An iodide ion may combine with one $I_{2}$ or two $I_{2}$ molecules to form $I_{3}^{-}$ and $I_{5}^{-}$ ions. Regarding these ions the correct statements is

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Both have the same number lone pairs of electrons on the central iodine atom

$I_{3}^{-}$ is linear but $I_{5}^{-}$ is angular

Both $I_{3}^{-}$ and $I_{5}^{-}$ are linear and non polar

$I_{3}^{-}$ is linear but $I_{5}^{-}$ is square pyramidal

answer is C.

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Detailed Solution

$I_{3}^{-}$ linear the central iodine atom is involved in $s p^{3}$ hybridization with three lone pairs occupying the three equatorial positons of trigonal bipyramid structure. During the formation of $I_{5}^{-}$ from $I_{3}^{-}$ , one on the terminal iodine atom donate a lone pair to $I_{2}$ molecule and involves in $s p^{3}$ hybridization with two lone pairs and two bond pairs so it is angular.