Cuál query

Question

Could you please explain further why "cuál" is used instead of "qué" in these examples?

Ella quería saber cuáles eran mis intenciones.
Debes preguntar al médico cuáles son los efectos secundarios de las pastillas.

Answer

Hola R
Here, cuál is used in an indirect interrogative sentence. You can see a question inside that sentence "¿cuáles eran tus intenciones?". If we have this as a reference, it is easier to see the use of cuál and qué.
Cuál used with the verb ser is asking for a specific answer; for example: "Mis intenciones eran x and y."
When we use qué with the verb ser in questions, we are expecting a definition of something, so it wouldn't make sense to ask ¿qué eran tus intenciones? because the answer is not going to be a definition of what "mis intenciones" mean. 
Here are other more simple examples using qué and cuál:
1. ¿Qué es el COVID-19? What is COVID-19?
El COVID-19 es una enfermedad causada por un virus que..... (definition)
COVID-19 is a disease caused by a virus that...
2. ¿Cuál es el principal síntoma del COVID-19? Which is the main symptom of COVID-19?
El síntoma principal del COVID-19  es la fiebre alta.  (specific answer)
The main symptom of COVID-19 is a high temperature.
Un saludo
Inma

Answer

I'm still wondering about indirect questions. So, when you are asking for a list of things -- like one's intentions toward someone's daughter -- you always use "cuáles"? even if the list has only one item. for instance, the father suspects me of wanting to kiss his daughter, and he wants info on that subject-- he would use "cuáles."; but if you said, in a psychology class, "I want to know what an intention is"--then you'd use "que"?