jee-main 2016 Q80

jee-main · India · 10apr Curve Sketching Finding Parameters for Continuity

Let $a , b \in R , ( a \neq 0 )$. If the function $f$, defined as $$f ( x ) = \left\{ \begin{array} { c } \frac { 2 x ^ { 2 } } { a } , 0 \leq x < 1 \\ a , 1 \leq x < \sqrt { 2 } \\ \frac { 2 b ^ { 2 } - 4 b } { x ^ { 3 } } , \sqrt { 2 } \leq x < 8 \end{array} \right.$$ is continuous in the interval $[ 0 , \infty )$, then an ordered pair $( a , b )$ can be
(1) $( - \sqrt { 2 } , 1 - \sqrt { 3 } )$
(2) $( \sqrt { 2 } , - 1 + \sqrt { 3 } )$
(3) $( \sqrt { 2 } , 1 - \sqrt { 3 } )$
(4) $( - \sqrt { 2 } , 1 + \sqrt { 3 } )$

Let $a , b \in R , ( a \neq 0 )$. If the function $f$, defined as
$$f ( x ) = \left\{ \begin{array} { c } \frac { 2 x ^ { 2 } } { a } , 0 \leq x < 1 \\ a , 1 \leq x < \sqrt { 2 } \\ \frac { 2 b ^ { 2 } - 4 b } { x ^ { 3 } } , \sqrt { 2 } \leq x < 8 \end{array} \right.$$
is continuous in the interval $[ 0 , \infty )$, then an ordered pair $( a , b )$ can be\\
(1) $( - \sqrt { 2 } , 1 - \sqrt { 3 } )$\\
(2) $( \sqrt { 2 } , - 1 + \sqrt { 3 } )$\\
(3) $( \sqrt { 2 } , 1 - \sqrt { 3 } )$\\
(4) $( - \sqrt { 2 } , 1 + \sqrt { 3 } )$

Paper Questions

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