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    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

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    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

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    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

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