Please give me a rational solution for this!

Let a, b, c and p be rational numbers such that p is not a perfect cube. If a + bp^1/3 + cp^2/3 = 0 , then prove that a=b=c=0 ?

Are core branches(Mechanical) in Top 3 NIT worth it ?

My rank in JEE Advanced 2022 is 1871. Should I go for IIT Guwahati ECE or IIT Kanpur Mechanical and try for a branch change to CS or Electrical Engineering? Is changing your branch very difficult?

Can i sacrifice board exams for jee mains as board exams are no where valueable as cuet and other will be seen for admission 

 

Is a student studying in IGCSE syllabus eligible for taking IOQP or IOQJS?

I have wasted my 11th? Is it still possible to get into my dream iit? Do i have to cover 11 th syllabus first? When and how can i finish it?