Treatment with lime can remove hardness of water caused by

If the amplitude of $z-2-3i$ is $\frac{\pi}{4}$,then the locus of $z=x+iy$ is:

Two solenoids have identical geometrical construction and the same number of turns,but one is made of thick wire and the other of thin wire. Which of the following quantities are different for the two solenoids?
$(a)$ Self-inductance
$(b)$ Rate of Joule heating if the same current flows through them
$(c)$ Magnetic potential energy if the same current flows through them
$(d)$ Time constant

Given that $K_w$ for water is $10^{-13} \ M^2$ at $62 \ ^oC$,compute the sum of $pOH$ and $pH$ for a neutral aqueous solution at $62 \ ^oC$.

The system shown in the figure is released from rest. The pulley and spring are massless,and friction is absent everywhere. The speed of the $5\, kg$ block when the $2\, kg$ block leaves contact with the ground is: (Take the force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2$)

When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \, cm$ or $100 \, cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $ \, Hz$)