Applied Mathematics 4 Question Paper - Dec 18 - Computer Engineering (Semester 4)

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Applied Mathematics 4 - Dec 18

Computer Engineering (Semester 4)

Total marks: 80
Total time: 3 Hours INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.

1(a) Find all the basic solutions to the following problem: Maximize z = $x_1 + x_2 + 3x_3$ subject to

$ x_{1}+2 x_{2}+3 x_{3}=9 $

$ 3 x_{1}+2 x_{2}+2 x_{3}=15 $

$ x_{1}, x_{2}, x_{3} \geq 0 $

(05 marks) 00

1(b) Evaluate $\oint z d z$ from z = 0 to z =1 + i along the curve z = $t^2$ +it.

(5 marks) 00

1(c) A sample of 100 students is taken from a large population. The mean height of the students in this sample is 160 cm. Can it be reasonably regarded that in the population, the mean height is 165 cm, and the standard deviation is 10 cm?

(5 marks) 00

1(d) The sum of the Eigen values of a 3 × 3 matrix is 6 and the product of the Eigen values is also 6. If one of the Eigen value is one, find the other two Eigen values.

(5 marks) 00

2(a) Evaluate $ \oint \frac{\sin ^{6} z}{(z-\pi / 6)^{n}} d z $ where c is the circle |z| = 1 for n = 1, n =3

(6 marks) 00

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