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BITSAT2019MathematicsFunctionsActual

Number of solution of the equation | cos x | = 2 [ x ] are (where | x | , [ x ] are modulus and greatest integer function respectively).

Options

  1. A0
  2. B2
  3. C1
  4. Dinfinitely many

Correct answer

A. 0

Step-by-step solution

Given, | cos x | = 2 [ x ] 0 ≤ | cos x | ≤ 1 ∴   0 ≤ 2 [ x ] ≤ 1 0 ≤ [ x ] ≤ 1 2 x = 0 ⇒ x ∈ [ 0 , 1 ) But | cos x | = 0 ⇒ x = n π + π 2 for any value of n ∈ Z Hence, the equation has no solution.

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