jee-main 2021 Q76

jee-main · India · session3_20jul_shift2 First order differential equations (integrating factor)

Let $y = y ( x )$ satisfies the equation $\frac { d y } { d x } - | A | = 0$, for all $x > 0$, where $A = \left[ \begin{array} { c c c } y & \sin x & 1 \\ 0 & - 1 & 1 \\ 2 & 0 & \frac { 1 } { x } \end{array} \right]$. If $y ( \pi ) = \pi + 2$, then the value of $y \left( \frac { \pi } { 2 } \right)$ is:
(1) $\frac { \pi } { 2 } + \frac { 4 } { \pi }$
(2) $\frac { \pi } { 2 } - \frac { 1 } { \pi }$
(3) $\frac { 3 \pi } { 2 } - \frac { 1 } { \pi }$
(4) $\frac { \pi } { 2 } - \frac { 4 } { \pi }$

Let $y = y ( x )$ satisfies the equation $\frac { d y } { d x } - | A | = 0$, for all $x > 0$, where $A = \left[ \begin{array} { c c c } y & \sin x & 1 \\ 0 & - 1 & 1 \\ 2 & 0 & \frac { 1 } { x } \end{array} \right]$. If $y ( \pi ) = \pi + 2$, then the value of $y \left( \frac { \pi } { 2 } \right)$ is:\\
(1) $\frac { \pi } { 2 } + \frac { 4 } { \pi }$\\
(2) $\frac { \pi } { 2 } - \frac { 1 } { \pi }$\\
(3) $\frac { 3 \pi } { 2 } - \frac { 1 } { \pi }$\\
(4) $\frac { \pi } { 2 } - \frac { 4 } { \pi }$

Paper Questions

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