jee-main 2012 Q68

jee-main · India · 07may Straight Lines & Coordinate Geometry Collinearity and Concurrency

The point of intersection of the lines $\left( a ^ { 3 } + 3 \right) x + a y + a - 3 = 0$ and $\left( a ^ { 5 } + 2 \right) x + ( a + 2 ) y + 2 a + 3 = 0$ (a real) lies on the $y$-axis for
(1) no value of $a$
(2) more than two values of $a$
(3) exactly one value of $a$
(4) exactly two values of $a$

The point of intersection of the lines $\left( a ^ { 3 } + 3 \right) x + a y + a - 3 = 0$ and $\left( a ^ { 5 } + 2 \right) x + ( a + 2 ) y + 2 a + 3 = 0$ (a real) lies on the $y$-axis for\\
(1) no value of $a$\\
(2) more than two values of $a$\\
(3) exactly one value of $a$\\
(4) exactly two values of $a$

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