity = 0.345 W/m degree
A class III mathematics teacher gave the following questions to her students:  \(\begin{equation} \frac{ \begin{array}[b]{r} 256 \\ + 173 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 28 \\ + 32 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 129 \\ + 76 \end{array} }{ } \end{equation}\) Later she asks the students to solve a worksheet that has similar questions. Which of the following statements is appropriate for the given situation?
Singular solution of a differential equation is one that cannot be obtained from the general solution gotten by the usual method of solving the differential equation.
Consider the following second-order differential equation: y" - 4y' + 3y = 2t - 3t2
The particular solution of the differential equation is
Consider the differential equation $$\left( {{{\text{t}}^2} - 81} \right)\frac{{{\text{dy}}}}{{{\text{dt}}}} + 5{\text{ty}} = \sin \left( {\text{t}} \right)$$      with y(1) = 2π. Thereexists a unique solution for this differential equation when t belongs to the interval