A region in the x-y plane is bounded by the curve y=25−x2 and the line y =0 If the point (a, a+ 1) lies in the interior of the region then,

# A region in the x-y plane is bounded by the curve $\mathrm{y}=\sqrt{25-{\mathrm{x}}^{2}}$ and the line y =0 If the point (a, a+ 1) lies in the interior of the region then,

1. A

$\mathrm{a}\in \left(-4,3\right)$

2. B

$\mathrm{a}\in \left(-\mathrm{\infty },-1\right)\in \left(3,\mathrm{\infty }\right)$

3. C

$\mathrm{a}\in \left(-1,3\right)$

4. D

none of these

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### Solution:

bound the semicircle above the x-axis. Therefore,
$\mathrm{a}+1>0$…………(i)
and
or ${\mathrm{a}}^{2}+\mathrm{a}-12<0$
or  $-4<\mathrm{a}<3$ …….(ii)
From (i) and (ii),
$-1<\mathrm{a}<3$

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