The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

$A$ straight line which makes equal intercepts on positive $X$ and $Y$ axes and which is at a distance of $1$ unit from the origin intersects the straight line $y = 2x + 3 + \sqrt{2}$ at $(x_0, y_0)$. Then $2x_0 + y_0$ is equal to

Which one of the following statements is not correct?

$A$ millivoltmeter of $25 \, mV$ range is to be converted into an ammeter of $25 \, A$ range. The value (in $\Omega$) of the necessary shunt will be:

The three lines given by the combined equation $y^3 - 4x^2y = 0$ represent:

Given below are two statements:
Statement $I$: $[CoBr_{4}]^{2-}$ ion will absorb light of lower energy than $[CoCl_{4}]^{2-}$ ion.
Statement $II$: In $[CoI_{4}]^{2-}$ ion, the energy separation between the two sets of $d$-orbitals is more than $[CoCl_{4}]^{2-}$ ion.
In the light of the above statements, choose the correct answer from the options given below: