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A 1 litre solution containing \( \mathrm{NH}_{4} \mathrm{Cl} \) and \( \mathrm{NH}_{4} \mathrm{OH} \) has hydroxide ion concentration of \( 10^{-6} \) mol/litre. Which of the following hydroxides could be precipitated when the solution is added to 1 litre solution of \( 0.1 \mathrm{M} \) metal ions?
(I) \( \mathrm{Ba}(\mathrm{OH})_{2}\left(K_{s p}=5 \times 10^{-3}\right) \)
(II) \( \mathrm{Ni}(\mathrm{OH})_{2}\left(K_{s p}=1.6 \times 10^{-16}\right) \)
(III) \( \mathrm{Mn}(\mathrm{OH})_{2}\left(K_{s p}=2 \times 10^{-13}\right) \)
(IV) \( \mathrm{Fe}(\mathrm{OH})_{2}\left(K_{s p}=8 \times 10^{-16}\right) \)
(a) I, II, IV
(b) IV
(c) II and IV
(d) II, III, IV
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