Assume internuclear axis to be z-axis, the correct molecular orbital representation of \(\pi^*\) antibonding molecular orbital formed by overlapping between two \(p\) orbitals will be:

Two atoms are bonding along the Z-axis. How will the \( \pi^* \) orbital look like (Z is the internuclear axis)? 
Find the area of the region \[ R = \{(x, y) : xy \le 27,\; 1 \le y \le x^2 \}. \]
An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ____ ($g$ is acceleration due to gravity at the surface of earth)