jee-main 2024 Q70

jee-main · India · session2_08apr_shift1 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions

For the function $f ( x ) = ( \cos x ) - x + 1 , x \in \mathbb { R }$, between the following two statements (S1) $f ( x ) = 0$ for only one value of $x$ in $[ 0 , \pi ]$. (S2) $f ( x )$ is decreasing in $\left[ 0 , \frac { \pi } { 2 } \right]$ and increasing in $\left[ \frac { \pi } { 2 } , \pi \right]$.
(1) Both (S1) and (S2) are correct.
(2) Both (S1) and (S2) are incorrect.
(3) Only (S2) is correct.
(4) Only (S1) is correct.

For the function $f ( x ) = ( \cos x ) - x + 1 , x \in \mathbb { R }$, between the following two statements (S1) $f ( x ) = 0$ for only one value of $x$ in $[ 0 , \pi ]$. (S2) $f ( x )$ is decreasing in $\left[ 0 , \frac { \pi } { 2 } \right]$ and increasing in $\left[ \frac { \pi } { 2 } , \pi \right]$.\\
(1) Both (S1) and (S2) are correct.\\
(2) Both (S1) and (S2) are incorrect.\\
(3) Only (S2) is correct.\\
(4) Only (S1) is correct.

Paper Questions

Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76 Q77 Q78 Q79 Q80 Q81 Q82 Q83 Q84 Q85 Q86 Q87 Q88 Q89 Q90