Which of the following octahedral complexes does not exhibit geometric isomerism? ($A$ and $B$ are monodentate ligands.)

If $z = \sec^{-1}\left(\frac{x^4+y^4-8x^2y^2}{x^2+y^2}\right)$,then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ is equal to

An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15 ~cm/s$ and the period is $628 ~ms$. The amplitude of the motion in $cm$ is:

The first operation involved in a Carnot cycle is

${\left( -\frac{1}{2} + \frac{\sqrt{3}}{2}i \right)^{1000}} = .....$

One mole of alkene $\underline{X}$ on ozonolysis gave one mole of acetaldehyde and one mole of acetone. The $IUPAC$ name of $\underline{X}$ is