Thursday, August 6, 2020

NUMBER THEORY, COMPLEX VARIABLES AND 2D - 2016 | B.SC CS 1ST YEAR | MJPRU | EXAM PAPER | My CS Tutorial

My CS Tutorial August 06, 2020

Number theory,complex variable | My CS Tutorial

Paper Code: 13503
1503
B.Sc. (Computer Science) (Part 1)
Examination, 2016
Paper No. 1.3
NUMBER THEORY, COMPLEX VARIABLES AND 2D

Time: Three Hours][Maximum Marks: 50

Note: Attempt all the five questions. All questions carry equal marks. Symbol used are as usual. Attempt any two parts of each question.

1. (a) Find the latus rectum, vertex, focus and axis of the parabola:

$y^2-2y+8x-23=0$

(b) Find the equation to the conic section whose focus is (1, -1), eccentricity is and the directrix is the line $x-y=3$ .

(c) Find the points common to the hyperbola $4x^2-4y^2=15$ and the straight line $x-2y-3=0$ . Find also the lengths of the straight line intercepted by the hyperbola.

2. (a) Find four fourth roots of unity.

(b) State and prove De-Moivers theorem.

(c) If $\bar{a}=2\hat{i}-3\hat{j}+5\hat{k}$ and $\bar{a}=3\hat{i}-\hat{j}-2\hat{k}$ . Evaluate $(\bar{a}+\bar{b}).(\bar{a}-\bar{b})$ .

3. (a) Prove that the representative of the complex numbers $1+4i,2+7i,3+10i$ are collinear.

(b) If $\bar{r}=x\hat{i}-y\hat{j}-z\hat{k}$ , then show that:

$\left (\bar{r}\times \hat{i} \right )^{2}=y^{2}+z^{2}$
$\left (\bar{r}\times \hat{i} \right ).\left (\bar{r}\times \hat{i} \right )+xy=0$

4. (a) What do you know about the Euclidean algorithm?

(b) State and prove Gauss theorem.

5. (a) Discuss special divisibility test.

(b) State and prove Farmat’s theorem.

https://1drv.ms/w/c/19c065de02d3d2fd/EVEWfU9n-PxLknw24Qk1-WkB5xewwSt0WPP1AONx1Kfhsg?e=OiC4jU

https://1drv.ms/w/c/19c065de02d3d2fd/EVEWfU9n-PxLknw24Qk1-WkB5xewwSt0WPP1AONx1Kfhsg?e=XikAKm

https://1drv.ms/w/c/19c065de02d3d2fd/EfftMYL5VfFJqTLYzvnM2F0BSV8Dt1zGSkdqXu22hYUfnQ?e=UQ0D2h

https://docs.google.com/spreadsheets/d/1Y72FryugAbBdS0HKtuN5H9sk4txEysZwERHxfDIJb9k/edit?usp=sharing

https://1drv.ms/w/c/19c065de02d3d2fd/ET5Bp3mrwA9BoEA3AqVWdPEBGt2-xKp7DX8y4zAqAvvqSA?e=uKIOJt

https://1drv.ms/w/c/19c065de02d3d2fd/EeoIP0Ds4bJCtzShPw-QcCYBQ0M2rV3JcJwHVQnqpH0XDg?e=OnH5tf

https://1drv.ms/w/c/19c065de02d3d2fd/EZff6GrMSEVAgazuB9AHI8MBpCAVi02VjQA2eNTvhzlESA?e=dzthZy

_______________________________________

https://1drv.ms/w/c/19c065de02d3d2fd/ERSIqXFjbbtFtrPaPsDD6foBWjIcdtoXuYX36Z776jlfrQ?e=WWBNbj

Please share this post and blog link with your friends.For more programs use this blog.

https://1drv.ms/w/c/19c065de02d3d2fd/EfQHyAux4ZdAqlbJs7wyb-4BUizgePYBb8zZCgLmrEwG5w?e=EBujQa

https://1drv.ms/w/c/19c065de02d3d2fd/EVSqt6IJDS9AklNWOHixWbIBs_N_fG931rZ4SwYYRpOUpA?e=Tm8so5

https://1drv.ms/w/c/19c065de02d3d2fd/ETNLfQdQsO1NhlI3EAOfWwgB6U8bA5BkwJ775lE_C1oJ8g?e=Hd4ZSl

