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STD 12 - 1. relation and function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 1. relation and function4 Marks
MCQ
If $x = {\log _2}\left( {\sqrt {56 + \sqrt {56 + \sqrt {56 +  .... + \infty } } } } \right)$ then 
  • A
    $x < 0$
  • B
    $0 < x < 2$
  • ✓
    $2 < x < 4$
  • D
    $3 < x < 4$
✓

Answer

Correct option: C.
$2 < x < 4$
c
$x=\log _2(\sqrt{56+\sqrt{56+\ldots \infty}})$

het $t=\sqrt{56+t}$

$t^2-t-56=0$

$(t+7)(t-8)=0$

$t=8,-7 \quad$ [log can't be negative]

$\therefore x=\log _2 8$

$\therefore x=3$ (c)

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