CAT Exam Model Paper 3 with solutions for free online practice

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Question : 76 of 100

Marks: +1, -0

If

27 √{ 2 } ( 6√{ 3 } + 3 ) = 6 ^ { M } 3 ^ { N } ( 2 √ { 3 } + 1 )

Find M and N

$1,3/2$
$-1/2,3/2$
$1/2,-7/2$
$1/2,7/2$

Solution:

( \d ) 27 √ { 2 } ( 6 √ { 3 } + 3 ) = 27 ×3 √ { 2 } ( 2 √ { 3 } + 1 )

= 81 √ { 2 } ( 2√{ 3 } + 1 ) = ( √ { 3 } ) ^ { 8 } ( √{ 2 } ) ( 2 √ { 3 } + 1 )

= √ { 6 } ( √ { 3 } ) ^ { 7 } ( 2 √{ 3 } + 1 ) = 6 ^ { 1 / 2 } ×3 ^ { 7 / 2 } ( 2 √ { 3 } + 1 )

∴ m =

1/2

and n =

7/2

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