The feasible region corresponding to an LPP represented by the constraints \( x \geq 7, y \geq 4, x + 2y \geq 8 \) is:

If \( f(x) = \begin{cases} \frac{\tan (\frac{\pi}{4} - x)}{\cot 2x}, & x \neq \frac{\pi}{4} \\ k, & x = \frac{\pi}{4} \end{cases} \) is continuous at \( x = \frac{\pi}{4} \), then the value of \( k \) will be equal to:

If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( |\vec{a}| = 7 \) and \( |\vec{b}| = 4 \), then the value of the scalar product of vectors \( 2\vec{a} - 3\vec{b} \) and \( 2\vec{a} + 3\vec{b} \) is:

OA BC is a parallelogram. If \( \overrightarrow{OB} = \vec{a} \) and \( \overrightarrow{AC} = \vec{b} \), then \( \overrightarrow{OA} \) is equal to:

If \( A \) is a square matrix such that \( A^2 = 2I \), then the value of \( (A - I)^2 + (A + I)^2 - 7A \) is:

Area of the region bounded by \( |x| + |y| \leq 2 \) is:

If \( A \) is a square matrix of order 3 and \( |A| = -3 \), then the value of \( |2AA^T| \) is:

If \( \tan^{-1}(-3x) + \tan^{-1}(-2x) = \frac{\pi}{4} \), then the values of \( x \) are:

Let \( R \) be the relation on \( \mathbb{N} \) (set of natural numbers) defined by \( R = \{(a, b) : a, b \in \mathbb{N} \) and \( b \) is divisible by \( a\} \). Then the relation \( R \) is: