Problem in electrostatics: E-field near 2 point charges

[ubergewehr273]

Homework Statement

Refer the image.

Homework Equations

kq1q2/r^2 = F
Potential energy = kq1q1/r

The Attempt at a Solution

Obviously since both charges are unequal in magnitude option a is incorrect.
Calculating field at large distance r,
E = kq1/r^2 - kq2/r^2
= kq2/r^2
Also potential energy at q1 is lesser than near q2 for negative charge.
So options c,d are correct. However I don't understand how the angle beta can be calculated from the given information.

 

[Doc Al]

However I don't understand how the angle beta can be calculated from the given information.

No need to calculate the angle to disqualify answer b.

 

[ubergewehr273]

No need to calculate the angle to disqualify answer b.

I'm sorry but I don't quite understand. The answers given are b,c,d.

 

[Doc Al]

Hmm. What book is this from?

 

[ubergewehr273]

Hmm. What book is this from?

It's from an exam paper called NEST (National Entrance Screening Test) conducted in India. Its for the year 2016.