What is both possible and impossible at the same time?

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?

Can you find the hidden mobile that is lost in the rug?

I have branches, but no fruit, trunk or leaves. What am I?

The owner of a popular clothing store comes up with his own method of pricing items. A vest costs $8, socks cost $10, a tie costs $6, and a blouse costs $12. Using the owner’s method, how much would a pair of underwear cost?

Why are televisions attracted to people?

12345 a famous South Indian actor
567 is a path in jumbled form
8 & 10 are same letters
9 is one among the first six alphabets.
WHO AM I?

One day Jenifer meets the Lion and the Tiger in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Tiger, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Jenifer:

Lion: Yesterday was one of my lying days.

Tiger: Yesterday was one of my lying days too.

What day is it?

A landlord calls both of his sons and tells them that their horses will now decide who will transfer the inheritance. He tells them to race along the land till the end and the one whose horse will be slower will win and be the heir to all the property.

Both of them keep wandering for days but to no result. Then they ask a wise man regarding it. The man advises them on the matter after which they jump on the horses and race as fast as they can till the end. Why did they do it?

What did the wise man say?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?