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...

The value of $\sin^{-1}\left(\sin\dfrac{5\pi}{6}\right) + \cos^{-1}\left(\cos\dfrac{7\pi}{6}\right) + \tan^{-1}\left(\tan\dfrac{2\pi}{3}\right)$ is equal to...

Let $f(x) = 1 - \dfrac{1}{x}, g_2(x) = f(f(x)), g_3(x) = f(f(f(x)))$ and so on. If $\int x \cdot g_{2026}(x)\,dx = \int g_{2025}(x)\,dx + h(x) + c$, then $h(x) = $...

If $g(x) = 1 - \sqrt{x}$ and $f(g(x)) = 5 + 4\sqrt{x} + x$, then the value of $f(6)$ is...