JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q62

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MathematicsSingle correct+4 / -1Question 62 of 90

A value of θ for which $\dfrac{2+3i\sin\theta}{1-2i\sin\theta}$ is purely imaginary, is :

\dfrac\pi3

\dfrac\pi6

\sin^{-1}\left(\dfrac{\sqrt3}4\right)

\sin^{-1}\left(\dfrac1{\sqrt3}\right)

Answer and worked solution

Official answer: D

Multiplying by the conjugate, the real part is proportional to $2-6\sin^2\theta$ . It vanishes when $\sin^2\theta=\frac13$ , i.e. $\theta=\sin^{-1}\frac1{\sqrt3}$ .

Topics:Algebra of complex numbers

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 62