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$I f θ \in [0, 5 π] a n d r \in R s u c h t h a t 2 \sin θ = r^{4} - 2 r^{2} + 3, t h e n t h e m a x i m u m n u m b e r o f v a l u e s o f t h e p a i r (r, θ) i s$

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Correct option is C

We have 2sinθ=r4−2r2+3=r2-12+2≥2 ⇒2sinθ≥2 ⇒2sinθ=2 ∵-1≤sinθ≤1 ⇒sinθ=1 ⇒θ=π2,5π2,9π2 ∵θ∈0,5π Also r2-1=0⇒r=±1 ∴r,θ=±1,π2,±1,5π2,±1,9π2 ∴there are 6 pairs of r,θ

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If θ∈0,5π and r∈R such that 2sinθ=r4−2r2+3, then the maximum number ofvalues of the pair r,θ is

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$I f θ \in [0, 5 π] a n d r \in R s u c h t h a t 2 \sin θ = r^{4} - 2 r^{2} + 3, t h e n t h e m a x i m u m n u m b e r o f v a l u e s o f t h e p a i r (r, θ) i s$