MHT CET202416 May 2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
The maximum value of ( ₁ ) ( ₂ ) ( _n ) under the constraints 0 ₁, ₂, , _n 2 and ( ₁ ) ( ₂ ) ( _n )=1 is
Options
- A1 2^ ( n 2 )
- B1 2^ n
- C2^n
- D2^ n 2
Correct answer
A. 1 2^ ( n 2 )
Step-by-step solution
array ll & Here, ( ₁ ) ( ₂ ) ( _n )=1 & ₁ ₂ _n & = ₁ ₂ _n & Now, ( ₁ ₂ _n )^2...(i) array = ( ₁ ₂ _n ) ( ₁ ₂ _n )= ( ₁ ₂ _n ) array r ( ₁ ₂ _n ) [ From (i)] array = 1 2^ n 2 ₁ 2 ₂ 2 _n [ 2 ~A =2 ~A ~A ] But each of 2 _i 1 ( ₁ ₂ _n )^2 1 2^n But each of _i is positive ₁ ₂ _n 1 2^n = 1 2^ n 2