Arrange the following compounds in decreasing order of reactivity towards nucleophilic addition reactions:
$(I) HCHO$
$(II) CH_3CHO$
$(III) CH_3COCH_3$
$(IV) CH_3CH_2COCH_2CH_3$

The equation of the locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$ is a complex number,is

The circuit diagram shows a logic combination with the states of outputs $X, Y$ and $Z$ given for inputs $P, Q, R$ and $S$ all at state $1$. When inputs $P$ and $R$ change to state $0$ with inputs $Q$ and $S$ still at $1$,the states of outputs $X, Y$ and $Z$ change to:

Which of the following is an exception in terms of its life cycle?

The yellow colour solution of $Na_2CrO_4$ changes to orange-red on passing $CO_2$ gas due to the formation of

$A$ rotating body has angular momentum $L$. If its frequency of rotation is halved and its rotational kinetic energy is doubled,what will be its new angular momentum?