The arrangement of $X^{-}$ ions around $A^{+}$ ion in solid $AX$ is given in the figure. If the radius of $X^{-}$ is $250 \ pm$,the radius of $A^{+}$ is ............. $pm$.

The major product formed in the following reaction is .... .

Two strings $A$ and $B$ of lengths $L_A = 80 \ cm$ and $L_B = x \ cm$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency,the value of $x$ is:

Lithium metal crystallises in a body-centred cubic $(BCC)$ crystal. If the length of the side of the unit cell of lithium is $351 \ pm$,the atomic radius of the lithium will be ............. $pm$.

Production of a human protein in bacteria by genetic engineering is possible because

In the following figure,a body of mass $m$ is tied at one end of a light string and this string is wrapped around a solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$,the system starts moving. If the friction is negligible,the angular velocity at time $t$ would be