Veer Narmad South Gujarat University 2010-1st Year B.B.A Quantitative Methods - 1 ( semII) . - Question Paper

RB-1714 First Year B. B. A. (Sem. II) Examination April/May - 2010 Quantitative Methods - I

(Mathematics Oriented)

Time : 3 Hours]

Instructions :

(1)

6silq<3i Puunkiufl SnwiA u* qsq d-onql. 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

-Subject Code No.

1 7 1 4

-Section No. (1,2,.....): NIL

(2)    All questions are compulsory.

(3)    Indicate your options clearly.

(4)    Figures to the right indicate full marks.

(5)    Use of one simple calculator is allowed.

Answer the following questions :

(1)    Define powerset with illustration.

Q O

(2)    If cost function is C (x) = 2x -x +1 then find total cost when x = 2

(3) Evaluate lim (1--]

n>oo V 11/

(4) Define absolute value of a real number.

(6) If _y = _xⁿ+n^x

(7)    If cost function is C (x) = 2x + 9 and if selling price is Rs. 15 then find profit function.

(8)    State demand law.

(9)    Evaluate j*9^Xdx.

3 2

(10)    If marginal revenue function is 4x -3x +1 then find total revenue when x = 1.

2 (a) For two real number a and b prove that, \a - b\ > |a| -16| 4

(b) A manufacturer of electronics company is planning 4 production of new varieties of laptops. The fixed cost of production is Rs. 3 lakhs and a variable cost is Rs. 200 for producing each laptop. If each laptop can be sold at Rs. 450 then find break even point.

(c) In a group of 100 students of M.B.A., 65 have taken finance, 55 have taken marketing and all the students have taken atleast one of the two subjects. How many students have taken both finance and marketing ? How many students have taken any finance ?

OR

(a) In usual notation prove that,

Au(5nC) = (Au5)n(iuC)

(b) If A = lx\x gN,

B = {y\ysN, |y-l|<3}

C = {z\z gN, \z\ < l} then prove that 4x(5nC) = (Ax5)n(AxC)

selling price per item is Rs. 25 then find break even point. If the profit is Rs. 1000 then find the number of units produced.

3 (a) Evaluate

2n² -5n + l

3n⁴ + 8n³ -1

(ii) lim

(b) Find dy/dx if

2 at , 2 at²

(i) x = -- and y =

1+t 1+t

5^X

(ii) y =

x

(c) The demand function of a firm is x = 400-20/? and 4

oc

its average cost function is C(x) = 6 + . Find the

ou

output at which the profit of the firm is maximum.

OR

3 (a) Evaluate :    4

_v 2 - Vl - x

(i)    lim --

x>-3 3 + X

(ii)    lim-

x0 X

(b) If y = [ J then find dy/dx.

(c) Find maximum and minimum values of f{x) = x + 9/x. 4

r 4x - 3

4 (a) Find J / ₂    ^dx

V2x - 3x + 9

(b) Find j(x²-5x + 6jdx

(c) The marginal cost function of firm is given by    4

MC = 50 - 0.004x Find total cost function and average cost if fixed cost is Rs. 50.

OR

4 (a) Find J +J^dx

(b) Find

r x² - 5x + 6

J

(n)

(c) If the marginal revenue and marginal cost for an    4

output x of a commodity are given as,

MR = 20-Sx- 4x² MC = 10-2x-x²

Find the profit function and find output of which profit is maximum and total profit at that point.

5 (a) Solve the following equations using matrix inversion : 4

4x - y - z = 32

3x + y + 2z - 39 3x - y + z = 24

" 4 2 3" "3 0 1 II 11 e -1 0 2 and B = 5 2 1 1 5 9 1 0 8	then find matrix 4
C such that 2A + C = SB

	" 0	2	3"
ii 11	-2	0	5	then find (A + AT\ and
	-3	-5	0	2 \ /

2

OR

(a) Prove that

x y z z x y y z x

(b) A man boys 8 dozen of mangoes, 10 dozen of apples 4 and 4 dozen of bananas. Mangoes cost Rs. 180 per dozen, apples cost Rs. 120 per dozen and banana Rs. 20 per dozen. Find the total cost using matrix multiplication.

(c) If A =

1 2" , B = a b 0 8 c d

and

find a, b,c,d.

6 Attempt any two :    12

(a)    Solve the following L.P.P. using graphical method : Minimum Z = 30x + 50y

subject to the constraints,

Sx + y > 15

x + 2y > 12 3x + 2y> 24 x, y > 0

(b)    Solve the following assignment problem to minimize the cost :

(c) Find the optimum solution of the following transportation problem :

	Dl	D2	3	D4	db	ai
0.	7	5	6	5	9	8
	8	7	8	5	4	12
o CO	9	8	7	10	6	14
hJ	4	4	6	10	10

RB-1714]    7    [ 3500 ]

Attachment: veer-narmad-south-gujarat-university-2010-b-b-a-28165-1.pdf

Earning:   Approval pending.