Two oxides of nitrogen,$NO$ and $NO_2$,react together at $253 \ K$ to form a compound of nitrogen $X$. $X$ reacts with water to yield another compound of nitrogen $Y$. The shape of the anion of $Y$ molecule is:

If $\cos A = \frac{3}{4}$,then $32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5A}{2}\right) = $

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of $100^{\circ} C$,while the other one is kept at $0^{\circ} C$. If the two are brought into contact,then assuming no heat loss to the environment,the final temperature that they will reach is

The structure of a mixed oxide is cubic close packed $(ccp)$. The cubic unit cell of the mixed oxide is composed of oxide ions. One-fourth of the tetrahedral voids are occupied by divalent metal $A$,and the octahedral voids are occupied by a monovalent metal $B$. The formula of the oxide is:

The $IUPAC$ name of $(CH_3)_2CH-CH_2-CH_2Br$ is

$A$ mass $M$ attached to a horizontal spring executes $S.H.M.$ of amplitude $A_1$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio $\left(\frac{A_1}{A_2}\right)$ is