Five balls numbered 1 to 5 are suspended using separate thread pairs ( 1,2 ) ( 2,4 ) ( 4,1 ) show electrostatic attraction while pairs ( 2,3 ) ( 4,5 ) show repulsion therefore ball1 must be

Yes must be neutral because of we image that ball 2 is positively charged then ball 4 is negatively charged because 2 and 4 show attractions. Now ball if ball 2 is positively charged then ball 3 is also positively charged because 2 and 3 show repulsion and similarly ball 5 is negatively charged because ball 4 and 5 show repulsion. And we left with ball 1 and it never be positively charged because ball 2 and 1 show attraction it means ball 1 is negatively charged but it is also not possible because ball 1 and 4 also show attraction. And in the end we know that ball 1 is nor be positively or neither be negatively charged. It means ball 1 have no charg so it must be neutral.

Dear Student

It should be neutral.
Because 2, and 4 show attraction means have opposite charge 2 too show attraction with 1 means 1 and 4 should have same charge but as they are showing attraction too then.1 should be electricity neutral.
Besides, it can be seen that ball 2 is positively charged then ball 4 is negatively charged because 2 and 4 show attraction. Now ball if ball 2 is (+ve)charged then ball 3 is also (+ve)charged because 2 and 3 also show repulsion and similarly ball 5 is (−ve)charged because ball 4 and 5 show repulsion and we left with ball 1 and it never be (+ve) by charged because ball 2 and 1 show attraction it means ball 1 is negatively charge but it is also not possible because ball 1 and 4 also show attraction and in the end we know that ball1is nor be positively or neither be negatively charge. It means be ball 1 have no charge so it must be neutral.

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya