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Solution


Q.

The least value of n for which the number of integral terms in the Binomial expansion of (73+1112)n is 183, is :          [2025]
1 2148  
2 2184  
3 2196  
4 2172  

Ans.

(2)

General term = Crn(71/3)n–r(111/12)r

                      = Crn(7)n–r3(11)r/12

For integral terms, r must be multiple of 12

∴   r = 12k, k = 0, 1, 2, .....

Total number of values of r = 183

Hence, max r = 12(182) = 2184

Minimum value of n = 2184.