Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsNumber of Solutions (graph)Medium2 minPYQ_2019

MathematicsMediumsingle choice

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

Answer:

Solution:

Given, $| \cos x | = 2 [x]$

$0 \leq | \cos x | \leq 1$

$∴ 0 \leq 2 [x] \leq 1$

$0 \leq [x] \leq \frac{1}{2}$

$[x] = 0$

$\Rightarrow x \in [0, 1)$

But $| \cos x | = 0$

$\Rightarrow x = n π + \frac{π}{2}$ for any value of $n \in Z$

Hence, the equation has no solution.

Stream:BITSATSubject:MathematicsTopic:FunctionsSubtopic:Number of Solutions (graph)

⏱ 2mℹ️ Source: PYQ_2019

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