Fluent Essays

urgentneed it in 4 hourssee file attached,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, question_paper_set_b__1_.pdf Unformatted Attachment Preview IBRACOLLEGE OF TECHNOLOGY FINAL ASSESSMENT ‫اﻻﺧﺗﺑﺎر اﻟﻧﮭــﺎﺋـــﻲ‬ Academic Year: 2019 - 2020:‫اﻟﺳﻧﺔ اﻻﻛﺎدﯾﻣﯾﺔ‬ Semester‫اﻟﻔﺻل‬: !Sem I – Fall‫ اﻻول‬Sem II – Spring ‫ ! اﻟﺛﺎﻧﻲ‬Summer‫اﻟﺻﯾﻔﻲ‬ Instructions to the Students: • Students must write their name, college ID and page number on all pages and mention the question number for each answer. • Students need to use Microsoft word processing (black colour) while answering their assignments and upload it in the Moodle. • During the completion of assignment, the students are NOT ALLOWED TO CONTACT THE COURSE LECTURER or any other staff members for any form of clarification with regard to the questions of the final assignment. • Students must submit the final exam answer through college Moodle link within the 48 hours scheduled in examination time table. • Answers will be checked for detecting plagiarism using Turnitin, and if any plagiarism is detected zero marks will be awarded for all students who are found to copy from each other’s. • Students should STRICTLY OBSERVE THE COPYRIGHT PRINCIPLES AND ACADEMIC HONESTY in dealing with this examination system. Cheating, sharing, copying or any other kind of malpractice are strictly prohibited. Violation in this regard will be dealt according to the “Article 80, Bylaws of Colleges of Technology” and zero marks will be awarded to all tstudents invloved. • Identical answers will be considered as plagiarism. Department: IT Course Name: MATHEMATICS FOR IT Specialization: NETWORKING/SOFTWARE DEVELOPMENT ‫ﺗﻌﻠﯿﻤﺎت ﻟﻠﻄﻠﺒﺔ‬ ‫ﯾﺟب ﻋﻠﻰ اﻟطﻠﺑﺔ ﻛﺗﺎﺑﺔ أﺳﻣﺎﺋﮭم ورﻗم اﻟطﺎﻟب ﺑﺎﻟﻛﻠﯾﺔ ورﻗم‬ .‫اﻟﺻﻔﺣﺔ ﻋﻠﻰ ﺟﻣﯾﻊ اﻟﺻﻔﺣﺎت وذﻛر رﻗم اﻟﺳؤال ﻋﻧد ﻛل إﺟﺎﺑﺔ‬ ‫ )اﻟﻠون اﻷﺳود( ﻋﻧد‬Microsoft word ‫ﻋﻠﻲ اﻟطﻠﺑﺔ اﺳﺗﻌﻣﺎل‬ .Moodle‫اﻹﺟﺎﺑﺔ ﻋﻠﻰ ورﻓﻌﮭﺎ ﻓﻲ اﻟﻣودل‬ ‫ﺧﻼل ﻓﺗرة إﻧﺟﺎز اﻻﺧﺗﺑﺎر ﯾﻣﻧﻊ ﻋﻠﻰ اﻟطﻠﺑﺔ اﻟﺗواﺻل ﻣﻊ‬ ‫ﻣدرس اﻟﻣﺎدة اوﻣﻊ أي ﻋﺿو ﻣن أﻋﺿﺎء اﻟﮭﯾﺋﺔ اﻟﺗدرﯾﺳﯾﺔ‬ .‫ﻟطﻠب أي ﺗوﺿﯾﺢ ﻓﯾﻣﺎ ﯾﺗﻌﻠق ﺑﺎﺳﺋﻠﺔ اﻻﻣﺗﺣﺎن اﻟﻧﮭﺎﺋﻲ‬ ‫ﯾﺟب ﻋﻠﻰ اﻟطﻠﺑﺔ إرﺳﺎل اﻹﺟﺎﺑﺔ اﻟﻧﮭﺎﺋﯾﺔ ﻋن طرﯾق راﺑط‬ .‫ ﺳﺎﻋﺔ ﻛﻣﺎ ھو ﻓﻲ ﺟدول اﻻﻣﺗﺣﺎﻧﺎت‬48 ‫ﻣﻧﺻﺔ اﻟﻣودل ﺧﻼل‬ ‫ﺳﯾﺗم اﻟﺗﺣﻘق ﻣن اﻻﺟﺎﺑﺎت اﻟﻣﺳﻠﻣﺔ ﻣن ﻗﺑل اﻟطﻠﺑﺔ ﻟﻠﻛﺷف ﻋن‬ Turnitin ‫أي ﺷﻛل ﻣن أﺷﻛﺎل اﻹﻧﺗﺣﺎل اﻷﻛﺎدﯾﻣﻲ ﺑﺎﺳﺗﻌﻣﺎل‬ ‫وﻓﻲ ﺣﺎﻟﺔ ﺛﺑوت أي اﺣﺗﯾﺎل أﻛﺎدﯾﻣﻲ ﺗﻣﻧﺢ ﻋﻼﻣﺔ ﺻﻔر ﻟﻠطﺎﻟب‬ .‫اﻟﻣﻌﻧﻲ‬ ‫ﯾﺟب ﻋﻠﻰ اﻟطﻠﺑﺔ اﻻﻟﺗزام ﺑﺎﻟﺻدق واﻷﻣﺎﻧﺔ ﻋﻧد اﻟﺗﻌﺎﻣل ﻣﻊ‬ ‫ﻧظﺎم اﻻﻣﺗﺣﺎﻧﺎت وﯾﻣﻧﻊ ﻣﻧﻌﺎ ﺑﺎﺗﺎ اﻟﻐش واﻟﻧﺳﺦ وﺗﺑﺎدل اﻹﺟﺎﺑﺎت‬ ‫ ﯾﺗم اﻟﺗﻌﺎﻣل ﻣﻊ‬.‫واي ﺷﻛل ﻣن أﺷﻛﺎل اﻟﺗﺻرﻓﺎت اﻟﺧﺎطﺋﺔ‬ ‫ ﻣن اﻟﻠواﺋﺢ اﻟﻣﻧظﻣﺔ ﻟﻠﻛﻠﯾﺎت اﻟﺗﻘﻧﯾﺔ‬80 ‫اﻟﻣﺧﺎﻟﻔﺎت طﺑﻘﺎ ﻟﻠﻣﺎدة‬ .‫وﺗﺳﻧد ﻟﻠطﺎﻟب ﻋﻼﻣﺔ ﺻﻔر ﻓﻲ ﺣﺎﻟﺔ اﻟﻣﺧﺎﻟﻔﺔ وﻋدم اﻻﻟﺗزام‬ .‫ﺗﻌﺗﺑر اﻹﺟﺎﺑﺎت اﻟﻣﺗطﺎﺑﻘﺔ )اﻟﻣﺗﺷﺎﺑﮭﺔ( اﺣﺗﯾﺎﻻ أﻛﺎدﯾﻣﯾﺎ‬ Section: Date of Exam: Course Code: 21/05/2020 Level: Starting Time: MATH201 DIPLOMA 2ND YEAR 9.00 A.M Last Date/Time for submission through Moodle: [48 Hours from exam starting time] On or before: 23 /05/2020; 9.00 A.M Question No. Marks allocated 1 10 2 10 3 10 4 10 5 10 Total 50 ________________ 1st Marker Signature Marks Obtained TOTAL MARKS ___ 50 __________________ 2nd Marker Signature ___________________ Examination Committee • • • • • • • IBRACOLLEGE OF TECHNOLOGY ANSWER ALL THE QUESTIONS. Q1. A. Find