Which of the following is a $\pi$-complex?

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

The equation of the sphere passing through the points $(1,0,0)$, $(0,1,0)$, and $(1,1,1)$ and having the smallest radius is:

For any integer $n \geq 1$,the sum $\sum_{k=1}^n k(k+2)$ is equal to

An alloy of gold and copper crystallizes in a cubic lattice in which the gold atoms occupy the lattice points at the corners of the cube and copper atoms occupy the centers of each of the cube faces. Determine the formula of this compound.

In the circuit shown,the reading of the Ammeter is doubled after the switch is closed. Each resistor has a resistance $1\,\Omega$ and the ideal cell has an $e.m.f.$ $10\,V$. Then,the Ammeter has a coil resistance equal to ............... $\Omega$.