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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The number of values of x in the interval [0, 5π] satisfying the...

The number of values of xx in the interval [0,5π]\left[0, 5\pi\right] satisfying the equation 3sin⁡2x−7sinx+2=03\sin^{2} x - 7sin x + 2 = 0 isThe number of values of x in the interval [0, 5π] satisfying the equation 3 ^ 2 x - 7sin x + 2 = 0 is

Options

  1. A00
  2. B55
  3. C66
  4. D1010

Correct answer

C. 66

Step-by-step solution

3sin⁡2x−7sinx+2=03\sin^{2} x - 7sin x + 2 = 0
3sin⁡2x−6sinx−sinx+2=03\sin^{2} x - 6sin x - sin x + 2 = 0
\left(3sin x - 1\right)\left(sin x - 2\right) = 0<br/><br />⇒ sin x = \dfrac{1}{3}, sin x = 2notpossible<br/><imgsrc="/api/proxy−image?url=httpsnot possible<br /><img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fnta_abhyas%252Fjee_main%252Fimages%252F8bdde3ba-788e-48d7-8e8c-81281e061f29.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2F8bdde3ba-788e-48d7-8e8c-81281e061f29.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2F8bdde3ba-788e-48d7-8e8c-81281e061f29.png?alt=media" style="max-width:100%; object-fit:contain" style="width:3.03333in;height:1.21319in" /><br />Fro the figure,6rootsin[0,5π]roots in \left[0, 5\pi\right]
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