Atom $\mathrm{X}$ occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in $\%$) of the resultant solid is closest to

For the following reaction, the equilibrium constant ${\mathrm{K}}_{\mathrm{e}}$ at $298\mathrm{ }\mathrm{K}$ is $1.6\times {10}^{17}.$
$\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{S}}^{2-}\left(\mathrm{a}\mathrm{q}\right)\mathrm{ }\rightleftharpoons \mathrm{F}\mathrm{e}\mathrm{S}\left(\mathrm{s}\right)$
When equal volumes of $0.06\mathrm{ }\mathrm{M}\mathrm{ }\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)$ and $0.2\mathrm{ }\mathrm{M}{\mathrm{ }\mathrm{S}}^{2-}\left(\mathrm{a}\mathrm{q}\right)$ solutions are mixed, the equilibrium concentration of $\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)$ is found to be $\mathrm{Y}\times {10}^{-17}\mathrm{M}.$ The value of $\mathrm{Y}$ is __________

According to Bohr's model, the highest kinetic energy is associated with the electron in the

The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula \(=\mathrm{C}_5 \mathrm{H}_{10}\) is

The compound(s) with two lone pairs of electrons on the central atom is (are)

A compound \(\mathrm{M}_{\mathrm{p}} \mathrm{X}_{\mathrm{q}}\) has cubic close packing (ccp) arrangement of \(\mathrm{X}\). Its unit cell structure is shown below. The empirical formula of the compound is

Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, \(\mathrm{Na}, \mathrm{Ti}\)

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A fair die is tossed repeatedly until a six is obtained. Let \(X\) denotes the number of tosses required.Question:
The probability that \(X=3\) equals

Among \(H_2, H e_2^{+}, L i_2, B e_2, B_2, C_2, N_2, O_2^{-}\), and \(F_2\), the number of diamagnetic species is -
(Atomic number : \(H=1, H e=2, L i=3, B e=4, B=5,\) \(C=6, N =7, O=8, F=9\) )

Consider the reaction $\mathrm{A}\rightleftharpoons \mathrm{B}$ at $1000\mathrm{K}$. At time ${\mathrm{t}}^{\text{'}}$, the temperature of the system was increased to $2000\mathrm{K}$ and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of $\mathrm{A}$ was maintained at $1$ bar. Given below is the plot of the partial pressure of $\mathrm{B}$ with time. What is the ratio of the standard Gibbs energy of the reaction at $1000\mathrm{K}$ to that at $2000\mathrm{K}$?

Let $X$ be the set of all five digit numbers formed using $1,2,2,2,4,4,0$. For example, $22240$ is in $X$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of $20$ given that it is a multiple of $5$. Then the value of $38 p$ is equal to

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of ${5.7}^{\mathrm{o}}\mathrm{C}$ was measured for the beaker and its contents (Expt.1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant $(-57.0\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1})$ , this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid $({\mathrm{K}}_{\mathrm{a}}=2.0\times {10}^{-5})$ was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of ${5.6}^{\mathrm{o}}\mathrm{C}$ was measured. (Consider heat capacity of all solutions as $4.2\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{g}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ and density of all solutions as $1.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}{\mathrm{L}}^{-1}$ )
The pH of the solution after Expt. 2 is

The locus of the orthocentre of the triangle formed by the lines \((1+p) x-p y+p(1+p)=0\), \((1+q) x-q y+q(1+q)=0\) and \(y=0\), where \(p \neq q\), is