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BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
MCQ
${ }^{(n+1)} C_1+{ }^{(n+1)} C_2+{ }^{(n+1)} C_3+\ldots . .+{ }^{(n+1)} C_n=$
  • A
    $2\left(2^n+1\right)$
  • ✓
    $2\left(2^n-1\right)$
  • C
    $2^{n+1}$
  • D
    $\left(2^{\mathrm{n}+1}-1\right)$
✓

Answer

Correct option: B.
$2\left(2^n-1\right)$
  1. $2\left(2^n-1\right)$
Solution
As in the hint required expression $+{ }^{n+1} C_0+{ }^{n+1} C_{n+1}=2^{n+1}$
$\Rightarrow$ required. expression $=2^{n+1}-2=2\left(2^n-1\right)$

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