Algebra
Binomial
MMTS_Full_Test_01
Grade 12
Question:
If the coefficient of $x^{10}$ in $(ax^2+\frac{1}{bx})^{11}$ is equal to the coefficient of $x^{-10}$ in $(ax-\frac{1}{bx^2})^{11}$, then $a\cdot b$ is
$-1$
0
$1$
Cannot be determined
Step-by-Step Solution
Key Concept: General term of $(ax^2+1/(bx))^{11}$: $\binom{11}{r}(ax^2)^{11-r}(1/bx)^r$
Coeff 1: $\binom{11}{4}a^7/b^4$. Coeff 2: $\binom{11}{7}a^4/b^7$. Equal: $a^7/b^4=a^4/b^7\Rightarrow a^3=b^{-3}\Rightarrow ab=1$ or $a^3b^3=1\Rightarrow ab=1$.
Correct Answer: 3