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BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
MCQ
In the expansion of $(1+x)^n \cdot(1+y)^n \cdot(1+z)^n$ the sum of the coefficients of the terms of degree $r$ is:
 
  • A
    $\left({ }^n \mathrm{C}_r\right)^3$
  • ✓
    ${ }^{3 n} \mathrm{C}_{\mathrm{r}}$
  • C
    ${ }^{3 \times n} C_r$
  • D
    ${ }^n \mathrm{C}_{3 \mathrm{r}}$
✓

Answer

Correct option: B.
${ }^{3 n} \mathrm{C}_{\mathrm{r}}$
  1. ${ }^{3 n} \mathrm{C}_{\mathrm{r}}$
Solution:
The given expression contains 3n factors
Using combination to choose r brackets out of 3n brackets for a term of degree r, we get
${ }^{3 n} \mathrm{C}_{\mathrm{r}}$

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