jee-main 2024 Q66

jee-main · India · session1_27jan_shift2 Inequalities Solve Polynomial/Rational Inequality for Solution Set

Let $R$ be the interior region between the lines $3 x - y + 1 = 0$ and $x + 2 y - 5 = 0$ containing the origin. The set of all values of $a$, for which the points $\mathrm { a } ^ { 2 } , \mathrm { a } + 1$ lie in R , is :
(1) $( - 3 , - 1 ) \cup - \frac { 1 } { 3 } , 1$
(2) $( - 3,0 ) \cup \frac { 1 } { 3 } , 1$
(3) $( - 3,0 ) \cup \frac { 2 } { 3 } , 1$
(4) $( - 3 , - 1 ) \cup \frac { 1 } { 3 } , 1$

Let $R$ be the interior region between the lines $3 x - y + 1 = 0$ and $x + 2 y - 5 = 0$ containing the origin. The set of all values of $a$, for which the points $\mathrm { a } ^ { 2 } , \mathrm { a } + 1$ lie in R , is :\\
(1) $( - 3 , - 1 ) \cup - \frac { 1 } { 3 } , 1$\\
(2) $( - 3,0 ) \cup \frac { 1 } { 3 } , 1$\\
(3) $( - 3,0 ) \cup \frac { 2 } { 3 } , 1$\\
(4) $( - 3 , - 1 ) \cup \frac { 1 } { 3 } , 1$

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