jee-advanced 2011 Q45

jee-advanced · India · paper2 Exponential Equations & Modelling Evaluate Expression Given Exponential/Logarithmic Conditions
If $$\lim _ { x \rightarrow 0 } \left[ 1 + x \ln \left( 1 + b ^ { 2 } \right) \right] ^ { \frac { 1 } { x } } = 2 b \sin ^ { 2 } \theta , b > 0 \text { and } \theta \in ( - \pi , \pi ]$$ then the value of $\theta$ is
(A) $\pm \frac { \pi } { 4 }$
(B) $\pm \frac { \pi } { 3 }$
(C) $\pm \frac { \pi } { 6 }$
(D) $\pm \frac { \pi } { 2 }$ 
If
$$\lim _ { x \rightarrow 0 } \left[ 1 + x \ln \left( 1 + b ^ { 2 } \right) \right] ^ { \frac { 1 } { x } } = 2 b \sin ^ { 2 } \theta , b > 0 \text { and } \theta \in ( - \pi , \pi ]$$
then the value of $\theta$ is\\
(A) $\pm \frac { \pi } { 4 }$\\
(B) $\pm \frac { \pi } { 3 }$\\
(C) $\pm \frac { \pi } { 6 }$\\
(D) $\pm \frac { \pi } { 2 }$
Paper Questions
Q41 Q42 Q43 Q44 Q45 Q46 Q47 Q48 Q49