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a)$2 \theta \leq \cos^{-1} (2 \mu)$
b)$2 \theta \leq \sin ^{-1}(2 \mu)$
c)$ 2 \theta \leq \tan ^{-1} (\mu/2)$
d)$ \theta \leq \tan^{-1}\mu$

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The bodies slide down with out slipping

So the acceleration of bodies A and B is along the incline=a

$a=g \sin \theta$

Vertical component of a ie $a_v=a \sin \theta$

and horizontal component of a $a_H=a \cos \theta$

$a_H=g \sin \theta \cos \theta $

$a_v=g \sin ^2 \theta$

Normal reaction between A and B =V

$mg-N=ma_v$

$N=mg-ma_v$

$\quad=mg-mg \sin^2\theta$

$N=mg \cos ^2 \theta$

Now for B not slipping from A

frictional force $f \geq ma_H$

$\mu N \geq ma_H$

$\mu mg \cos^2 \theta \geq mg \cos \theta \sin \theta $

$\mu \geq \tan \theta$

$ \theta \leq \tan^{-1} \mu$

Hence d is the correct answer

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