Doubt from electromagnetic wave

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Q23
Answer is a

Option c and d is straightforward incorrect,
For option a, there is k in amplitude, can we say that option a is incoorect due to this presence of k?
The book I am referring further do anothet analysis to tell why option a is incorrect
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Is this analysis necessary or can say that presence of k makes option a incorrect

Answer is b, wrote a by mistake

Also can anyone explain what they have done in solution something related to travelling wave

Presence of k doesn't make any sense as they have not defined any k. We can't treat it as unit vector as sign of unit vector is also not present in k.