EASTER SCIENCE

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: It the co-ordinates of one extremity of a focal chord of a parabola y^{2} 4ax are (at^{2}, 2at), find the co-ordinates of the other extremity. Find the equation of ellipse whose foci are at the point s(2,0) and {s}'(-2,0) and whose let us rectum is 6. Find the centre, foci, let us return and equation of directix of the hyperbola: x^{2} - y^{2} + 2x + 4y 4 2. Attempt any two of the following parts: State and prove Euler formula. Find all the values of (1+i)^{\frac{1}{3}}. Prove that: (1+ \cos \theta +i\sin \theta)^{n}+(1+ \cos \theta -i\sin \theta)^{n}2^{n+1}.\left (\cos \frac {\theta}{2} \right )^{n}.\cos \frac {n\theta}{2} 3. Attempt any two of the following parts: |z_{1}|-|z_{2}|\leq |z_{1}- z_{2}| and |z_{1}|+|z_{2}|\geq |z_{1}+ z_{2}| Represent on complex plane the complex number w_{1}3+4i and w_{2}6-3i together with w_{1}+w_{2} and w_{1}-w_{2}. Determine the conjugate and the reciprocal of \sqrt{-3}-3. 4. Attempt any two of the following parts: State and prove Wilson’s theorem. Discuss about division algorithm and greatest common divisor with an example. If a > b and m, n be positive integers, then: (a^{m}-1)-(a^{n}-1)(a^{(m,n)}-1), where (m,n) g.c.d(m,n). 5. Attempt any two of the following parts: State and prove fundamental theorem of arithmetic. The liner conquence ax\beta(\mod n) is solved if d\mid \beta where d(a,n) if d\mid \beta then it has d in congruent solutions. Discuss the Fermat’s factorization method with an example. ............End...........

Easterscience: Gallery

EasterScience Latest News about Technology