Extraction of metal from the ore cassiterite involves

The reagent(s) that can selectively precipitate ${\mathrm{S}}^{2-}$ from a mixture of ${\mathrm{S}}^{2-}$ and $\mathrm{S}{\mathrm{O}}_4^{2-}$ in aqueous solution is (are)

A solution of $0.1\mathrm{M}$ weak base $\left(\mathrm{B}\right)$ is titrated with $0.1\mathrm{M}$ of a strong acid $\left(\mathrm{HA}\right)$. The variation of $\mathrm{pH}$ of the solution with the volume of $\mathrm{HA}$ added is shown in the figure below. What is the ${\mathrm{pK}}_{\mathrm{b}}$ of the base? The neutralization reaction is given by$\mathrm{B}+\mathrm{HA}\to {\mathrm{BH}}^{+}+{\mathrm{A}}^{-}$.

The reagent(s) for the following conversion,

is/are

A closed vessel with rigid walls contains 1 mol of ${}_{92}{}^{238}\mathrm{U}$ and 1 mol of air at 298 K. Considering complete decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{P}\mathrm{b}$ , the ratio of the final pressure to the initial pressure of the system at 298 K is

LIST-I contains compounds and LIST-II contains reactions

List - I	List - II
(I) \(H _2 O _2\)	(P) \(Mg \left( HCO _3\right)_2+ Ca\) \((OH)_2 \rightarrow\)
(II) \(Mg ( OH )_2\)	(Q) \(BaO _2+ H _2 SO _4 \rightarrow\)
(III) \(BaCl _2\)	(R) \(Ca \left( OH _2\right) 2\) \(+ MgCl _2 \rightarrow\)
(IV) \(CaCO _3\)	(S) \(BaO _2+ HCl \rightarrow\)
	(T) \(Ca \left( HCO _3\right)_2\) \(+ Ca ( OH )_2\)

Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option

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Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper include chalcanthite \(\left(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\right)\), atacamite \(\left(\mathrm{Cu}_2 \mathrm{Cl}(\mathrm{OH})_3\right)\), cuprite \(\left(\mathrm{Cu}_2 \mathrm{O}\right)\), copper glance \(\left(\mathrm{Cu}_2 \mathrm{~S}\right)\) and malachite \(\left(\mathrm{Cu}_2(\mathrm{OH})_2 \mathrm{CO}_3\right)\). However, 80\% of the world copper production comes from the ore chalcopyrite \(\left(\mathrm{CuFeS}_2\right)\). The extraction of copper from chalcopyrite involves partial roasting, removal of iron and self-reduction.
Question:
Partial roasting of chalcopyrite produces

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are unit vectors satisfying \(|\vec{a}-\vec{b}|^{2}+|\vec{b}-\vec{c}|^{2}+|\vec{c}-\vec{a}|^{2}=9\), then \(|2 \vec{a}+5 \vec{b}+5 \vec{c}|\) is

Consider a disc rotating in the horizontal plane with a constant angular speed \(\omega\) about its centre \(\mathrm{O}\). The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles \(P\) and \(Q\) are simultaneously projected at an angle towards \(R\). The velocity of projection is in the \(y\) - \(z\) plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed \(1 / 8\) rotation, (ii) their range is less than half the disc radius, and (iii) \(\omega\) remains constant throughout. Then

The total number of lone pairs of electrons in ${\mathrm{N}}_2{\mathrm{O}}_3$ is

Mixture(s) showing positive deviation from Raoult's law at ${35}^{\mathrm{o}}\mathrm{C}$ is (are)

Let $\hat{i},\hat{j}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let $\overrightarrow{a}=3\hat{i}+\hat{j}-\hat{k}$ $\overrightarrow{b}=\hat{i}+b_2\hat{j}+b_3\hat{k}, b_2,b_3\in \mathrm{ℝ}$ $\overrightarrow{c}=c_1\hat{i}+c_2\hat{j}+c_3\hat{k},c_1,c_2,c_3\in \mathrm{ℝ}$ be three vectors such that $b_2{b}_3>0,\overrightarrow{a}·\overrightarrow{b}=0$ and $\left(\begin{array}{ccc}0& -c_3& c_2\\ c_3& 0& -c_1\\ -c_2& c_1& 0\end{array}\right)\left(\begin{array}{l}1\\ b_2\\ b_3\end{array}\right)=\left(\begin{array}{c}3-c_1\\ 1-c_2\\ -1-c_3\end{array}\right).$ Then, which of the following is/are TRUE?

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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 conditional probability that \(X \geq 6\) given \(X>3\) equals