SECTION 3 (Maximum Marks: 24)

• This section contains SIX (06) questions. The answer to each question is a NUMBERICAL VALUE.

• For each question, enter the correct numerical values of the answer using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer. If the numerical value has more than two decimal places, truncate/round-off the value of TWO decimal places.

• Answer to each question will be a evaluated according to the following marking scheme:

Full Marks : +4 If ONLY the correct numerical value is entered;

Zero Marks : 0 in all other cases.

Let m be the minimum possible value of , where y 1 , y 2 , y 3 are

real numbers for which y 1 + y 2 + y 3 = 9. Let M be the maximum possible value of (log 3 x 1 + log 3 x 2 + log 3 x 3 ), where x 1 , x 2 , x 3 are positive real numbers for which x 1 + x 2 + x 3 = 9. Then the value of log 2 (m 3 ) + log 3 (M 2 ) is