jee-main 2021 Q76

jee-main · India · session2_17mar_shift1 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution
Which of the following statement is correct for the function $g ( \alpha )$ for $\alpha \in R$ such that $g ( \alpha ) = \int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 3 } } \frac { \sin ^ { \alpha } x } { \cos ^ { \alpha } x + \sin ^ { \alpha } x } d x$
(1) $g ( \alpha )$ is a strictly increasing function
(2) $g ( \alpha )$ has an inflection point at $\alpha = - \frac { 1 } { 2 }$
(3) $g ( \alpha )$ is a strictly decreasing function
(4) $g ( \alpha )$ is an even function
Which of the following statement is correct for the function $g ( \alpha )$ for $\alpha \in R$ such that $g ( \alpha ) = \int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 3 } } \frac { \sin ^ { \alpha } x } { \cos ^ { \alpha } x + \sin ^ { \alpha } x } d x$\\
(1) $g ( \alpha )$ is a strictly increasing function\\
(2) $g ( \alpha )$ has an inflection point at $\alpha = - \frac { 1 } { 2 }$\\
(3) $g ( \alpha )$ is a strictly decreasing function\\
(4) $g ( \alpha )$ is an even function