Which of the following statements is true?

The voltage of an $ac$ source varies with time according to the equation $V = 100 \sin(100 \pi t) \cos(100 \pi t)$,where $t$ is in $seconds$ and $V$ is in $volts$. Then:

Among the electrolytes $Na_2SO_4$,$CaCl_2$,$Al_2(SO_4)_3$ and $NH_4Cl$,the most effective coagulating agent for $Sb_2S_3$ sol is

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x+y)$ is equal to

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to generate caustic soda. When $CO_2$ is bubbled through $A$,it turns cloudy,what is $A$?