In $\triangle ABC$, with usual notations, $(a + b + c)(b + c - a)(c + a - b)(a + b - c) = 3b^2c^2$, then $\angle A = $

If ABC is a triangle of area $\Delta$ with $a = 2, b = \dfrac{7}{2}, c = \dfrac{5}{2}$, where $a, b, c$ are the lengths of the sides of the triangle opposite to angles A, B and C respectively, then $\dfrac{2\sin A - \sin 2A}{2\sin A + \sin 2A}$ is equal to...

If matrix $A = \begin{bmatrix} -1 & 2025 & 2026 \\ 0 & 2 & 2027 \\ 0 & 0 & -1 \end{bmatrix}$, then the sum of all elements in $\text{adj}(A^{-1})$ is equal to...

The inverse of the matrix $A = \begin{bmatrix} 2 & -1 & 4 \\ 4 & -3 & 1 \\ 1 & 2 & 1 \end{bmatrix}$ is $B = \dfrac{1}{37}\begin{bmatrix} -5 & 9 & 11 \\ -3 & -2 & 14 \\ 11 & -5 & k \end{bmatrix}$, then the value of $k$ is...