jee-main 2024 Q82

jee-main · India · session2_06apr_shift2 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients

If $\mathrm { S } ( x ) = ( 1 + x ) + 2 ( 1 + x ) ^ { 2 } + 3 ( 1 + x ) ^ { 3 } + \cdots + 60 ( 1 + x ) ^ { 60 } , x \neq 0$, and $( 60 ) ^ { 2 } \mathrm {~S} ( 60 ) = \mathrm { a } ( \mathrm { b } ) ^ { \mathrm { b } } + \mathrm { b }$, where $a , b \in N$, then $( a + b )$ equal to $\_\_\_\_$

If $\mathrm { S } ( x ) = ( 1 + x ) + 2 ( 1 + x ) ^ { 2 } + 3 ( 1 + x ) ^ { 3 } + \cdots + 60 ( 1 + x ) ^ { 60 } , x \neq 0$, and $( 60 ) ^ { 2 } \mathrm {~S} ( 60 ) = \mathrm { a } ( \mathrm { b } ) ^ { \mathrm { b } } + \mathrm { b }$, where $a , b \in N$, then $( a + b )$ equal to $\_\_\_\_$

Paper Questions

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