jee-advanced 2015 Q54

jee-advanced · India · paper1 First order differential equations (integrating factor)

Let $y ( x )$ be a solution of the differential equation $\left( 1 + e ^ { x } \right) y ^ { \prime } + y e ^ { x } = 1$. If $y ( 0 ) = 2$, then which of the following statements is (are) true?
(A) $\quad y ( - 4 ) = 0$
(B) $\quad y ( - 2 ) = 0$
(C) $\quad y ( x )$ has a critical point in the interval $( - 1,0 )$
(D) $y ( x )$ has no critical point in the interval $( - 1,0 )$

Let $y ( x )$ be a solution of the differential equation $\left( 1 + e ^ { x } \right) y ^ { \prime } + y e ^ { x } = 1$. If $y ( 0 ) = 2$, then which of the following statements is (are) true?\\
(A) $\quad y ( - 4 ) = 0$\\
(B) $\quad y ( - 2 ) = 0$\\
(C) $\quad y ( x )$ has a critical point in the interval $( - 1,0 )$\\
(D) $y ( x )$ has no critical point in the interval $( - 1,0 )$

Paper Questions

Q41 Q42 Q43 Q44 Q45 Q46 Q47 Q48 Q49 Q50 Q51 Q52 Q53 Q54 Q55 Q56 Q57 Q58 Q59 Q60