If you have any problem, please comment in comment box, subscribe this blog for notifications of new post on your email and follow this blog.If you have any method of this tutorial or program or want to give any suggestion send email on hc78326@gmail.com

https://1drv.ms/w/c/19c065de02d3d2fd/ETXbMShLt-pPv-XFt26jOUgBaiEH52iqP3rxcgzf7_Zpeg?e=krmFig

https://1drv.ms/w/c/19c065de02d3d2fd/EfMlIAYUIsFMv8xSKune9tIBQzO64SovZ6BYdl_VCRnWHg?e=mxFWc9

https://1drv.ms/w/c/19c065de02d3d2fd/EX8WvtAIQMVMqUPru3a2EzcBPCa5TGP4yrbJpUE1TjkEjQ?e=w59bQ9

https://1drv.ms/w/c/19c065de02d3d2fd/EQNG3UvnsUtCi9ks13YWMCIBQ9JRcpS8W3rYbBCV49w88A?e=FjcDER

Created by-- HARSH CHAUHAN

https://1drv.ms/w/c/19c065de02d3d2fd/EfftMYL5VfFJqTLYzvnM2F0BSV8Dt1zGSkdqXu22hYUfnQ?e=5EbVSN

https://1drv.ms/w/c/19c065de02d3d2fd/Eb4OcHnO7LpElo7oyJMrQjsBGRZT3aXlXXlg9BYOTCp79w?e=zgvabd

https://1drv.ms/w/c/19c065de02d3d2fd/Eebuv8XKtrlCltU07iiXK3wBu0ntHzlNWZkT9NfslPMIKQ?e=odmDbP

https://1drv.ms/w/c/19c065de02d3d2fd/EeqIxIABouRHjIlmTv5fzUgB9LAoIofE7EaMSSIEBtG2Vw?e=aCN63W

https://1drv.ms/w/c/19c065de02d3d2fd/EfPf6djVOB9Nnr4pTtsrXRUBl7GEA4WvVwYXeyDi4em4sw?e=MgIWJ4

https://1drv.ms/w/c/19c065de02d3d2fd/EfPf6djVOB9Nnr4pTtsrXRUBl7GEA4WvVwYXeyDi4em4sw?e=4TuP0v

https://1drv.ms/w/c/19c065de02d3d2fd/EXxOkX26NRtAt1bBct7-fkEBJR-KCFQvstd_-begBjXRig?e=lLYz5x

https://1drv.ms/w/c/19c065de02d3d2fd/Ecn3OeXKztxNhY2GUPqUgncBSGWZcwZ8fcdwGefDWxczbA?e=32u3fg

https://1drv.ms/w/c/19c065de02d3d2fd/ERr8_M0akl9PntfdjKMCElABzU9pIFN121PemCHPpoDJkw?e=vjSFFs

https://1drv.ms/w/c/19c065de02d3d2fd/EYlfdnH8kKJJjpiE9fpnpxEBEEXjgd-30AwREJ-1AkU6DQ?e=o2m5La

https://my-store-ee2803.creator-spring.com/?fbclid=IwZXh0bgNhZW0CMTEAAR0O03xAy2TSnivcnm1Mjen2QGzM5z6CqynJi-FZYSCQ4fkWVsG-r05Ju1E_aem_QWi7N68FR3X-em3mJQK4xw

https://1drv.ms/w/c/19c065de02d3d2fd/Eb8M3OkzSLFCmH1DxPCazC0BA17DlSN9EVY9g6FQFA24Qw?e=61VsKF

https://1drv.ms/w/c/19c065de02d3d2fd/ERXz5BKCPrtHo-AKI8_ne80B69BFgwe_SLbuipSqP3XZhg?e=Qfr8fB

About My CS Tutorial
SoraTemplates is a blogger resources site is a provider of high quality blogger template with premium looking layout and robust design. The main mission of SoraTemplates is to provide the best quality blogger templates.