the computer number format of 302.45 which occupies 32 bits in computer memory and is known as 32-bit IEEE 754 single precision binary floating point number. [5 marks] B. Let 𝑃 𝑥 = 𝑥 ! + 3𝑥 ! − 𝑥 + 2.45 i) Evaluate P at 𝑥 = 2.48 (use 4 digit rounding arithmetic). [1 mark] ii) Find the nested form Q (𝑥) of P (𝑥). [2 marks] iii) Evaluate Q at 𝑥 =2.48 (use 4 digit rounding arithmetic). [1 mark] iv) Compute absolute error of P (2.48) and Q (2.48). [1 mark] Q2. A. i) By seeing the equation 𝑓 𝑥 = 𝑥 ! + 4𝑥 ! − 10 = 0, Amina says that it has a root between 1 and 2. Check whether her guess is correct or not. [1mark] ii) Setting up Bisection method in a math software Amina found approximations of a solution of the equation 𝑓 𝑥 = 𝑥 ! + 4𝑥 ! − 10 = 0 in the interval [1,2]. Write down the first four approximations, she did for the solution between 1 and 2. [3 marks] iii) In a computational problem of mathematical analysis, the number 5 is approximated with the relative error at most 10!! .Find the largest interval in which the approximation must lie. [1 mark] B. i) Salim was using iterative methods to solve equations in MATLAB. For the equation 𝑓 𝑥 = 𝑥 ! − 𝑥 − 1 = 0, he gave an initial estimate as 1.5 and by using Newton’s method he found the first three approximations of solution. What will be his third approximation according to the initial estimate and using 3 – digit rounding arithmetic? [3 marks] ii)While studying about symmetry to develop algorithms, Amir noticed that every square matrix added to its transpose will give a symmetric matrix and difference of the square matrix with its 1 0 5 transpose gives a skew symmetric matrix. Verify this with the matrix 𝐴 = 2 4 1 . 3 1 2 [2 marks] Q3. A. Ahmed borrowed a book from a library and it is 3 weeks overdue. The amount of fine in OMR for respective weeks of overdue is listed in the table. Using Newton’s divided difference formula, find the amount of his fine. 4 5 6 8 𝑥 (in weeks) 2 10 96 196 350 868 𝑦 (fine in OMR) [5marks] IBRACOLLEGE OF TECHNOLOGY B. The observed values of a function 𝑓 𝑥 at the four positions of the independent variable 𝑥 are as follows: 0 2 3 6 𝑥 707 819 866 966 𝑓(𝑥) Using Lagrange’s interpolation formula, find the best estimate for the value of the function at the position 4 of the independent variable. [5 marks] Q4. A. i) Given matrices A= 3 2 2 3 and B= , verify that det (AB)= det(A). det(B). 4 5 1 4 [3 marks] ii) Find the third Taylor’s polynomial generated by 𝑓(𝑥) = 𝑐𝑜𝑠 6𝑥 about 𝑥 = 0. [2 marks] 1 −2 0 B. i) Find the inverse of the matrix A = −2 −4 5 , using elementary row operations. 1 1 −2 [5 marks] Q5. A. The sum of three integers 𝑥, 𝑦, 𝑧 is 9. If the third integer is subtracted from the sum of the second integer and two times the first integer the result is zero. If we add two times the first integer with five times the second integer and seven times the third integer we get 52. Find the value of the integers 𝑥, 𝑦, 𝑧 by solving the system of equation using Gauss-Jordan reduction Method. [5 marks] B. Solve the following system of equations using Gaussian elimination. 𝑥 + 𝑦 = 9 − 𝑧; 𝑥 + 3𝑧 = 8 + 2𝑦; 2𝑥 + 𝑦 = 3 + 𝑧. [5 marks] ... Purchase answer to see full attachment