Assam Board Class 12 Mathematics 2026 Question Paper with Solution PDF

If \( A \) is a skew-symmetric matrix of odd order, write the value of \( |A| \).

Find the principal value of \( \sin^{-1}\!\left(-\frac{\sqrt{3}}{2}\right) + \cosec^{-1}\!\left(-\frac{2}{\sqrt{3}}\right). \)

Find the value of \( x \) if \( \begin{bmatrix} -5 & 6
2 & 3 \end{bmatrix}^{T} = \begin{bmatrix} 9y & 6z
2x & 3 \end{bmatrix}. \)

Show that the relation \( R \) in the set of natural numbers \( N \times N \) defined by \( (a, b)\, R\, (c, d) \) if \( a + d = b + c \) is an equivalence relation.

Using determinants, find the value of \( \lambda \) if the points \( (1, -5) \), \( (-4, 5) \), and \( (\lambda, 7) \) are collinear.

Find the shortest distance between the skew lines whose vector equations are given.

Evaluate the integral \( \displaystyle \int \frac{x^2}{(x^2 + 1)(x^2 + 4)} \, dx \) using partial fractions.

If \( |\vec{a}| = \sqrt{26},\ |\vec{b}| = 7,\ and\ |\vec{a} \times \vec{b}| = 35 \), find the angle between \( \vec{a} \) and \( \vec{b} \).