University of Mumbai 2008 Post Graduate Diploma FYPGDORM Part - I - Business Mathematics - Question Paper
Kindly obtain the attachment.
15-4-08-Nk-Ex. 121 ec** A) 0-* tO Cty sva HW 5 & etr> e*V|
A0<K/
Con. 2320-08.
(3 Hours)
BB-8959
[Total Marks : 100
N.B.(1) Attempt any five questions.
(2) Figures to the right indicate full marks.
(3) Necessary explanations at intermediate stages must be given.
(4) Use of non-programmable Calculator, Statistical Tables and Log tables is permitted.
(5) Answers should be brief and to the points.
(6) Assumptions, required in the questions, where necessary must be explained.
1. (a) 3 metal spheres whose radii are 3, 4 and 5 cm. melted and formed into one sphere. If 10 volume of a sphere varies as the cube of its radius, find the radius of the new sphere.
(b) Solve for x, the equation 10
Vx + 2 + yx - 1 V* + 2 - Vx - 1
= 3
2. (a) Find the square root of
10
10
10
10
12 + V24 +- V56 + a/84 (b) Solve for x and y : *
ax = xv and a = xx.
3. (a) If a, b and c are any 3 consecutive positive integers, prove that
log ( 1 + ac) = 2 log b (b) Derive the equation of a common tangent to
x2 + y2 - z and y? = 8x and plot the graph.
4. (a) A contractor builds 3 types of houses. The raw materials needed are given in the form 10 of a matrix A and the cost of buying and tranporting each of the raw materials are also given in the form of a matrix B. Find AB and interpret the entries of <AB)
|
A = Type I Type II Type III |
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(b) A rectangular area of 1000 square feet is to be enclosed by a fence and then divided in the middle by another fence.
10
10
10
The fence drawn in the middle cost Rs. 0-70 per running foot and the other fence costs Rs. 2-00 per running foot.
Find the minimum cost of fencing.
(a) Define (i) Consumers surplus, and (ii) Producers surplus.
(b) The demand function of the commodity is p = 20 - 3x and the supply function is p = 2x Determine the equilibrium price and show that at this price,
Consumers surplus = 24 and Producers surplus = 16.
6. (a) Evaluate
dx
dx
dx
oii) |
(ii) |
(j> I
and
-Jx2 -
(x + 2) (x + 1)
2x + 7x + 8x + 3
(b) If Z = x3 + 3x2y + 6xy2 - y2, show that when x = 2, y = 3, d2z
10
-30, . 6, and A ,48.
dxdy
dy
dx
7. (a) Find the sum of n terms of the following series :
10
1
1 1
+
(i)
+
8.
2-5 5-8 8-11
(ii) 2-5 + 5-8 + 8-11 + 11-14 +.......
(b) A rectangular box with a square base and open top is to be made from 1200 square material. 10 Find volume of the largest box that can be made.
(a) An Institute of Management uses aptitude test and group discussion for selecting 10 candidates for its management course of those obtaining satisfactory grades in these tests and group discussion. 75% pass the management course examination while only 35% of those whose performance in aptitude test and group discussion was unsatisfactory, pass the management course examination. Can it be said that the aptitude test and group discussion are necessary before admission to the course.
(b) If '10
1
+ 11-14
1_1 (V
3 2 U,
1
+ -3
+
y =
then find the sum of the following series :
+
+
+
2!
3!
4!
y +
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Attachment: |
| Earning: Approval pending. |
