JEE Main 2004Annual, Paper 1MathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002If Sn=∑r=0n1nCr and tn=∑r=0nrnCr, {S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}},\,}Sn=r=0∑nnCr1andtn=r=0∑nnCrr,then tnSn{{{t_{ n}}} \over {{S_n}}}Sntn is equal toAOption A. 2n−12{{2n - 1} \over 2}22n−1BOption B. 12n−1{1 \over 2}n - 121n−1COption C. n - 1DOption D. 12n{1 \over 2}n21nCheckSkip · show solution
