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BACHELOR IN COMPUTER APPLICATIONS (BCA) BCA/ASSIGN/2/JULY/01 ASSIGNMENTS JULY 2001 (2nd SEMESTER) CS-612 CS-60 CS-62 SCHOOL OF COMPUTER AND INFORMATION SCIENCES INDIRA GANDHI NATIONAL OPEN UNIVERSITY MAIDAN GARHI, NEW DELHI – 110 068 CONTENTS Course Code Assignment No. CS-612 BCA(2)-612/TMA/01 CS-612 BCA(2)-612/Project/01 CS-60 BCA(2)-60/TMA/01 CS-60 BCA(2)-60/Project/01 CS-62 BCA(2)-62/TMA/01 CS-62 BCA(2)-62/Project/01 Assignment Type Last date of Submission Page No. TMA 30th September, 2001 4 Project 31st October, 2001 5 TMA 30th September, 2001 6 Project 31st October, 2001 7 TMA 30th September, 2001 9 Project 31st October, 2001 10 (3) Course Code Course Title Assignment No. Maximum Marks Last Date of Submission : : : : : CS-612 PC Software and Application Skills BCA(2)-612/TMA/01 10 30th September, 2001 This is a Tutor Marked Assignment. There are three questions in this Assignment. Answer all the questions. Each question carries equal weightage. Question 1: Compare and contrast Internet Explorer with MSN Explorer (newer version) . Question 2: Compare and contrast MS-Excel with LOTUS-123 in detail. Question 3: Prove that the sum of the squares of the first n integers is 1/24 (2n) (2n+1) (2n+2). (4) Course Code Course Title Assignment No. Maximum Marks Last Date of Submission : : : : : This is a Project Assignment. weightage. CS-612 PC Software and Application Skills BCA(2)-612/Project/01 15 31st October, 2001 Answer all the questions. Each question carries equal Question 1: Give detailed information on the topic “ Supply Chain Management” by browsing the Internet. List the browsed URLs and the information associated with them. Question 2: Create a Student’s worksheet (for 25 students) for a computer institute with the student’s details such as Student name, Roll No., Date and Year of enrollment, Courses enrolled for, Fees paid, Balance in fees (if any) etc. Provide a suitable title and date on the top of the worksheet. Arrange the information in two pages. Write all the steps followed. Question 3: a) What is the remainder left after dividing 1! + 2! + 3! + …………..+ 100! By 6? b) Prove that there is an infinite number of primes of the type 6k+5. (5) Course Code Course Title Assignment Number Maximum Marks Last date of Submission : : : : : CS-60 Foundation course in Mathematics in Computing BCA(2)-60/TMA/01 10 30th September, 2001 This is a Tutor Marked Assignment. There are four questions in the assignment. Answer all questions. Each question carries equal weightage. You may use illustrations and diagrams to enhance explanations. Question 1(a). For any two sets A and B, show that A B = (A\B) (A B) (B\A) (b) Apply De Moivre’s formula to prove that Cos2 = Cos2 – Sin2 (c) Obtain all the fifth roots of i in C, the space of complex numbers. Question 2(a). If , , are the roots of the equation x 3 7 x 2 x 5 0, find the equation whose roots are + , + and + (b) Solve the following equations, using any of the standard methods described in the book: x 4 4 x 3 7 x 2 22 x 24 0 (i) 2 x 3 3x 2 4 x 1 0 (ii) Question 3(a). Check the consistency of the following set of linear equations. If consistent, find out the solution: x– y+ z=0 –3x – y – 4z = 0 7x – 3y – 9z = 0 4x – 2y – 5z = 0 (b) Show that 1 2 ... n n 1 2 Question 4(a). Find the equations of tangents and normals at the vertices and ends of the minor axis of the ellipse. x2 y2 1 a2 b2 (b) Find the angle between the planes x + 2y + 2z = 5 2x + 2y + 3z = 0 (c) Find the equations of the spheres that pass through 2x + y + 3z = 3 and touch the plane 3x + 4y = 15. (6) x2 + y2 + z2 = 5, Course Code Course Title Assignment No. Last Date of Submission Maximum Marks : : : : : CS-60 Foundation Course in Mathematics in Computing BCA(2)-60(Project)/01 31st October, 2001 15 This is a Project Assignment. You may use illustrations and diagrams to enhance explanations. Answer all the following questions. Each question carries equal weightage. Question 1(a). Show that the functions f: X X such that f ( x) 2x 3 2x 3 3 is 1 – 1 and on to where X R and R is the set of real numbers. 2 Find the inverse of the function f. (b) Find the limit, if it exists 2 x 3 54 (i) lim x 3 x3 3 x 125 (ii) lim x 5 4( x 5) 2 (iii) For the function f(x) 2 x 7, 3x 8, for x 0 for x < 0, lim f ( x ) x 0 (c) (d) (e) Find the derivative from the first principle of f(x) given by f ( x) x 2 Sin x 1 x2 Differentiate log(3x + 7) w.r.t. Cos 1 2 1 x If y = eax.x2, using Leibinitz Theorem or otherwise, prove that y n e ax a n x 2 2na n 1 x n(n 1)a n 2 , Where y(n) denotes the nth derivative of y w.r.t. x. Question 2(a). Write down Maclaurin’s series for the following function: 1 f ( x) 1 x 3 (7) (b) State the various Mean Value theorems included in your CS-60 course material. Further verify Lagrange’s mean value theorem for the function: f (x) Sin x on the interval [0, 2]. (c) Trace the following curves, incorporating all the steps including finding out of the tangents, asymptotes, singular points, points of inflection, etc., if required: (i) y(1 + x2) = x (ii) r = a Sin 2, a > 0 Question 3(a). Evaluate the following: x 3 4x (i) x 2 1 2 dx dx (ii) 5 7Cosx (iii) x 1 2 1 x 1 dx 4 (b) Prove the following inequalities: tan 1 x x (i) e x e x 2x (ii) (8) for all positive x. for all x > 0. Course Code Course Title Assignment Number Maximum Marks Last date of Submission : : : : : CS-62 Data Structure through C & Pascal BCA (2) -62/ TMA/ 01 10 30th September, 2001 This is Tutor Marked Assignment. There are two questions in this assignment. Answer both questions. Each question carries equal weightage. You may use illustrations and diagrams to enhance explanations. Question 1: Write a program in ‘C’ language for the concatenation of two strings. Question 2: Write a program in ‘C’ language for printing first 10 prime numbers. Use Recursion. (9) Course Code Course Title Assignment Number Maximum Marks Last date of Submission : : : : : CS-62 Data Structure through ‘C’ & ‘Pascal’ BCA(2) -62/Project/01 15 31st October, 2001 This is a Project Assignment. Answer the following question. You may use illustrations and diagrams to enhance explanation. Question 1: Write a program for the creation of a doubly linked list using pointers in ‘C’ language. Also, there should be provision for insertion and deletion of elements from the list. ( 10 )