Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2013MathematicsTrigonometric Equations

The maximum value of ( ₁ ) ( ₂ ) ( _n ) . Under the restrictions 0 ₁, ₂, _n 2 and ( ₁ ) ( ₂ ) ( _n )=1 is

Options

  1. A1 2^ n / 2
  2. B1 2^n
  3. C1 2 n
  4. D1

Correct answer

A. 1 2^ n / 2

Step-by-step solution

We are given that, ( ₁ ) ( ₂ ) ( _n )=1 aligned ( ₁ ( ₂ ) ( _n )= ( ₁ ) . ( ₂ ) ( _n ) aligned ....(i) Let y= ( ₁ ) ( ₂ ) ( _n ) (to be max.) Squarring both sides, we get y^2= ( ^2 ₁ ) ( ^2 ₂ ) ( ^2 _n )= ₁ ₁ ₂ ₂ _n _n [using (i)] = 1 2^n [ 2 ₁ 2 ₂ 2 _n ] As 0 ₁, ₂, , _n 2 0 2 ₁, 2 ₂, , 2 _n 0 2 ₁, 2 ₂, , 2 _n 1 y^2 1 2^n 1 y 1 2^ n / 2 Maximum value of y is 1 2^ n / 2 .

Practice Trigonometric Equations on Quantrex Academy →

More from Trigonometric Equations

Suppose ' a ' and ' b ' are non-zero constants satisfying the following system of equations a ^3 x + b ^3 x = x x and a x - b x = 0 , then 2(a^6 + b^6) - 3(a^4 + b^4) + 1 = 2026The number of common solutions of the pair of equations 2 ^2 - 2 ^2 + 1 = 0 and 2 ^2 + 3 - 2 = 0 in the interval [0, 2 ] , is 2026The general solution of x + x = 2x + 2x is x = np or x = nq 3 + 6 for n Z then p : q = 2026Let x [0, 6 ] satisfy the equation x - x = -1 . If x = k ( 3 ) where k N , then find the number of possible values of k is ..... 2026If the equation 3 - ^2 = 1 4 and [0, ] , then the number of solutions is... 2026The general solution of the equation 2 = 1 is... 2026If 0 x 2 , then the number of values of x for which x - 2x + 3x = 0 is 2026If 4 - 2 = 2 , then = 2026 Full Trigonometric Equations list All Manipal MET PYQs