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Model Paper 5 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 51 Mark
MCQ
$\sum_{r=0}^n 4^r \cdot{ }^n C_r$ is equal to
  • A
    $6^{ n }$
  • B
    $5^{-n}$
  • C
    $4^{ n }$
  • D
    $5^{ n }$
✓

Answer

(d) $5^{ n }$
Explanation: $\sum_{r=0}^n 4^{r \cdot n} C_r=4^0 \cdot{ }^n C_0+4^1 \cdot{ }^n C_1+4^2 \cdot{ }^n C_2+\ldots+4^n \cdot{ }^n C_n$
$\begin{array}{l}=1+4 \cdot^n C_1+4^2 \cdot{ }^n C_2+\ldots .+4^n \cdot{ }^n C_n \\ =(1+4)^n=5^n\end{array}$

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