Veer Narmad South Gujarat University 2011-1st Year B.B.A SB-1368 Quantitative Methods - 1 (old) ( Sem - 2 ) - Question Paper
SB-1368
First Year B. B. A. (Sem. - II) Examination March / April - 2011 Quantitative Methods - I
(Old Course)
[Total Marks : 70
Time : Hours]
Instructions
""'N Seat No.:
6silq<3i Puunki(l faaim SuwiA u*
Fillup strictly the details of signs on your answer book.
Name of the Examination :
F. Y. B. B. A. (SEM. - 2)
Name of the Subject:
QUANTITATIVE METHODS -1 (OLD)
Student's Signature
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-Subject Code No. |
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NIL |
Answer the following questions :
10
(1) Define powerset with illustration.
(2) If f(x) = 3x1 +ax + 5 and /(2) = 27 then find a.
(3) If f{x) = xex then find f'(x).
(4) Evaluate lim(l-3x
X0
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(6) Define marginal revenue. | |||||||||
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then find AA-3B | ||||||||
1 2 1
2 4 2
1 6 9
(9) If /(x) = 2x2 -x + 3 then find /"(l).
(8) Evaluate
50-2 p
(10) If the demand function is x = - then find revenue function.
2 (a) For two real numbers a and b prove that 4
\a + b\ <\ a\ + \b\
(b) The survey of housing society of 350 residents on 4 Bombay provides the following information :
(1) Every residents can speak Gujarati or Hindi
(2) 140 residents can speak Gujarati
(3) 170 residents can speak Hindi.
Find out how many residents of this society can speak both the languages and how many speak only Hindi ?
(c) If A = ja|a < 3, a e TV], B = {b \ \b <\\,b 1, 4 C = {c|c3 = 27, C e iVj then verify that,
A-(BC) = (A-B){](A-C)
2 (a) In usual notation P.T. yU(5C,) = (yU5)(-4UC,). 4
(b) The cost function is C(x) = 5x + 9 and selling price is 4 Rs. 16. Find profit function.
(c) If A = {2, 3,4}, B = {1, 3,4},P = {l, 2, 3}, Q = {l, 3, 5} then 4
verify that, (AxB) f](PxQ) = {A[}P)x{B[}Q)
3 (a) Evaluate : 4
(1) l'Z2 + J2/ (2) j
dy 1 + jc
dx 1 + x
(c) The demand and supply function of commodity are 4 as follows :
D:(x + 10)(/? + 20) = 300
S : x = 2p-%
Find equilibrium price and equilibrium quantity.
125x3-l 625x4-1
(a)
(b) (c)
logx
(i) y = x2ex
(ii)
4
4
The cost function for an output x is, C = x3 -12x2 + 48x -11 and revenue function is r = 83x-4x2-21- Find output for which profit is maximum and maximum profit.
f 10x4 -16x3 +3 I = ax
(a) Evaluate J /;-:-
V 2x5-4x4+3x + 2
1
(b) Evaluate J(*2+2x-ljdx
Find %if
Evaluate
-l
(c) If the marginal revenue of a firm is MR = 9-3x2. Find 4
(i) Total Revenue R
(ii) Average Revenue
(iii) Demand function.
(a) Evaluate | xex dx
m
(b) Evaluate J V2x + 3 dx
(c) The marginal cost function for the product is l + 2x + 6x2 4 where x is the output. Find the total cost function if fixed cost is Rs. 100.
Solve the following equations using inverse matrix method :
(a)
(b)
(c)
x + 2_y + 3z = 6, 2x + 4_y + z = 7, 3x + 2_y + 9z = 14 Find inverse of the following matrix :
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'10 |
15 |
20' | ||||
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20 |
15 |
5 | ||||
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5 |
10 |
20 | ||||
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Evaluate | ||||||
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1 2 |
1 |
201 |
210 |
220 | ||
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(i) |
3 1 |
5 |
(ii) |
151 |
155 |
140 |
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\/ |
2 4 |
2 |
50 |
55 |
80 | |
3
0 4 3
1 -3 -3 -14 4
5 (a) If A--
4
4
(b) Solve the following equations using inverse matrix method :
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then verify that, |
(.A + Bf =A2+B2
Attempt any two :
6
12
Solve the following LPP using graphical method. Minimum Z = 2x1 + 3x2 Subject to the constraints,
Xj +4x2 >12 Xj + x2 > 6 5xj + x2 >10 Xj, x2 > 0
Obtain an optimal solution of the following transportation problem :
(b)
(c)
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D\ |
d2 |
D3 |
D, |
ai | ||
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5 |
3 |
6 |
2 |
19 | ||
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02 |
4 |
7 |
9 |
1 |
37 | |
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0.3 |
3 |
4 |
7 |
5 |
24 | |
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bJ |
16 |
18 |
31 |
25 | ||
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Solve the following |
cost minimising assignment problem | |||||
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P |
0 |
R |
S | |||
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A |
12 |
15 |
18 |
8 | ||
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B |
13 |
10 |
9 |
14 | ||
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C |
10 |
12 |
15 |
13 | ||
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D |
7 |
8 |
9 |
14 | ||
SB-1368] 4 [ 1000 ]
All questions are compulsory.
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Attachment: |
| Earning: Approval pending. |
