Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202317 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

Match the ranges of the functions given in List - I with those of the items given in List - II

Options

  1. A(1) (c) (II) (a) (III) (d) (IV) (b)
  2. B(1) (c) (II) (d) (III) (a) (IV) (b)
  3. C(1) (b) (II) (d) (III) (a) (IV) (e)
  4. D(1) (b) (II) (e) (III) (d) (IV) (c)

Correct answer

B. (1) (c) (II) (d) (III) (a) (IV) (b)

Step-by-step solution

(I) aligned 3 ^2 x+4 ^2 x-2 & =3 ^2 x+3 ^2 x+ ^2 x-2 & =3+ ^2 x-2= ^2 x+1 aligned Also, 0 ^2 x 1 1 ^2 x+1 2 1 3 ^2 x+4 ^2 x-2 2 Range of (3 ^2 x+4 ^2 x-2 ) is [1,2] aligned & (II) ^2 x+ ^4 x= ^2 A+ (1- ^2 A )^2 & = ^2 A+1+ ^4 A-2 ^2 A & =- ^2 A+1+ ^4 A & =- ^2 A (1- ^2 A )+1 & =1- ^2 A ^2 A & =1- ( 2 A 2 )^2 & 0 ^2 2 x 1 0 ^2 2 x 4 1 4 & 0 - [ 2 x 2 ]^2 - 1 4 & 1 1- [ 2 x 2 ]^2 1- 1 4 & 1 ^2 A+ ^4 x 3 4 aligned aligned & (III) ^6 x+ ^6 x= ( ^2 x )^3+ ( ^2 x )^3 & = ( ^2 x+ ^2 x )^3-3 ^2 x ^2 x ( ^2 x+ ^2 x ) & =1-3

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

If x+ x= 1 2 and 0 < x < , then x= 2025If A and B are acute angles satisfying 3 ^2 A+2 ^2 B=4 and 3 A B = 2 B A , then A+2 B= 2025In a ABC , if ^2 ~B = A and 2 ^2 ~A =3 ^2 ~B , then the triangle is 202512 2 12 3 12 4 12 5 12 6 12 = 2025If ( 4 + )= ^3 ( 4 + ) , then ( + ) ( - )= 2025If A+B+C+D=2 , then A+ B+ C+ D= 2025(4 ^2 20 -1 ) (4 ^2 3 20 -1 ) (4 ^2 5 20 +1 ) (4 ^2 7 20 -1 ) (4 ^2 9 20 -1 )= 2025If A and B are the values such that (A+B) and (A-B) are not odd multiples of 2 and 2 (A+B)=3 (A-B) , then A A= 2025 Full Trigonometric Ratios & Identities list All AP EAMCET PYQs