is the answer for the 1st one correct?? give reasons

Yeah the IUPAC name provided in the solution is correct.

First select the parent chain. Over here we have parent chain with four carbon atoms.

The numbering is done from left to right so that the double bond gets the lowest possible number.

In this case the position of the double bond is given number 1 and we have -Br group attached to fourth carbon atom.

So the IUPAC name of the given organic compound is 4-bromobut-1-ene.