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BITSAT 2019
Exam
BITSAT
Year
2019
Subject
Mathematics
Chapter
Functions

BITSAT 2019 · Mathematics · Functions

Number of solution of the equation | x | = 2 [ x ] are (where | x |...

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

Options

  1. A00
  2. B22
  3. C11
  4. Dinfinitely many

Correct answer

A. 00

Step-by-step solution

Given, ∣cos⁡x∣=2[x]| \cos x | = 2 [ x ]

0≤∣cos⁡x∣≤10 \le | \cos x | \le 1

∴0≤2[x]≤1∴ 0 \le 2 [ x ] \le 1

0≤[x]≤120 \le [ x ] \le \dfrac{1}{2}

\left[x\right] = 0</p><p></p><p>⇒ x \in [ 0, 1 )</p><p>But </p><p>But~| \cos x | = 0</p><p></p><p>⇒ x = n\pi + \dfrac{π}{2} foranyvalueof~for any value ofn \in Z$

Hence, the equation has no solution.

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