Fusion of $\mathrm{M}\mathrm{n}{\mathrm{O}}_2$ with $\mathrm{K}\mathrm{O}\mathrm{H}$ in presence of ${\mathrm{O}}_2$ produces a salt $\mathrm{W}.$ Alkaline solution of $\mathrm{W}$ upon electrolytic oxidation yields another salt $\mathrm{X}.$ The manganese containing ions present in $\mathrm{W}$ and $\mathrm{X},$ respectively, are $\mathrm{Y}$ and $\mathrm{Z}.$ Correct statement(s) is (are)

The complete hydrolysis of \(\mathrm{ICl}_2 \mathrm{ClF}_3\) and \(\mathrm{BrF}_5\), respectively, gives

When ${\mathrm{O}}_2$ is adsorbed on a metallic surface, electron transfer occurs from the metal to ${\mathrm{O}}_2$ . The TRUE statement(s) regarding this adsorption is(are)

Among the following, the coloured compound is

The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, $\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}\mathrm{}$ and $\mathrm{C}{\mathrm{H}}_3{\left(\mathrm{C}{\mathrm{H}}_2\right)}_{11}\mathrm{O}\mathrm{S}{\mathrm{O}}_3^{-}\mathrm{}\mathrm{N}{\mathrm{a}}^{+}$ at room temperature. The correct assignment of the sketches is -

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p-amino-N, N-dimethylaniline is added to a strongly acidic solution of \(X\). The resulting solution is treated with a few drops of aqueous solution of \(Y\) to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of \(Y\) with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of \(Y\) with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of \(Z\).
Question:
The compound \(Z\), is

The colour of the $X_2$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -

Let $f:\mathrm{ℝ}\to \mathrm{ℝ}$ and $g:\mathrm{ℝ}\to \mathrm{ℝ}$ be functions satisfying $f\left(x+y\right)=f\left(x\right)+f\left(y\right)+f\left(x\right)f\left(y\right)\text{ and }f\left(x\right)=xg\left(x\right)$ for all $x,y\in \mathrm{ℝ}.$ If $\underset{x\to 0}{\lim }g\left(x\right)=1,$ then which of the following statements is/are TRUE?

Let $\left[x\right]$ be the greatest integer less than or equals to $x$. Then, at which of the following point(s) the function $f\left(x\right)=x\cos \left(\pi \left(x+\left[x\right]\right)\right)$ is discontinuous?

A physical quantity $\overrightarrow{S}$ is defined as $\overrightarrow{S}=\frac{\left(\overrightarrow{E}\times \overrightarrow{B}\right)}{{\mu }_0}$. where $\overrightarrow{E}$ is electric field, $\overrightarrow{B}$ is magnetic field and ${\mu }_0$ is the permeability of free space. The dimensions of $\overrightarrow{S}$ are the same as the dimensions of which of the following quantity/quantities?

Let $b_i>1$ for $i=1, 2,\dots .,101.$ Suppose ${\log }_e{b}_1,{\log }_e{b}_2,\dots ..,{\log }_e{b}_{101}$ are in Arithmetic Progression (A.P.) with the common difference ${\log }_{e}2.$ Suppose $a_1, a_2,\dots .,a_{101}$ are in A.P. such that $a_1=b_1$ and $a_{51}=b_{51}.$ If $t=b_1+b_2+\dots +b_{51}$ and $s=a_1+a_2+\dots +a_{51}$ then

The correct statement(s) related to processes involved in the extraction of metals is(are)

Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :

List - i	List - II
A. Alpha decay	P. \({ }_8^{15} O \rightarrow{ }_7^{15} N+\ldots \ldots \ldots\).
B. \(\beta^{+}\)decay	Q. \({ }_{92}^{238} U \rightarrow{ }_{90}^{234} Th +\ldots \ldots \ldots\).
C. Fission	R. \({ }_{83}^{185} Bi \rightarrow{ }_{82}^{184} Pb+\ldots \ldots \ldots\).
D. Proton emission	S. \({ }_{94}^{239} Pu \rightarrow{ }_{57}^{140} La +\ldots \ldots \ldots\).