​A B D PLZZZZZ

Dear student,
as you are asking for multiple question.
so i suggest you to ask these questions seprately.
here i am answering its A part only.
let $y=\frac{{x}^{2}+2x+4}{x+2}$
$⇒y\left(x+2\right)={x}^{2}+2x+4$
$⇒yx+2y={x}^{2}+2x+4$
${x}^{2}+x\left(2-y\right)+\left(4-2y\right)=0$
since x is real so its Discriminent must be non-negative.
i.e ${B}^{2}-4AC\ge 0$
or $\left(2-y{\right)}^{2}-4\left(4-2y\right)\ge 0$
or ${y}^{2}+4y-12\ge 0$
or ​${y}^{2}+6y-2y-12\ge 0$
or $\left(y+6\right)\left(y-2\right)\ge 0$

$⇒$minimum value of y will be 2

enjoy

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(A) is R
(B) is P
(D) is Q

this is not log topic this is iit jee matrix topic
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