new doc 9
TRANSCRIPT
-
Scanned by CamScanner
O M 0 0
I n d i a n I n s t i t u t e o f M a n a ge m e n t C a l c u t t a
F I R ST Y E A R,
2 0 1 0
QU A L I F Y I N G M A T H E M A T I C S
A t t e m p t I
(T i m e a l l o w e d : T W O h o u r s )
N O T E : A n s w e r A l l q u es t io n sT o t a l m n r k s fo r U r e p a p e r is 1 0 0 n r k s fo r e a c h q u e s t io n a r e w r i t t e n n p x t t o t h e q u e s t io 1tw r i t t y o u r & 11s w e r s i n t h e c o r r e s p o n d i n g s p a c p p r o v ide d i n t he a n s w e r s h e e t o n lyA n s w c t s wi t Tc n i 1r t l 1e q u e s t io n p a p e r w i l l N O T b e e w lu a t c d
,
h o w e v t r r s h o w y o t 1t ' w o r k i n g i n t l c :q n e s t i o n p a p e rA t t h e e r 1d o f c x a l n i n a t io n
, p le a s e s u b 1n i t t h is q u e s t io 11 p a p e r a lo p n g w i t h t l 1e a n s w e r s h t x t
S E C T I O N A
M U L T I P L E C H O I C E QU E ST I O N SW r i t e t i l e c o r r e c t o p t i o n (s ) o n t h e a n s w e r s h e e t p r o v i d e d I n c e s e o f m u t l i p le c o r r e c t o p t io n s w r i a l lt h e c o r n r t o p t i o 1t s
1 L c t f (1 ) = f t ( I ) T2 (r ) , w h e r e f l (r ) a n d f z (z ) a r e o d d f u n c t i o n s T he n ( 1 i n n r k !(n ) f (: r ) is 1 1 ( ) ( M f u l m i o n( ) ) f ( J : ) C i u ] e v , 1 l u n c t io n(> ) f ( . r ) is e v e n u r o cl d o ]. N t : i t l 1c r l lu p u l l d i n R 0 11 f + (J : ) a 1 9l ! 2 (J : )
2 1 e t f (1 ) b > a c u b i> l u u t : t i o n o r t l l > ib > i n f (J ) = r w a + b : r z B K r + r w i t l 1 a 1) 1 t t I 1 > J n 1u l r 1 s n t is t \t l w t x l u n t Io n ! t r ) 0E t t t l ( w i r> t l r e r \ I u %) l la \ v i r i A 1a t e 1n e n t t a r e T R U E a r P L S 1c
1 l l t
-
Scanned by CamScanner
0M
00
c
x
l
X
c&
be
s
ch
ha
l
=
l
0
N
TnH
n
a
k
Fa
e
3
Le
E
E
an
d
E
be
h
ee
se
s
a
f
En
E
=
E
hen
wh
ch
o
he
o
ow
ng
8
rue
E
E
ma
k
E
E
8
YE
b
E
u
E
u
Ea
Y
s
he
sa
e
as
1
u
w
u
q
inak
E
UE
n
E
Wn
E
u
E
4
Fo
appop
a
e
n
an
dJ
>
"
s
equa
o
a
"
+
;-
ma
k
5
Fo
ma
r
ces
A
Ban
d
cd
e
ne
d
be
ow
a
e
wh
e
he
he
o
ow
ngope
a
on
a
e
de
%n
do
no
a
A-
B
E
de
n
d
Wh
o
de
ne
d
m
k
AB
i}
hd
4
-
Scanned by CamScanner
OM00
e
CA
s d
e
ne
d
no
de
ne
d
mar
k
6
Ltfz
=
og
r
an
dgT
=
2
og
z
Th
en
mar
k
a
fz
=
gz
b
fz
B9a
7
Le
A
be
a
qua
e
ma
x
a
4+
AT
s
&ma
x
wh
ch
s
ymme
kew
synune
c
ma
k
mme
c
or
kew
symme
c
o
ne
he
depen
dngon
he
ma
x
A
b
4
-
Ar
s
a
ma
x
wh
ch
s
s
mne
c
kew
y-
e
c
mme
c
o
kew
ymme
c
or
ne
he
depen
dngon
he
ma
x
A
c
A_
AT
hen
he
nv
se
ma
x
A-
sjmmetric
na
x
kew
yn
une
c
ma
x
ymmetric
o
kew
yn
ne
c
o
ne
he
depen
dngon
he
ma
x
A
mar
k
mar
k
-
Scanned by CamScanner
OAT
00
SECTION
B
W
e
your
a
swe
n
he
cor
espon
dngspace
prov
de
d
n
he
answer
sh
ee
t
8
Le
fan
dg
be
wo
unc
ons
de
ne
don
he
se
o
ea
num
be
s
SUc
h
ha
a
Deine
he
unc
on
f
-
gz
Use
he
o
ma
shown
be
ow
3
ma
b
Wha
th
e
doma
n
o
f=
-
gz
?
c
Wha
s
he
ange
offz
-
gz
?
ma
k
ma
k
d
De
ne
he
unc
on
f
9
Use
he
o
ma
shown
be
ow
ma
9
tfz
=
og
.
z
a
Expres
fz
n
e
-
o
na
ura
ogar
hm
n
ma
k
b
Fn
d
he
oo
s
o
he
equa
on
f
=
0
na
k
c
=
e
a
n
r
n
10
It
9an
d27be
he
oo
s
o
he
qua
d
a
c
equa
on
z
+b=
+c
-
0
Fn
d
he
va
ue
o
au
dc
u
11
Le
fT
=
z
_
3z
+
2
be
a
qua
d
a
c
unc
on
o
5
W
e
he
ange
o
z
va
u
o
h
a
fr
>
0
o
b
f
z