NET JRF PART - A : Questions and Solutions : NET JUNE-2014

NET JRF PART - A : Questions and Solutions:

NET JUNE-2014

1.) Suppose 

x∆y = ( x - y )² ;

xoy = ( x + y )² ;

x*y = ( x × y )^-1 ;

x•y = x × y ;

+, – and × have their usual meanings. What is the value of { ( 197o315 ) - ( 197∆315 ) } • ( 197*315 ) ?

(a) 118 (b) 512 (c) 2 (d) 4 

Ans. : (d) 4 .

Solution:

{ ( 197o315 ) - ( 197∆315 ) } • ( 197*315 ) 

= { ( 197 + 315 )² - ( 197 - 315 )² } • ( 197 × 315 )^-1

= { ( 197 + 315 + 197 - 315 ) ( 197 + 315 - ( 197 - 315 ) ) } • 1 / ( 197 × 315 )

= { ( 197 + 315 + 197 - 315 ) ( 197 + 315 - 197 + 315 ) ) } • 1 / ( 197 × 315 )

= { 394 × 630 } •1 / ( 197 × 315 ) = 4 .

Thus,

 { ( 197o315 ) - ( 197∆315 ) } • ( 197*315 ) = 4 .