Question

Assertion :$\underset{x\to 1}{lim}\frac{x^{15}-1}{x^{10}-1}=\frac{3}{2}$ Reason: $\underset{x\to a}{lim}\frac{x^n-a^n}{x-a}=n{a}^{n-1}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\frac{\underset{x\to 1}{lim}\frac{x^{15}-1}{x-1}}{\underset{x\to 1}{lim}\frac{x^{10}-1}{x-1}}=\frac{15{\left(1\right)}^{14}}{10{\left(1\right)}^9}$ (Applying Reason)

$=\frac{3}{2}$
Hence, option 'A' is correct.