Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202411 May 2024Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The number of solutions of x+ x=2 x in [0,2 ] is

Options

  1. A2
  2. B3
  3. C0
  4. D1

Correct answer

A. 2

Step-by-step solution

The given equation is defined for x 2 , 3 2 . Now, x+ x=2 x aligned & x x + 1 x =2 x & ( x+1)=2 ^2 x & ( x+1)=2 (1- ^2 x ) aligned aligned & ( x+1)=2(1- x)(1+ x) & (1+ x)[2(1- x)-1]=0 & 2(1- x)-1=0 & [ array r x -1 otherwise x=0 and x, x will be undefined array ] & x= 1 2 & x= 6 , 5 6 in [0,2 ] & number of solutions =2 aligned

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 MHT CET PYQs