Aayush, from what you've said it would appear that this young woman would be a great person to have as a friend, but that she is not the right person for you to get romantically involved with.
We can all have different definitions of what intelligence is. An unsupervised, untimed intelligence test means almost nothing in terms of how intelligent someone is. An official, timed and supervised test is - according to my definitions - a great test of intelligence and possibly the only real indication of how intelligent someone is.
This in the same way that a measure of someone's stamina is how quickly they can finish a marathon or a Tour de France mountain stage or a tri-athlon.
Being able to maintain an intellectual conversation might just be an indication of how pretentious someone is. Or how good they are at repeating sound bytes that they may not understand, or how well educated or experienced or interested they are on a particular subject. You may also have a highly intelligent person that is shy or that in a given situation prefers to keep their thoughts to themselves. Or a highly intelligent person that hasn't been educated in a particular subject or range of subjects.
It's possible that you are a lot more intelligent than you think Aayush. Have you ever taken a test?
One big tip about the having conversation thing is: don't worry too much about having conversations. You can focus on doing things together instead.
Like playing pool down the pub, or a couple of sets of tennis, or a round of golf, or going to a tourist attraction, or swimming in the sea, or going for a picnic, or coming home from uni or work and eating together and then making love. For sure it's great to have a chat over a pint or whilst sitting round the supper table, but it doesn't have to be about anything intellectual. It could be about sex, or relationships or about some funny anecdotes that happened in the past.