The vector $c \cdot (b+c) \times (a+b+c)$ is equal to

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

Which of the following properties does not support the anomalous behavior of boron?

The function $f(x) = (x^2 - 1) | x^2 - 3x + 2 | + \cos(| x |)$ is not differentiable at

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ \AA}$. The maximum energy of a photon in the radiation in $eV$ is $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$. (in $27,500$)

$A$ current-carrying rectangular loop is placed near a straight infinitely long current-carrying wire as shown in the figure. The torque acting on the loop is