Treatment with lime can remove hardness of water caused by

The most general value of $\theta$ which satisfies both the equations $\tan \theta = -1$ and $\cos \theta = \frac{1}{\sqrt{2}}$ is

The $emf$ of the cell $Ag | Ag^{+}(0.1 \, M) || Ag^{+}(1 \, M) | Ag$ at $298 \, K$ is ............ $V$.

Acidified potassium permanganate solution is decolourised by

Match the items of column $I$ with column $II$. Select the correct option from the following:

Column $I$	Column $II$
$(a)$ $XX$-$XO$ method of sex determination	$(i)$ Turner's syndrome
$(b)$ $XX$-$XY$ method of sex determination	$(ii)$ Female heterogametic
$(c)$ Karyotype-$45$	$(iii)$ Grasshopper
$(d)$ $ZW$-$ZZ$ method of sex determination	$(iv)$ Female homogametic

$A$ clock which keeps correct time at $20^{\circ} C$,is subjected to $40^{\circ} C$. If the coefficient of linear expansion of the pendulum is $12 \times 10^{-6} /{ }^{\circ} C$,how much time will it gain or lose per day?