Answer

`P - a, c; Q - a,c,e,f;R-a,bc ; S-a,c,d;T-a,c,g; U-a,c `

Explanation

(P) `NH_(4)Cl` - salt of strong acid ans weak base - soluble in water
`NH_(4)Cl +H_(2)O rarr NH_(4)OH +H^(+)+Cl^(Theta)` - gives brown ring test
`NH_(4)ClhArrunderset("reacts with nessler.s reagent")underset(uarr" ")(NH_3+HCl)`
(Q) `NH_(4)NO_(3)` - water soluble, gives brown ppt with nessler.s reagent
`NH_(4)NO_(3)overset(Delta)rarrN_(2)O+2H_(2)O`
`NH_4^(+)+NO_(3)^(Theta)impliesNO_(3)^(Theta)` gives +ve test with for brown ring test
(R) `(N_(4))_(3)PO_(4) rarr 3NH_(4)^(+)+PO_(4)^(3-)` water soluble , gives brown ppt with nessler.s reagent
`PO_(4)^(3-)` gives yellow ppt with ammonium molybdate
`HPO_(4)^(2-)+3NH_(4)^(+)+12MoO_(4^(-2)+23H^(+)rarr(NH_4)_(3)underset("yellow")([PMo_(12)O_(40)]darr)12H_2O`
(S) `(NH_4)_(2)SO_(4)rarar 2NH_(4)^(+)+SO_(4)^(2)` water soluble gives test with nessler.s reagent
`BaCl_(2)+SO_(4)^(2-)rarrunderset("white ppt")(BaSO_(4))+2Cl^(Theta)`
`{:((NH_4)_2Cr_(2)O_(7)overset(Delta)rarrN_(2)+4H_(2)O+Cr_(2)O_3,),(darr,),(2NH_(4)^(+)+Cr_(2)O_(7)^(2-),),((T) uarr,(U)(NH_(4))_(2)HPO_(3)rarr2NH_(4)^(+)+HPO_(3)^(2-)),("Gives Brown ppt",uarr),("with"k_(2)[HeI_4],"Gives Brown ppt with"),(,K2[HrI_4]):}`