Consider the following complex ions, P, Qand R.

The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is

Match the following

In a metal deficient oxide sample, \(\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4\) ( \(\mathbf{M}\) and \(\mathbf{Y}\) are metals), \(\mathbf{M}\) is present in both +2 and +3 oxidation states and \(\mathbf{Y}\) is in +3 oxidation state. If the fraction of \(\mathbf{M}^{2+}\) ions present in \(\mathbf{M}\) is \(\frac{1}{3}\), the value of \(\mathbf{X}\) is ________.

The solubility of barium iodate in an aqueous solution prepared by mixing 200 mL of 0.010 M barium nitrate with 100 mL of 0.10 M sodium iodate is \(\boldsymbol{X} \times 10^{-6} \mathrm{~mol} \mathrm{dm}^{-3}\). The value of \(\boldsymbol{X}\) is \(\qquad\) .
Use: Solubility product constant \(\left(K_{\mathrm{sp}}\right)\) of barium iodate \(=1.58 \times 10^{-9}\)

The concentration of \(R\) in the reaction \(R \longrightarrow P\) was measured as a function of time and the following data is obtained :
\(\begin{array}{lllll}{[R] \text { (molar) }} & 1.0 & 0.75 & 0.40 & 0.10 \\ t \text { (min) } & 0.0 & 0.05 & 0.12 & 0.18\end{array}\)
The order of the reaction is

The maximum number of electrons that can have principal quantum number, \(n=3\) and spin quantum number, \(m_s=-\frac{1}{2}\), is

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 __________

Let $S=\left(0,1\right)\cup \left(1, 2\right)\cup \left(3, 4\right)$ and $T=\left\{0, 1, 2, 3\right\}$. Then which of the following statements is(are) true?

Match each of the compounds is Column I with its characteristic reaction(s) is Column II.

Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits \(S_1\) and \(S_2\). In each of these cases \(S_1 P_0=S_2 P_0\), \(S_1 P_1-S_2 P_1=\frac{\lambda}{4}\) and \(S_1 P_2-S_2 P_2=\frac{\lambda}{3}\), where \(\lambda\) is the wavelength of the light used. In the cases \(\mathrm{B}, \mathrm{C}\) and \(\mathrm{D}\), a transparent sheet of refractive index \(\mu\) and thickness \(t\) is pasted on slit \(S_2\). The thickness of the sheets are different in different cases. The phase difference between the light waves reaching a point \(P\) on the screen from the two slits is denoted by \(\delta(P)\) and the intensity by \(I(P)\). Match each situation given in Column-I with the statement(s) in Column-II valid for that situation.

A monochromatic light is incident from air on a refracting surface of a prism of angle ${75}^{\mathrm{o}}$ and refractive index ${\mathrm{n}}_0=\sqrt{3}.$ The other refracting surface of a prism is coated by a thin film of material of refractive index $\mathrm{n}$ as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\mathrm{\theta }\le {60}^{\mathrm{o}}.$ The value of ${\mathrm{n}}^2$ is_______.

Perpendiculars are drawn from points on the line $\frac{\text{x}+2}{2}=\frac{\text{y}+1}{-1}=\frac{\text{z}}{3}$  to the plane $x+y+z=3$. The feet of perpendiculars lie on the line

Two resistances $R_1=X \mathrm{\Omega }$ and $R_2=1 \mathrm{\Omega }$ are connected to a wire $AB$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \mathrm{mm}$ at $A$ to $1 \mathrm{mm}$ at $B$. A galvanometer $\left(G\right)$ connected to the center of the wire, $50 \mathrm{cm}$ from each end along its axis, shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is _______.