jee-advanced 2005 Q11

jee-advanced · India · screening Circles Optimization in a triangle

11. Tangent at a point of the ellipse $x ^ { 2 } / a ^ { 2 } + y ^ { 2 } / b ^ { 2 } = 1$ is drawn which cuts the coordinate axes at $A$ and $B$. The minimum area of the triangle $O A B$ is ( $O$ being the origin) :
(a) $a b$
(b) $\left( a ^ { 3 } + a b + b ^ { 3 } \right) / 3$
(c) $a ^ { 2 } + b ^ { 2 }$
(d) $\left( \left( a ^ { 2 } + b ^ { 2 } \right) \right) / 4$

A six faced fair dice is thrown until 1 shows. The probability that 1 comes at an even numbered trial is

11. Tangent at a point of the ellipse $x ^ { 2 } / a ^ { 2 } + y ^ { 2 } / b ^ { 2 } = 1$ is drawn which cuts the coordinate axes at $A$ and $B$. The minimum area of the triangle $O A B$ is ( $O$ being the origin) :\\
(a) $a b$\\
(b) $\left( a ^ { 3 } + a b + b ^ { 3 } \right) / 3$\\
(c) $a ^ { 2 } + b ^ { 2 }$\\
(d) $\left( \left( a ^ { 2 } + b ^ { 2 } \right) \right) / 4$\\

Paper Questions

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