Chapter 3

Given that the abundances of isotopes ${}^{54}\mathrm{Fe},{}^{56}\mathrm{Fe}$ and ${}^{57}\mathrm{Fe}$ are $5\mathrm{\%},90\mathrm{\%}$ and $5\mathrm{\%}$, respectively, the atomic mass of $\mathrm{Fe}$ is (A) $55.85$ (B) $55.95$ (C) $55.75$ (D) $56.05$

The term that correets for the attractive forces present in a real gas in the van der Waals equation is (A) $nb$ (B) $\frac{a{n}^2}{r^2}$ (C) $-\frac{a{n}^2}{u^2}$ (D) $-nb$

The Henry's law constant for the solubility of ${\mathrm{N}}_2$ gas in water at $298\mathrm{K}$ is $1.0\times {10}^5$ atm. The mole fraction of ${\mathrm{N}}_2$ in air is $0.8.$ The number of moles of ${\mathrm{N}}_2$ from air dissolved in 10 moles of water at $298\mathrm{K}$ and 5 atm pressure is (A) $4.0\times {10}^{-4}$ (B) $4.0\times {10}^{-5}$ (C) $5.0\times {10}^{-4}$ (D) $4.0\times {10}^{-6}$

The reaction of ${\mathrm{P}}_4$ with $\mathrm{X}$ leads selectively to ${\mathrm{P}}_4{\mathrm{O}}_6$. The $\mathrm{X}$ is (A) Dry ${\mathrm{O}}_2$ (B) A mixture of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$ (C) Moist ${\mathrm{O}}_2$ (D) ${\mathrm{O}}_2$ in the presence of aqueous $\mathrm{NaOH}$

Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest is (A) Nylon (B) Poly(vinyl chloride) (C) Cellulose (D) Natural Rubber

The compound(s) that exhibit(s) geometrical isomerism is(are) (A) $[$ Pt $(en){\mathrm{Cl}}_2]$ (B) $[\mathrm{Pt}(\mathrm{en}{)}_2/{\mathrm{Cl}}_2$ (C) $\mid \mathrm{Pt}(\mathrm{en}{)}_2{\mathrm{Cl}}_2]{\mathrm{Cl}}_2$ (D) $\mid \mathrm{Pt}{\left({\mathrm{NH}}_3\right)}_2{\mathrm{Cl}}_2]$

The correct statement $(\mathrm{s})$ about the compound ${\mathrm{H}}_3\mathrm{C}(\mathrm{HO})\mathrm{HC}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH}){\mathrm{CH}}_3(\mathbf{X})$ is(are) (A) The total number of stereoisomers possible for $\mathbf{X}$ is 6 (B) The total number of diastereomers possible for $\mathbf{X}$ is 3 (C) If the stereochemistry about the double bond in $\mathbf{X}$ is trans, the number of enantiomers possible for $\mathbf{X}$ is 4 (D) If the stereochemistry about the double bond in $\mathbf{X}$ is cis, the number of enantiomers possible for $\mathbf{X}$ is 2

Let $P(3,2,6)$ be a point in space and $Q$ be a point on the line $$\overrightarrow{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu (-3\hat{i}+\hat{j}+5\hat{k})$$ Then the value of $\mu$ for which the vector $\overrightarrow{PQ}$ is parallel to the plane $x-4y+3z=1$ is (A) $\frac{1}{4}$ (B) $-\frac{1}{4}$ (C) 1 (D) $-\frac{1}{8}$ $\bar{8}$

The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $$x^2+9y^2=9$$ meets its auxiliary circle at the point $M.$ Then the area of the triangle with vertices at $A,M$ and the origin $O$ is (A) $\frac{31}{10}$ (B) $\frac{29}{10}$ (C) $\frac{21}{10}$ (D) $\frac{27}{10}$

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ and $\overrightarrow{d}$ are unit vectors such that $$(\overrightarrow{a}\times \overrightarrow{b})\cdot (\overrightarrow{c}\times \overrightarrow{d})=1$$ and $$\overrightarrow{a}\cdot \overrightarrow{c}=\frac{1}{2},$$ then (A) $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar (B) $\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}$ are non-coplanar (C) $\overrightarrow{b},d$ are non-parallel (D) $\overrightarrow{a},\overrightarrow{d}$ are parallel and $b,\overrightarrow{c}$ are paraliel