`{:(List-I,List-II),((A)"Energy",(1)(2pize^(2))/(nh)),((B)"Velocity",(2)(-2pi^(2)mz^(2)e^(4))/(n^(2)h^(2))),((C)"Rydberg constant",(3)(2pi^(2)mz^(2)e^(4))/(h^(3)c)),((D)"Radius",(4)(n^(2)h^(2))/(4pi^(2)mze^(2))),(,(5)(-4pi^(2)mz^(2)e^(4))/(n^(2)h^(2))):}`
The correct match is

Identify the correctly matched set from the following lists {:(,"List - A",,"List - B",),((I),"Energy",(a),(2pi z e^(2))/(nh),),((II),"Velocity",(b),-(2pi^(2)m z^(2)e^(4))/(n^(2)h^(2)),),((III),"Rydberg constant",(c),(2pi^(2)m z^(2)e^(4))/(h^(3)c),),((IV),"Radius",(d),(n^(2)h^(2))/(4pi^(2)m z e^(2)),),(,,(e),-(4pi^(2) m z^(2)e^(4))/(n^(2)h^(2)),):}

Observe the following lists. {:("LIST - I","LIST - II"),((A) 8^(th)" term of log"_(e)^(2) " is",(1)log((n+1)/(n-1))),((B)7^(th)" term of log"_(e )(5//4)" is",(2)(-1)/(8)),((C )n^(th)" term of log"_(e )(3//2)" is",(3)(1)/(7.4^(7))),((D)(2)/(n^(2)+1)+(1)/(3)((2n)/(n^(2)+1))^(3)+.....,(4)( (-1)^(n-1))/(n.2^(n))):} The correct match for List-I from List-II is

Range of tan^(-1)((2x)/(1+x^(2))) is (a) [-(pi)/(4),(pi)/(4)] (b) (-(pi)/(2),(pi)/(2))(c)(-(pi)/(2),(pi)/(4)) (d) [(pi)/(4),(pi)/(2)]

4sin ((pi) / (6)) sin ^ (2) ((pi) / (3)) + 3cos ((pi) / (3)) tan ((pi) / (4)) + cos e ^ ( 2) ((pi) / (2)) = 2sec ^ (2) ((pi) / (4))

{:("LIST - 1","LIST - 2"),("A) "H_(2)SO_(4),"1) "+4),("B) "H_(2)(S)_(n)O_(6),"2) "+3),("C) "H_(2)SO_(3),"3) "+2"," -2),("D) "H_(2)SO_(3),"4) "+6),(,"5) "+5","0):} The correct match is

{:("LIST - 1","LIST - 2"),("A) "4NH_(3)+5O_(2)rarr,"1) "PbO+NO_(2)+O_(2)),("B) "P_(4)+3NaOH+3H_(2)Orarr,"2) "N_(2)O+H_(2)O),("C) "NH_(4)NO_(3)rarr,"3) "N_(2)O_(5)+H_(2)O),("D) "Pb(NO_(c))_(2)overset(Delta)rarr,"4) "4NO+6H_(2)O),(,"5) "3NaH_(2)PO_(2)+PH_(3)):} The correct match is