List of top Mathematics Questions on inequalities asked in JEE Main

let \(S\) be the set of positive integral values of a for which \(\frac {ax^2+2(a+1)x+9a+4}{x^2+8x+32}< 0,\) \(∀x∈R\). Then, the number of elements in \(S\) is

Let A=\(\begin{pmatrix} 2 &-1  &-1 \\   1&0  &-1 \\   1&-1  &0  \end{pmatrix}\) and B=A–I. If ω=\(\frac{\sqrt3 i-1}{2}\), then the number of elements in the set {n∈{1,2,⋯,100}:\(A^n+(ωB)^n\)=A+B} is equal to _______.

If the maximum value of the term independent of t in the expansion of (t²x\(^{\frac{1}{5}}\)+\(\frac{(1−x)^{\frac{1}{10}}}{t}\)),x≥0 is K, then 8 K is equal to__________.