**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 : **

**15****th**** October, 2019 (For July, 2019 Session**

**15****th**** 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.