Q61 / 155 · WBJEE 2020 · Mathematics

If $\mathrm{c}_{0}, \mathrm{c}_{1}, \mathrm{c}_{2}, \ldots \ldots \mathrm{c}{15}$ are the Binomial co-efficients in the expansion of $(1+\mathrm{x})^{15}$, then the value of $\frac{\mathrm{C}{1}}{\mathrm{c}{0}}+2 \frac{\mathrm{C}{2}}{\mathrm{c}{1}}+3 \frac{\mathrm{c}{3}}{\mathrm{c}{2}}+\ldots \ldots+15 \frac{\mathrm{c}{15}}{\mathrm{c}{14}}$ is

  • A
    1240
  • Correct answer
    B
    120
  • C
    124
  • D
    140

Solution

Hint: $S_{n}=\sum_{r=1}^{15} r \frac{{ }^{15} C_{r}}{{ }^{15} c_{r-1}}=\sum_{r=1}^{15}(15-r+1)=16 \times 15-\frac{15 \times 16}{2}=120$

Hence, the correct answer is option: 'B'.

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