In a code language, 'CUTE' is written as 'FQWA', and 'BLUE' is written as 'EHXA'. How will 'VOTE' be written in that language?

Let's determine the pattern by looking at the alphabetical position changes:
For **CUTE $\to$ FQWA**:

* $\text{C}(3)+3=\text{F}(6)$
* $\text{U}(21)-4=\text{Q}(17)$
* $\text{T}(20)+3=\text{W}(23)$
* $\text{E}(5)-4=\text{A}(1)$

For **BLUE $\to$ EHXA**:

* $\text{B}(2)+3=\text{E}(5)$
* $\text{L}(12)-4=\text{H}(8)$
* $\text{U}(21)+3=\text{X}(24)$
* $\text{E}(5)-4=\text{A}(1)$

The pattern followed is alternating $+3$ and $-4$.

Applying the same logic to VOTE:

* $\text{V}(22)+3=\text{Y}(25)$
* $\text{O}(15)-4=\text{K}(11)$
* $\text{T}(20)+3=\text{W}(23)$
* $\text{E}(5)-4=\text{A}(1)$

Thus, 'VOTE' is coded as YKWA.