List of top Mathematics Questions asked in IIT JAM MS

The value of
\(\int^2_0 \int_0^{2-x}(x+y)^2e^{\frac{2y}{x+y}}\ dy\ dx\)
equals __________ (round off to 2 decimal places)

Let \(A=\begin{pmatrix} 1 & -1 & 2 \\ -1 & 0 & 1 \\ 2 & 1 & 1 \end{pmatrix}\) and let \(\begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix}\)be an eigenvector corresponding to the smallest eigenvalue of A, satisfying \(x^2_1+x^2_2+x^2_3=1\). Then the value of |x₁| + |x₂| + |x₃| equals __________ (round off to 2 decimal places)