This is an interesting (read tricky!) variation of Rydberg Eqn calculation. 
Rydberg Eqn: 1/λ = R [1/n1^2 - 1/n2^2] 
Where λ is the wavelength of the light; 1282.17 nm = 1282.17×10^-9 m 
R is the Rydberg constant: R = 1.09737×10^7 m-1 
n2 = 5 (emission) 
Hence 1/(1282.17 ×10^-9) = 1.09737× 10^7 [1/n1^2 – 1/25^2] 
Some rearranging and collecting up terms: 
1 = (1282.17 ×10^-9) (1.09737× 10^7)[1/n2 -1/25] 
1= 14.07[1/n^2 – 1/25] 
1 =14.07/n^2 – (14.07/25) 
14.07n^2 = 1 + 0.5628 
n = √(14.07/1.5628) = 3
        
                    
             
        
        
        
Usually nice weather , i dont know the answer to the second part                                                                                       
        
             
        
        
        
Is this a true and false question?
        
             
        
        
        
Answer:
The sphere C carries no net charge.
Explanation:
- When brougth close to the charged sphere A, as charges can move freely in  a conductor, a charge equal and opposite to the one on the sphere A, appears on the sphere B surface facing to the sphere A. 
- As sphere B must remain neutral (due to the principle of conservation of charge) an equal charge, but of opposite sign, goes to the surface also, on the opposite part of the sphere.
- If sphere A is removed, a charge movement happens in the sphere B, in such a way, that no net charge remains on the surface.
- If in such state, if  the sphere B (assumed again uncharged completely, without any local charges on the surface), is touched by an initially uncharged sphere C, due to the conservation of  charge principle, no net  charge can be built on sphere C.