Event E : Card drawn is king or queen
Event F : Card drawn is queen or jack
Independent event : We say two events are independent if happening of one , doesn't effect the chances of happening of other. Like if India's capital is place X , you will drink milk :) funny :) they are independent i suppose.
another example is You throw a dice , every time 6 possibilities are there and they are independent , if this time 4 came , then in next throw , any thing can come.
Now come to your question.
There if you replace the card after outcome , they are Independent
If you don't replace , and put that card with you and choose one out of remaining cards , both event can never be independent.
In mathematical terms you say two Event E,F are independent iff P(E/F)=P(E)
which you can see P(K/Q)=8/52 P(Q/J)=8/52
BUt if you don't place outcome of event E and if outcome is K then P(Q/J)=8/51 and if outcome of event E is Queen then P(Q/J)=7/51