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An air filled rectangular waveguide has TE10 mode cut off frequency of 8Ghz. The signal frequency is 15 GHz and the ratio a/b is 2. If the waveguide is now filled with perplexed of relative permittivity 2.5 , find the guide wavelength of the signal.


Given the following parameters Vin = 14 V, R1 = 24 kΩ, R2 = 12 kΩ, R3 = 6 kΩ,

R4 = 3 kΩ and a feedback resistor of 10 kΩ. Calculate the output voltage V0. (9)


A combinational circuit has four inputs (A,B,C,D), which represent a binarycoded-decimal digit. The

circuit has two groups of four outputs - S,T,U,V(MSB digit) and W,X,Y,Z.(LSB digit)Each group

represents a BCD digit. The output digits represent a decimal number which is five times the input

number. Illustrate the minimum expression for all the outputs?


  1. if the voltage across an element is 8V and the current i entering the positive terminal is as shown, find the power delivered to the element at t=7 ms and the total charge and total energy delivered to the element between 1 and 10 ms.
  2. a copper wire has a resistance of 2 ohms it was drawn under pressure so that its diameter is reduced to one half its original diameter. the new resistance of wire is...
Complete the data given below:

X —> 15500 15510 15520 15530 15540

y= √x —> 124.4990 124.5392 124.5793 124.6194 124.6595

Hence obtain the value of VI550i and V15531 using Newton's forward and backward interpolation formula respectively, where i=unit digit and i=2
Complete the divided difference table for the data given below:

X —> 1 5 9 13 17
y = f(x) —> 13 16 18 21 26

Hence construct the interpolating polynomial that uses all this data. Also find f[15x0.(i+2)]. where i=2
Find the polynomial of degree three relevant to the following data using Lagrange's interpolation formula. Hence find f[4x0.(i+2)], where i= 2

X —> 1 3 5 6
y=f(x) —> -12 -14 -20 -20

For the following voltage function, find the numerical differentiation of first order using the finite divided-difference formula at a point, 1, - 4.5 s with step forward, backward and center finite divide-difference formula at a point t1=4.5 s with step size, h=0.i s, where i=72


v(t) = 20sint-t^3/18


Evaluate the values using the conventional differentiation formula aiso and hence comment which numerical method produce better result based on the percentage of true error.


For the following function, find the numerical differentiation of first order using forward, backward and center finite divided-difference formula at a point, 1, =3.2s with step size, h =0.i s, where i= 72,


i(r) = 40sint -10t^2


Evaluate the values using the conventional differentiation formula also and hence comment which numerical method produce better result based on the percentage of true error.


Evaluate f(N)=3√N, N=72, to five decimal places by Newton-Raphson iterative method.


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