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TRIBHUVAN UNIVERSITY

FACULTY OF MANAGEMENT

Office of the Dean

2011

Candidates are required to answer the questions in their own words as far as practicable

Group A

1. Brief Answers Quesions! "101#10$i. What must be true about two non empt sets A an! " if #ABBA =

ii. $f %&>x what are the possib'e rea' (a'ues for )#

iii. Write the po'ar form of a comp'e) number *+,

i%. What are the cube roots of unit#

%. $f ( )x

xxf

+=+

+fin! the (a'ue of

( ) ( )

( ) ( ),

+ yfxf

yfxf

%i. $f the cost function C-). / &) 0 1,2)3 -in 4s.% what is the mar5ina' cost when ) / 6#

%ii. E(a'uate the !eterminant+

+

+

c

b

c

a

b

a

,

%iii. What can ou sa about two non*7ero (ectors

a an!

b if #1, =

ba

i&. $f

=

1

+

3

1A % fin! the (a'ue of IAA 8133 where $ is unit matri) of 3 9 3,

&. Fin! the area boun!e! b cur(e ,+1%3 3+ === xandxwhenxy

Group B

S'or (nswer )uesions! "10*#*0$2. (. A'' the stu!ents of a co''e5e !rin: tea or coffee or both, $f ;3< !rin: tea an! 86< !rin: coffee%

what is the percenta5e of stu!ents !rin:in5 tea on' an! coffee on'#

+. Fin! the inter(a' within which ) 'ies in the re'ation ,2&3 x

,. a, $f ,% iyxibathatShowiyxiba +=+=

+. $f

be a comp'e) cube root of unit% show that ( )( )( )( ) ,=++++ 683

=

*. a, For what (a'ue of : is the function ( )

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6. @o'(e the fo''owin5 euations b usin5 Determinant or Matri) Metho!>

3&6

+83

+3

=

=+

=

zyx

zyx

zx

7. $f

+=+= kjibandkjia ;3+1%33 % fin! the (a'ue of

ba an! the unit (ector perpen!icu'ar to the

5i(en (ectors, A'so% fin! the cosine an5'e between them,

8. For a function ( ) %&?+23 3& xxxxf += fin! the inter(a's in which the f-). are increasin5 or !ecreasin5,

A'so% fin! the point of inf'ection on the cur(e% if possib'e,

10. $f the !eman! function for a pro!uct is p / 6 B 3) an! the supp' function is p / 3)% where p is the unit price

in 4s, an! ) is the ua'it !eman!e! the uantit supp'ie! in units% fin! the consumers surp'us an! the

pro!ucers surp'us at the eui'ibrium price 'e(e',

11. @o'(e the !ifferentia' euation ,1%1% ===+ yxwheneaydx

dy mx

Group 9

9opre'ensi%e (nswer )uesions! "110#10$12. The research !epartment of a manufacturer compan presents the price*!eman! euation p / 86 B &) for a

certain pro!uct% where p is the unit price -in 4s,. an! ) is the ua'it !eman!e! units, The financia' !epartment

pro(i!es the cost function C-). / ?) 0 +31% where C-). is the cost in rupees for manufacturin5 an! se''in5 the

pro!uct ) units,

a, Fin! the !omain an! ran5e of the function !efine! b the price*!eman! euation, "2$b, Fin! the mar5ina' re(enue at ) / ; % ) / 6 an! ) / = an! interpret these resu'ts, "2$

c, Fin! the brea:*e(en points a'5ebraica'', "2$

!, Fin! the best pro!uction 'e(e' of pro!ucts to pro!uce ma)imum profit b usin5 app'ication of

!eri(ati(es, What is the compans ma)imum profit# What is the price per pro!uct that pro!uces the

ma)imum profit# "*$