The prices of three commodities A, B and C are `x, `y and `z per unit respectively. P

purchases 4 units of C and sells 3 units of A and 5 units of B. Q purchases 3 units of B

and sells 2 units of A and 1 unit of C. R purchases 1 unit of A and sells 4 units of B and

6 units of C. In the process P, Q and R earn `6,000 , `5,000 and `13,000 respectively.

By using matrix inversion method, nd the prices per unit of A, B and C.

5. The sum of three numbers is 20. If we multiply the first by 2 and add the second

number and subtract the third we get 23. If we multiply the first by 3 and add second

and third to it, we get 46. By using matrix inversion method find the numbers.

6. Weekly expenditure in an office for three weeks is given as follows. Assuming that

the salary in all the three weeks of different categories of staff did not vary, calculate

the salary for each type of staff, using matrix inversion method

How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so

that the letters a) cannot be repeated b) can be repeated c) cannot be repeated

but must begin with E d) cannot be repeated but end with CAB.

7. From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder

of the first ticket wins a car, the second a motor cycle, the third a bicycle and the

fourth a skateboard. In how many different ways can these prizes be awarded?

8. In how many different ways, 2 Mathematics, 2 Economics and 2 History books can

be selected from 9 Mathematics, 8 Economics and 7 History books?

9. Let there be 3 red, 2 yellow and 2 green signal flags. How many different signals

are possible if we wish to make signals by arranging all of them vertically on a staff?

3) Gauss's Law. Cylindrical Gaussian Surface (Ch. 6) Axis AA An infinite charged wire with charge per unit length 1 = 4 x 10- C/m lies E along the central axis of a cylindrical surface of radius r = 0.5 m and length L = 10 m. What is the flux through the surface due to the electric field of the PAA charged wire? (Figure is from OpenStax)1. A 0.30-m radius infinitely long cylinder has a uniform charge density of p = 5.0 mc/m a. Draw a gaussian surface on the inside of this cylinder. b. Derive an expression for the charge inside of your gaussian surface. c. How much charge is enclosed by a cylindrical gaussian surface with a radius of 0.10 m? With a radius of 0.40 m? Equate the length of the cylinder to 1.00 m for this calculation. d. Derive an equation for the electric field inside and outside the cylinder of charge. e. What is the electric field at 0.10 m and 0.40 m from the center?I 5'. B A system has four components with the following reliability,r block diagram: as: The reliability of the four components is as follows: R. = 0.35 R; = 0.95 R; = 0.30 n. = 0.90. {it} Find the exact reliability of the above sysmm using the concepts of clerics and parallel models {b} Find all the minimum paths and minimum cuts for the above system