Sat. Dec 2nd, 2023

Aug 20, 2019

# IGNOU BCA (1)  BCS – 012 Solved Assignment 2019 – 2020

Course Code : BCS-012

Course Title : Basic Mathematics

Assignment Number : BCA(1)012/Assignment/2019-20

Maximum Marks : 100

Weightage : 25%

Last Date of Submission :

15th October, 2019 (For July, 2019 Session

15th April, 2020 (For January,2020 Session)

Notes: Answer all the questions in the assignment which carry 80 marks in total. All the questions are of equal marks. Rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation. Make suitable assumption if necessary.

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The solution includes the following questions….

Q.1. Show that :

where    is a complex root of  unity.

Q.2. If  show that   Also, find

Q.3. Show that 133 divides  for every natural number  .

Q.4. If term of an A.P. is  and term of the A.P. is  find its term.

Q.5. If  are cube roots of unity, show that

.

Q.6. If are roots of find the value(s) of  if  .

Q.7. If  find .

Q.8. If  show that  .

Q.9. Find the sum of all the integers between 100 and 1000 that are divisible by 9.

Q.10. Write De Moivre’s theorem and use it to find .

Q.11. Solve the equation Given that one of the roots exceeds the other by 2.

Q.12. Solve the inequality  and graph its solution.

Q.13. Determine the values of   for which is increasing and for which it is decreasing.

Q.14. Find the points of local maxima and local minima of

Q.15. Evaluate :

Q.16. Using integration, find length of the curve  from to .

Q.17. Find the sum upto    terms of the series

Q.18. Show that the lins    and    intersect.

Q.19. A tailor needs at least 40 large buttons and 60 small buttons. In the market, buttions are available in two boxes or cards. A box contains 6 large and 2 small buttons and a card contains 2 large and 4 small buttons. If the cost of a box is and cost of a card is , find how many boxes and cards should be purchased so as to minimize the expenditure.

Q.20. A manufacturer makes two types of furniture, chairs and tables. Both the products are processed on three machines and . Machine requires 3 hours for a chair and 3 hours for a table, machine requires 5 hours for a chair and 2 hours for a table and machine requires 2 hours for a chair and 6 hours for a table. The maximum time available on machines and is 36 hours, 50 hours and 60 hours respectively. Profits are per chair and \$ 30 per table. Formulate the above as a linear programming problem to maximize the profit and solve it.

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