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Find the equation of the family of all erhogonal trajectories of the family ofcircles which pass through origin and hav centres on the y-axis.


State Newton s law of cooling. If the temperature of the air is 30^{0}C and thetemperature of the body drops from 80°C to 60^{0}C in 10 minutes. What will beits temperature after 20 minutes.


Solve (x^{2}D^{2}+4xD+2)y=(logx/x)^{2},x>0 , where D=d/dx


Solve d^{2}y/dx^{2}-6dy/dx+13y=20e^{3x}cos(2x+5)


Solve the initial value problem y^{2}y -y^{3}tanx=sinxcos^{2}x,y(0)=1


the tunction f(z)= (z)^{2}/z,z≠0 0,z=0 suntistes -Rieman equations at z=0 Does f (0) exist?`


Evaluate ∫0^{π/2α}αsinαxdx,α>0 by using Leibniz formula.`


find the length of the curve y=ln(e^{x}+1/e^{x}-1) from x=1 to x=2 `


a short reinforced concrete column of section 200mm ×220mm is to be reinforce with 4 number steel bars and is required to carry n axial load of 850kn. the stress in the concrete must not exceed 7n/mm^2 and the stress in the steel must not exceed 150n/mm^2. determine the diameter required for the bars and the subsequent stresses occuring in the concrete and the steel under the specified load.[ young's modulus; concrete =14kn/mm^2, steel =210kn/mm^2]

A 3 cm diameter tube is used to measure the binary diffusion coefficient of water vapor in air at

20°C at an elevation of 1600 m where the atmospheric pressure is 83.5 kPa. The tube is partially

filled with water, and the distance from the water surface to the open end of the tube is 40 cm.

Dry air is blown over the open end of the tube so that water vapor rising to the top is removed

immediately and the concentration of vapor at the top of the tube is zero. In 15 days of

continuous operation at constant pressure and temperature, the amount of water that has

evaporated is measured to be 1.23 g. Determine the diffusion coefficient of water vapor in air at

20°C and 83.5 kPa. Given, the pressure of water at 20°C is 2.34 kPa.


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