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Model Paper 4 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 41 Mark
MCQ
$\sum_{r=0}^n 4^r \cdot{ }^n C_r$ is equal to
  • A
    $6^{ n }$
  • B
    $5^{-n}$
  • C
    $4^{ n }$
  • ✓
    $5^n$
✓

Answer

Correct option: D.
$5^n$
$\sum^n 4^r \cdot{ }^n C_r=4^0 \cdot{ }^n C_0+4^1 \cdot{ }^n C_1+4^2 \cdot{ }^n C_2+\ldots+4^n \cdot{ }^n C_n$
$=1+4 \cdot{ }^n C_1+4^2 \cdot{ }^n C_2+\ldots .+4^n \cdot{ }^n C_n$
$=(1+4)^{ n }$
$=5^{ n }$

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