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Will the answers be :

(a) $x:$Any person

$C(x) :$Cricketer

$A(x):$Admired by others

So $\exists x C(x) \land \forall x A(x)$ 

(b) $x:$Any person

$S(x) :$Student

$A(x):$got an A grade in AI course

$F(x) $ : Friend

So $ \forall x (S(x) ) \implies \exists x (F(x) \land A(x)) $ 

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The Question seems Incomplete and Not Self-Contained. So, I will answer it with some details altered/added. 

Domain has already been given All the Persons in the Universe. 

1. There exists a Cricketer whom Everyone admires.

Let some Predicates be defined as follows :

$A\left ( x,y \right ) = $ $x$ is Admired by $y$ 

There exists a Cricketer whom Everyone admires  = $\exists _x\left ( C\left ( x \right ) \wedge \forall _y\left ( A\left ( x,y \right ) \right ) \right )$


2. Every Student has a friend (also Student) who got an A grade in the AI course.

Let some Predicates be defined as follows :

$F\left ( x,y \right ) =$ $x$ and $y$ are friends.

$A\left ( x \right ) =$ $x$ got an A grade in AI course

Every Student has a friend (Student) who got an A grade in the AI course  = $\forall_x\left ( S\left ( x \right ) \rightarrow \exists_y\left ( S\left ( y \right ) \wedge \left ( x\neq y \right ) \wedge F(x,y) \wedge A\left ( y \right ) \right )\right )$

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