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Model Paper 6 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 61 Mark
MCQ
$\left\{C_0+3 C_1+5 C_2+\ldots+(2 n+1) C_n\right\}=?$
  • A
    $( n -2) . 2^{ n -2}$
  • B
    $( n -1)( n +2)$
  • C
    $( n +2) . 2^{ n -1}$
  • ✓
    $(n+1) 2^n$
✓

Answer

Correct option: D.
$(n+1) 2^n$
We have, $C _0+3 C _1+5 C _2+\ldots+(2 n +1) C _{ n }$
$=\left(C_0+C_1+C_2+\ldots+C_n\right)+2\left(C_1+2 C_2+\ldots+n C_n\right)$
$=2^n+2\left(n \cdot 2^{n-1}\right)$
$=(n+1) \cdot 2^n$

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