Yashwantrao Chavan Maharashtra Open University 2006 Certification TML Applied Mathematics-I - Question Paper
TML012/EE/20070813
Applied Mathematics - I Time : 180 minutes Marks : 100
Instructions for the students :
1. All questions are compulsory.
2. "Long Answer type Question (LAQ)" is a supply type question of 20 marks, which require typical answer of about 60-80 lines in about 32-40 minutes.
3. "Short Answer type Question (SAQ)" is a supply type question of 5 marks, which require typical answer of about 15-20 lines in about 08-10 minutes.
4. Use of non-programmable type of scientific calculator is allowed.
5. Draw neat diagrams wherever necessary.
6. Assume suitable data if necessary.
|
Q- No. |
Question (Q) |
Question Marks |
|
Long Answer type Questions (LAQ's) | ||
|
1. |
(a) For what values of 'k' are the roots of equation |
10 |
|
(k -1)x2 + (k -1)x + k2 = 0 equal 32 Suppose T4 = 3 and T9 = . Find the first three terms of G.P. 4 9 81 |
10 | |
|
2. |
(a) Prove that Sin6 A + Cos6 A = 1 - 3Sin2 ACos2 A (b) Write (V3 + i) in the form of a + bi |
10 10 |
|
3. |
(a) Solve graphically the following equations x + 2y = 4and 2 x - 3 y = 1 (b) Find the equation of the locus of a point such that the sum of the squares of its distances form the points (3, 0) and (0, -4) is 12. |
10 10 |
|
4. |
(a) Two fair dice are rolled. Find the probability that the score is 8. (b) Verify distributive law x (y + z) = (x y) + (x z) using truth table. |
10 |
|
10 | ||
|
Short Answer type Questions (SAQ's) | ||
|
5. |
Simplify Log5 27 - Log5 81 + Log5 243 - Log5 6 + Log518 |
5 |
|
6. |
, Sin26 Show that -= CotQ 1 - Cos2d |
5 |
|
7. |
Find the equation of the circle having centre (3, 4) and radius 4. |
5 |
|
8. |
Find x if vector 2xi + 5j - 3k and 3i - 6j - 2k are perpendicular. |
5 |
N-62 TML012/EE/20070813: 1
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Attachment: |
| Earning: Approval pending. |
