In a code language, ‘COOL’ is written as ‘EMQJ’, and ‘CARD’ is written as ‘EYTB’. How will ‘STAR’ be written in that language?

Let's study the logical shift pattern between letters of the word and its corresponding code using alphabetical positions:
For 'COOL' $\to$ 'EMQJ':

* C (3) $\stackrel{+2}{\to }$ E (5)
* O (15) $\stackrel{-2}{\to }$ M (13)
* O (15) $\stackrel{+2}{\to }$ Q (17)
* L (12) $\stackrel{-2}{\to }$ J (10)
The pattern is an alternating addition and subtraction: $+2,-2,+2,-2$.

Let's check 'CARD' $\to$ 'EYTB':

* C (3) $\stackrel{+2}{\to }$ E (5)
* A (1) $\stackrel{-2}{\to }$ Y (25) (since $1-2=-1\equiv 25$)
* R (18) $\stackrel{+2}{\to }$ T (20)
* D (4) $\stackrel{-2}{\to }$ B (2)

Applying the same pattern to 'STAR':

* S (19) $\stackrel{+2}{\to }$ U (21)
* T (20) $\stackrel{-2}{\to }$ R (18)
* A (1) $\stackrel{+2}{\to }$ C (3)
* R (18) $\stackrel{-2}{\to }$ P (16)

Thus, 'STAR' is written as URCP.