Number Theory, Complex Variables and 2-D 2015 – BSc Computer Science Part 1

Paper code: 13503
1503
B.sc. (Computer Science) (Part 1)
Examination, 2015
Paper No. 1.3
NUMBER THEORY, COMPLEX VARIABLES AND 2-D

Time: Three Hours] [Maximum Marks: 50

Note: Attempt all the five questions. All questions carry equal marks. Symbol used    are as usual.

1. Solve any two of the following parts:

1. It the co-ordinates of one extremity of a focal chord of a parabola  are , find the co-ordinates of the other extremity.
2. Find the equation of ellipse whose foci are at the point and  and whose let us rectum is 6.
3. Find the centre, foci, let us return and equation of directix of the hyperbola:

2. Attempt any two of the following parts:

1. State and prove Euler formula.
2. Find all the values of .
3. Prove that:

3. Attempt any two of the following parts:

1. and 
2. Represent on complex plane the complex number  and  together with  and .
3. Determine the conjugate and the reciprocal of .

4. Attempt any two of the following parts:

1. State and prove Wilson’s theorem.
2. Discuss about division algorithm and greatest common divisor with an example.
3. If and m, n be positive integers, then:

, where (m,n) = g.c.d(m,n).

5. Attempt any two of the following parts:

1. State and prove fundamental theorem of arithmetic.
2. The liner conquence  is solved if  where  if   then it has d in congruent solutions.
3. Discuss the Fermat’s factorization method with an example.

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