List of top Mathematics Questions asked in Mizoram (MBSE) Class XII

Find the derivative of \( (\sin x)^x + \sin^{-1}(\sqrt{x}) \) with respect to \(x\).
Find the principal value of \( \tan^{-1}(\sqrt{3}) - \sec^{-1}(-2) \).
Find the general solution of the differential equation \[ \frac{dy}{dx}+\frac{y}{x}=x^2 . \]
Evaluate the integral \[ \int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx . \]
Show that the relation \(R\) in the set \(A = \{1,2,3,4,5\}\) given by \[ R=\{(a,b): |a-b| \text{ is even}\} \] is an equivalence relation.
If \[ A=\begin{bmatrix}2 & 3\\ 1 & -4\end{bmatrix} \quad \text{and} \quad B=\begin{bmatrix}1 & -2\\ -1 & 3\end{bmatrix}, \] verify that \( (AB)^{-1} = B^{-1}A^{-1} \).
Solve the following system of equations using the matrix method: \[ 2x+3y+3z=5,\qquad x-2y+z=-4,\qquad 3x-y-2z=3. \]