Which of the following can be added to remove the permanent hardness of water?

If $\theta = \frac{\pi}{6}$,then the $10^{th}$ term of the series $1 + (\cos \theta + i \sin \theta) + (\cos \theta + i \sin \theta)^2 + (\cos \theta + i \sin \theta)^3 + \dots$ is equal to:

Which of the following factors exclusively affects reproduction in seasonal breeders,both plants and animals?

What is the vital capacity of our lungs?

The circuit shown contains a $12 \ V$ battery,a $4 \ \Omega$ resistor,and two branches in parallel,each containing an ideal diode and a resistor. Branch $1$ has diode $D_1$ and a $3 \ \Omega$ resistor,while branch $2$ has diode $D_2$ and a $2 \ \Omega$ resistor. Determine the total current flowing in the circuit. (in $A$)

Which of the following is the strongest conjugate base?