List-I (Evolutionary Processes) | List-II (Example) |
(A) Divergent evolution | (I) Wings of butterfly and birds |
(B) Convergent evolution | (II) Lemur and spotted cuscus |
(C) Anthropogenic evolution | (III) Hearts of vertebrates |
(D) Adaptive Radiation | (IV) Antibiotic resistant microbes |
If
\[ A = \{ P(\alpha, \beta) \mid \text{the tangent drawn at P to the curve } y^3 - 3xy + 2 = 0 \text{ is a horizontal line} \} \]
and
\[ B = \{ Q(a, b) \mid \text{the tangent drawn at Q to the curve } y^3 - 3xy + 2 = 0 \text{ is a vertical line} \} \]
then \( n(A) + n(B) = \)
If Rolle's Theorem is applicable for the function:
\[ f(x) = \begin{cases} x^p \log x, & x \neq 0 \\ 0, & x = 0 \end{cases} \]
on the interval \([0,1]\), then a possible value of \( p \) is: