Which of the following is the correct electronic configuration of $Cr$ $(Z = 24)$?

If $(a + \sqrt{2} b \cos x)(a - \sqrt{2} b \cos y) = a^2 - b^2$,where $a > b > 0$,then $\frac{dx}{dy}$ at $(\frac{\pi}{4}, \frac{\pi}{4})$ is

Chemical $A$ is used for the removal of temporary hardness of water. Compound $A$ reacts with $Na_2CO_3$ to produce caustic soda. When $CO_2$ gas is passed through $A$,it turns milky. What is the chemical formula of $A$?

$A$ capacitor is charged by using a battery,which is then disconnected. $A$ dielectric slab is then inserted between the plates. What is the result?

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number, then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}$, $\lambda \vec{b}+4 \vec{c}$, and $(2 \lambda-1) \vec{c}$ are non-coplanar for:

If $x^2+y^2+z^2 \neq 0, \quad x=c y+b z, \quad y=a z+c x$ and $z=b x+a y$,then $a^2+b^2+c^2+2 a b c$ is equal to