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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem1 Mark
MCQ
${ }^{15} C_3+{ }^{15} C_5+\ldots .+{ }^{15} C_{15}$ will be equal to:
  • A
    $2^{14}$
  • ✓
    $2^{14}- 15$
  • C
    $2^{14}+ 15$
  • D
    $2^{14}− 1$
✓

Answer

Correct option: B.
$2^{14}- 15$
We know
$ { }^{15} C_1+{ }^{15} C_3+{ }^{15} C_5+\ldots{ }^{15} C_{15}=2^{15-1} $
$ \therefore{ }^{15} C_3+{ }^{15} C_5+\ldots+{ }^{15} C_{15}=2^{14}-15 $

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