Question

Let $p$ be the number of positive integral values which are not contained in the set of values of ' $a$ '. Such that function $f :[-3,3]-\left\{\frac{\pi}{2}\right\} \rightarrow$ Rdefined by $f ( x )=\tan (\sin (\sin x ))+\left[\frac{( x -2)^2}{ a }\right]$ is an odd function. Then the value of $\left[\frac{ p -3}{7}\right]$, is
[Note : $[ k ]$ denotes greatest integer less than or equal to $k$.]

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

$ f ( x )=- f (- x ) $
$\Rightarrow\left[\frac{( x -2)^2}{ a }\right]=0 \forall x \in[-3,3] $
$\Rightarrow ( x -2)^2 \in[0,25] $
$\text { for }\left[\frac{( x -2)^2}{ a }\right]=0 \forall x \in[-3,3], a \in(25, \infty) $
$\Rightarrow p =25$
$\Rightarrow \left[\frac{25-3}{7}\right]=\left[\frac{22}{7}\right]=3 $