SSC CGL Tier II 12 Jan 2017 Paper 1

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Question : 69 of 100

Marks: +1, -0

If

a + b + c + d = 4

then the value of

\ { 1 } /{ ( 1 - a ) ( 1 - b ) ( 1 - c ) } +

{ 1 } /{ ( 1 - b ) ( 1 - c ) ( 1 - d ) }

+ { 1 }/ { ( 1 - c ) ( 1 - d ) ( 1 - a ) }

+ { 1 }/ { ( 1 - d ) ( 1 - a ) ( 1 - b ) }

is

0
1
4
$1+ abcd$

Solution:

(1)

a + b + c + d = 4

⇒

4 - a - b - c - d = 0 ...(i)

Expression

=\ { 1 } /{ ( 1 - a ) ( 1 - b ) ( 1 - c ) } +

{ 1 } /{ ( 1 - b ) ( 1 - c ) ( 1 - d ) }

+ { 1 }/ { ( 1 - c ) ( 1 - d ) ( 1 - a ) }

+ { 1 }/ { ( 1 - d ) ( 1 - a ) ( 1 - b ) }

= { ( 1 - d ) + ( 1 - a ) + ( 1 - b ) + ( 1 - c ) }/ { ( 1 - a ) ( 1 - b ) ( 1 - c ) ( 1 - d ) }

= { 4 - a - b - c - d } /{ ( 1 - a ) ( 1 - b ) ( 1 - c ) ( 1 - d ) } = 0

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