jee-advanced 2015 Q56

jee-advanced · India · paper2 Indefinite & Definite Integrals Integral Inequalities and Limit of Integral Sequences

Let $f ^ { \prime } ( x ) = \frac { 192 x ^ { 3 } } { 2 + \sin ^ { 4 } \pi x }$ for all $x \in \mathbb { R }$ with $f \left( \frac { 1 } { 2 } \right) = 0$. If $m \leq \int _ { 1 / 2 } ^ { 1 } f ( x ) d x \leq M$, then the possible values of $m$ and $M$ are
(A) $m = 13 , M = 24$
(B) $\quad m = \frac { 1 } { 4 } , M = \frac { 1 } { 2 }$
(C) $m = - 11 , M = 0$
(D) $m = 1 , M = 12$

Let $f ^ { \prime } ( x ) = \frac { 192 x ^ { 3 } } { 2 + \sin ^ { 4 } \pi x }$ for all $x \in \mathbb { R }$ with $f \left( \frac { 1 } { 2 } \right) = 0$. If $m \leq \int _ { 1 / 2 } ^ { 1 } f ( x ) d x \leq M$, then the possible values of $m$ and $M$ are\\
(A) $m = 13 , M = 24$\\
(B) $\quad m = \frac { 1 } { 4 } , M = \frac { 1 } { 2 }$\\
(C) $m = - 11 , M = 0$\\
(D) $m = 1 , M = 12$

Paper Questions

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