Answer
(a)$X=\beta^{-}$
(b)$X=\beta^{+}$
(c)$X=\gamma$
(d)$X=\alpha$
Work Step by Step
(a)
$X=\beta^{-}$
$^{211}_{82}Pb$ $\longrightarrow$ $^{211}_{83}Bi+^{0}_{-1}e$
Reason is in $\beta^{-}$ deacy
$^{A}_{Z}P$ $\longrightarrow$ $^{A}_{Z+1}D+^{0}_{-1}e$
(b)
$X=\beta^{+}$
$^{11}_{6}C$ $\longrightarrow$ $^{11}_{5}B+^{0}_{+1}e$
Reason is in $\beta^{+}$ deacy
$^{A}_{Z}P$ $\longrightarrow$ $^{A}_{Z-1}D+^{0}_{+1}e$
(c)
$X=\gamma$
$^{231}_{90}Th^{*}$ $\longrightarrow$ $^{231}_{90}Th+\gamma$
in $ \gamma$ decay there is no change both in $Z $ & $A$ ,only excited nucleus comes to its ground state.
(d)
$X=\alpha$
$^{210}_{84}Po$ $\longrightarrow$ $^{206}_{82}Pb+^{4}_{2}He$
Reason is in $\alpha $ deacy
$^{A}_{Z}P$ $\longrightarrow$ $^{A-4}_{Z-2}D+^{4}_{2}He$
