Answer:
Let solubility of\[Ni{{(OH)}_{2}}\]
in \[NaOH\]is s.
\[\underset{s}{\mathop{Ni{{(OH)}_{2}}}}\,\to
\underset{s}{\mathop{N{{i}^{2+}}}}\,+\underset{(2s+0.1)\approx
0.1}{\mathop{2O{{H}^{-}}}}\,\]
\[{{K}_{sp}}=[N{{i}^{2+}}]{{[O{{H}^{-}}]}^{2}}\]
\[2\times {{10}^{-15}}=s\times {{(0.1)}^{2}}\]
\[s=2\times
{{10}^{-13}}M\]
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