**BCS-012 Basic Mathematics**

Title Name | BCS-012 Solved Assignment 2019-20 |

University | IGNOU |

Service Type | Solved Assignment (Soft copy/PDF) |

Course | BACHELOR OF COMPUTER APPLICATIONS(BCA) |

Language | ENGLISH |

Semester | BCA(Revised Syllabus)/ASSIGN/SEMESTER-I |

Session | 2019-20 |

Short Name | BCS-012 |

Assignment Code | BCA (1)/012/Assignment/2019-20 |

Product | Assignment of BCA 2020 (IGNOU) |

Price | Rs. 30 |

| 15th October, 2019 (For July, 2019 Session)15th April, 2020 (For January, 2020 Session) |

Q1. Show that

Where 𝜔 is a complex cube root of unity.

Q2. Show that A2-4A + 5 I2 = 0. Also, find

Q3. Show that 133 divides 11n+2 + 122n+1 for every natural number n.

Q4. If p th term of an A.P is q and q th term of the A.P. is p, find its r th term.

Q5. If are cube roots of unity, show that

Q6. If α, β are roots of x2-3ax + a2 = 0, find the value(s) of a if α2 + β2 =

Q7. If y = 𝐼𝑛

√1+X − √1−X

√1+X + √1−X

, find dy

dX .

Q8. show that A (adj.A) = |A |I3.

Q9. Find the sum of all the integers between 100 and 1000 that are divisible by 9

Q10. Write De Moivre’s theorem and use it to find (√3 + i)

Q11. Solve the equation Given that one of the roots

exceeds the other by 2.

Q12. Solve the inequality and graph its solution.

Q13. Determine the values of x for which f(x) = x increasing and for which it is decreasing.

Q14. Find the points of local maxima and local minima of

Q15. Evaluate : ∫

Q16. Using integration, find length of the curve y = 3 – x from (-1, 4) to (3, 0).

Q17. Find the sum up to n terms of the series 0.4 + 0.44 + 0.444 + …

Q18. Show that the lines

Intersect.

Q19. 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 $ 3 and cost of a card is $ 2, find how many boxes and cards

should be purchased so as to minimize the expenditure.

Q20. A manufacturer makes two types of furniture, chairs and tables. Both the

products are processed on three machines A1, A2 and A3. Machine A1

requires 3 hours for a chair and 3 hours for a table, machine A2 requires 5

hours for a chair and 2 hours for a table and machine A3 requires 2 hours

for a chair and 6 hours for a table. The maximum time available on

machines A1, A2 and A3 is 36 hours, 50 hours and 60 hours respectively.

Profits are $ 20 per chair and $ 30 per table. Formulate the above as a

linear programming problem to maximize the profit and solve it.