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AIEEE 2012

JEE Main 2012 Mathematics question on Limits Continuity and Differentiability

Let α(a)\alpha(a) and β(a)\beta(a) be the roots of the equation (1+a3−1)x2−(1+a−1)x+(1+a6−1)=0(\sqrt[3]{1+a}-1)x^2-(\sqrt{1+a}-1)x+(\sqrt[6]{1+a}-1)=0, where a>−1a>-1. Then lim⁡a→0+α(a)\lim_{a\to 0^+}\alpha(a) and lim⁡a→0+β(a)\lim_{a\to 0^+}\beta(a) are
  1. A.
    −52-\dfrac{5}{2} and 11
  2. B.
    −12-\dfrac{1}{2} and −1-1
  3. C.
    −72-\dfrac{7}{2} and 22
  4. D.
    −92-\dfrac{9}{2} and 33
Show answer

Correct option: B

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