Calculus for JEE(M+A)

Easy problem , just a mixture of many famous problems , try solving tk check your concepts in different topics

For this problem

For trace i=j, for inverse just keep track of diagonal elements for a triangular matrix , if diagonal elements are a,b,c in inverse they become 1/a,1/b,1/c so aii=diagonal element= 1/2i^2 becomes 2i^2 in A^-1 , so we need to sum 2i^2 , for i=1 to n , that comes to n(n+1)(2n+1)/3 , now sum this for n=1 to 5 , ie becomes 2+ 10+28+60+110= 210 --> final answer =210/10=21 , just oral but no one answered

Mains level matrices

Try

Irrelevant

Old goated limit , let's see how many can solve , btw it's easy

Try and send soln too

Easy problem try

Try UGA Type

Try

Try this also

Soln https://youtu.be/dppeN6wH7gI?si=zRU3m0jqQzBIDpkc

Maybe this inequality will come into play in some questions so just posting here so that maybe you can use it directly...