IGNOU BCS-012 SOLVED ASSIGNMENT 2021-22

Q8. 2 -1 0
If A = 1 0 3 , show that A (adj.A) = |A |I3.
3 0 -1
9

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)
3
.

Q11. Solve the equation x3
– 13x
2 + 15x + 189 = 0,Given that one of the roots
exceeds the other by 2.

Q12. Solve the inequality 2
X−1
> 5 and graph its solution.
Q13. Determine the values of x for which f(x) = x
4
– 8x
3 + 22x
2
– 24x + 21 is
increasing and for which it is decreasing.

Q14. Find the points of local maxima and local minima of
f(x) = x
3
–6x
2+9x+2014, x ε .

Q15. Evaluate : ∫
dx
(e
x−1)
2

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 X − 5
4
=
y − 7
−4
=
z −3
−5
and X−8
4
=
y − 4
−4
=
z − 5
4
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.

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