Match List I with List II

Choose the correct answer from the options given below:

Correct option is C

Solution:
Series (a) 2,9,28,65,126 ….
The series can be decoded as:
$$2 = 1^3 +1$$​
$$9= 2^3+1$$​
$$28 = 3^3+1$$​
$$65 =4^3+1$$​
$$126= 5^3+1$$​
Next term in the series is $$6^3+1 =217$$​
Series(b) 2,10,30,68,130….
$$2 = 1^3 +1$$​
$$10= 2^3+2$$​
$$30 = 3^3+3$$​
$$68 =4^3+4$$​
$$130= 5^3+5$$​
Next term in the series is $$6^3+6$$​= 216+6 =222
Series(c): 3,4,11,30,67,128…
The series can be decoded as:
$$3= 0^3+3$$​
$$4=1^3+3$$​
$$11=2^3+3$$​
$$30=3^3+3$$​
$$67=4^3+3$$​
$$128=5^3+3$$​
Next term in the series is:
$$6^3+3 = 216+3 =219$$​
Series(d) 5,12,31,68,129….
The series can be decoded as:
$$5= 1^3+4$$​
$$12=2^3+4$$​
$$31= 3^3+4$$​
$$68=4^3+4$$​
$$129=5^3+4$$​
Next term in the series:
$$6^3+4 = 216+4 =220$$​
Here (A) - (III) 217
(B)-(II) 222
(C)-(IV)219
(D)(I) 220
Hence option(c) is correct