Identify the halogen exchange reaction from the following.

Let $f:[-1, 3] \to R$ be defined as $f(x) = \begin{cases} |x| + [x], & -1 \le x < 1 \\ x + |x|, & 1 \le x < 2 \\ x + [x], & 2 \le x \le 3 \end{cases}$ where $[t]$ denotes the greatest integer function. Then $f$ is discontinuous at:

If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$,then the locus of $P(h, k)$ is a conic $C$ whose eccentricity equals

The radius of Germanium $(Ge)$ nuclide is measured to be twice the radius of $_{4}^{9}\text{Be}$ . The number of nucleons in $Ge$ are

In which of the following processes,the bond order has increased and paramagnetic character has changed to diamagnetic?

If $k > 1$ and the determinant of the matrix $A^2$,where $A = \begin{bmatrix} k & k\alpha & \alpha \\ 0 & \alpha & k\alpha \\ 0 & 0 & k \end{bmatrix}$,is $k^2$,then $|\alpha|$ is equal to