In the complex acetylbromidodicarbonylbis(triethylphosphine)iron (II), the number of $\mathrm{F}\mathrm{e}-\mathrm{C}$ bond (s) is

The species formed on fluorination of phosphorus pentachloride in a polar organic solvent are :

The species present in solution when \(\mathrm{CO}_2\) is dissolved in water are

Among the following, the state function(s) is (are)

Liquids A and B form ideal solution over the entire range of composition. At temperature $\mathrm{T}$, equimolar binary solution of liquids A and B has vapour pressure $45 \mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$ . At the same temperature, a new solution of A and B having mole fractions ${\mathrm{x}}_{\mathrm{A}}\mathrm{ }\mathrm{and}\mathrm{ }{\mathrm{x}}_{\mathrm{B}}$, respectively, has vapour pressure of $22.5 \mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$. The value of $\frac{{\mathrm{x}}_{\mathrm{A}}}{{\mathrm{x}}_{\mathrm{B}}}$, in the new solution is ____.
(Given that the vapour pressure of pure liquid A is $20 \mathrm{Torr}$ at temperature $\mathrm{T}$)

A gas has a compressibility factor of $0.5$ and a molar volume of $0.4 {\mathrm{dm}}^3 {\mathrm{mol}}^{-1}$ at a temperature of $800 \mathrm{K}$ and pressure $\mathrm{x} \mathrm{atm}$. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be  $\mathrm{y} {\mathrm{dm}}^3 {\mathrm{mol}}^{-1}$ . The value of$\mathrm{x}/\mathrm{y}$ is _________
[Use: Gas constant, $\mathrm{R}=8\times {10}^{-2} \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ ]

The total number of compounds having at least one bridging oxo group among the molecules given below is
\(\text N _2\text O _5,\)\(\text P _4\text O _6,\)\(\text P _4\text O _8,\)\(\text H _4\text P _2\text O _5,\)\(\text H _5\text P _3\text O _{10},\) \(\text H _2\text S_2\text O _3,\text H _2\text S_2\text O _5\)

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A uniform thin cylindrical disk of mass \(M\) and radius \(R\) is attached to two identical massless springs of spring constant \(k\) which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance \(d\) from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is \(L\). The disk is initially at its equilibrium position with its centre of mass \((C M)\) at a distance Lfrom the wall. The disk rolls without slipping with velocity \(\mathbf{v}_0=v_0 \hat{\mathbf{i}}\) The coefficient of friction is \(\mu\).
Question :
The maximum value of \(v_0\) for which the disk will roll without slipping is

In the chemical reaction between stoichiometric quantities of ${\mathrm{KMnO}}_4$ $\mathrm{KI}$ in weakly basic solution, what is the number of moles of ${\mathrm{I}}_2$ released for $4$ ${\mathrm{KMnO}}_4$ consumed?

Let $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ be three non - coplanar unit vectors such that the angle between every pair of them is $\frac{\pi }{3}.$ If $\overrightarrow{a} \times \overrightarrow{b}+ \overrightarrow{b} \times \overrightarrow{c}=p\overrightarrow{a}+q\overrightarrow{b}+r\overrightarrow{c}$ , where p, q and r are scalars, then the value of $\frac{p^2+2q^2+r^2}{q^2}$ is _______

A student uses a simple pendulum of exactly \(1 \mathrm{~m}\) length to determine \(g\), the acceleration due to gravity. He uses a stop watch with the least count of \(1 \mathrm{~s}\) for this and records \(40 \mathrm{~s}\) for 20 oscillations. For this observation, which of the following statement(s) is/are true?

A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $xy$ plane with its center at the origin. The Coulomb potential along the $z$-axis is
$V\left(z\right)=\frac{\sigma }{2{ϵ}_0}\left(\sqrt{R^2+z^2}-z\right)$ A particle of positive charge $q$ is placed initially at rest at a point on the $z$-axis with $z=z_0$ and $z_0>0$. In addition to the Coulomb force, the particle experiences a vertical force $\overrightarrow{F}=-c\hat{k}$ with $c>0$. Let $\beta =\frac{2c{\epsilon }_0}{q\sigma }$. Which of the following statement(s) is(are) correct?

The calculated spin only magnetic moments of ${\left[\mathrm{Cr}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$ and ${\left[{\mathrm{CuF}}_6\right]}^{3-}$ in $\mathrm{BM},$ respectively, are (Atomic numbers of $\mathrm{Cr}$ and $\mathrm{Cu}$ are $24$ and $29,$ respectively)