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Find the critical point of the following problems
a. F(x)=8-3x+x^2
b. F(x)=x^4-18x^2+9
c. F(x)=x^3-5x^2-8x+3
d. F(x)= x^2/(x^2+1)
e F(x)=x^2/(x^2-1)
f F(x)=(x^2-1)^3

Derive mach number = V/C


Derive the isentropic relation of state.


7. Design 4 to 1 multiplexer using the design procedure :

8. Design 2 to 4 decoder

9. Design 4 bit comparator:

10. Design 1 bit ALU:

11. What is the difference between a combinational circuit and sequential circuit? Give example of each.

12. Describe the general setup for an arduino board when used to design a digital system. [8marks]

13. Use K-Map to Minimize the following boolean function- [10marks] F(A, B, C, D) = Σm(0, 1, 2, 5, 7, 8, 9, 10, 13, 15)


CEO of a well-known television show wants to build a new rectangular shaped acting stage. The width, thickness and length of the stage are 3 m, 0.2 m and 5 m, respectively. Both ends of the stage must be fixed. The stage should carry a musical instrument, and air conditioner of a total mass of 1500 kg and 800 kg at 1 m, and 2 m from the left end support. Such equipment acts as a concentrated loads on the stage that has a distributed load of 500 kg/m. The Young’s modulus of the material is 200 GPa. 1.1. Use the engineering sketch to illustrate the structure of the stage and calculate the transverse vibration frequency of the stage. (18) 1.2. Determine the amount of rection forces on the stage supports.
1.2 For the purpose of turbine design, there is a need for aerodynamics test of the nose corn design in a wind tunnel. Suppose that the fluid enters the test section of a circular tunnel with a uniform speed of 50 m/s and it flows over a nose corn placed at the centreline of the tunnel, as shown in Fig. 1, the nose corn rotates at a constant speed w=10 rad/s about the centreline of the tunnel. Assume that the flow is laminar and fully developed before exits from the tailpipe, with the information given above, provide a set of governing equations and boundary conditions in its simplest form that can be used to determine the unique flow through the tunnel, in terms of fluid velocity and pressure distributions.

A CEO of a well-known television show wants to build a new rectangular shaped acting stage. The width, thickness and length of the stage are 3 m, 0.2 m and 5 m, respectively. Both ends of the stage must be fixed. The stage should carry a musical instrument, and air conditioner of a total mass of 1500 kg and 800 kg at 1 m, and 2 m from the left end support. Such equipment acts as a concentrated loads on the stage that has a distributed load of 500 kg/m. The Young’s modulus of the material is 200 GPa. 1.1. Use the engineering sketch to illustrate the structure of the stage and calculate the transverse vibration frequency of the stage. (18) 1.2. Determine the amount of rection forces on the stage supports. 


A CEO of a well-known television show wants to build a new rectangular shaped acting stage. The width, thickness and length of the stage are 3 m, 0.2 m and 5 m, respectively. Both ends of the stage must be fixed. The stage should carry a musical instrument, and air conditioner of a total mass of 1500 kg and 800 kg at 1 m, and 2 m from the left end support. Such equipment acts as a concentrated loads on the stage that has a distributed load of 500 kg/m. The Young’s modulus of the material is 200 GPa.  


1.1. Use the engineering sketch to illustrate the structure of the stage and calculate the transverse vibration frequency of the stage.  (18)


1.2. Determine the amount of rection forces on the stage supports.  


. The force R is the resultant of the forces P1, P2, and P3 acting on the rectangular
plate. Find P1 and P2 if
QUESTION 4
(a) Derive the emf equation for the double wound transformer. [5 marks]
(b) Describe the principle of operation of the D.C machines operating on motor mode.
[5 marks]
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