A) 18
B) 12
C) 10
D) 11
Correct Answer: D
Solution :
Case-1, \[c-5>0\] | ?(i) | |
\[f(0)>0\] | ||
\[c-4>0\] | ?(ii) | |
\[f(c)<0\] | ||
\[4(c-5)-4c+c-4<0\] | ||
\[c<24\] | ||
\[f(2)>0\] | ||
\[c-4>0\] | ||
\[9(c-5)-6c+c-4>0\] | ||
\[4c-49>0\]\[\Rightarrow \]\[c>\frac{49}{4}\] | ||
Here, (i) \[\cap \] (ii) \[\cap \] (iii) \[\cap \] (iv) | ||
\[c\in \left( \frac{49}{4},24 \right)\] | ||
Case-II, \[c-5<0\] | ?(i) | |
\[f(0)<0\] | ||
\[C>4\] | ?(ii) | |
\[f(2)>0\] \[\Rightarrow \] \[c<24\] | ?(iii) | |
\[f(3)<0\]\[\Rightarrow \]\[c<49\] | ?.(iv) | |
4 \[\Rightarrow \]\[c\in \phi \] | ||
\[c\in \left( \frac{49}{4},24 \right).\] | ||
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