The IUPAC name of \(\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{NiCl}_4\right]\) is

The treatment of galena with ${\mathrm{HNO}}_3$ produces a gas that is

The number of optically active products obtained from the complete ozonolysis of the given compound is :

The number of water molecule(s) directly bonded to the metal centre in \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\) is

If the freezing point of a 0.01 molal aqueous solution of a cobalt (III) chloride-ammonia complex (which behaves as a strong electrolyte) is $-{0.0558}^{\mathrm{o}}\mathrm{C}$ , the number of chloride(s) in the coordination sphere of the complex is
$[{\mathrm{K}}_{\mathrm{f}}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}=1.86\mathrm{ }\mathrm{K}\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}]$

The total number of carboxylic acid groups in the product P is

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Upon heating \(\mathrm{KClO}_{3}\) in the presence of catalytic amount of \(\mathrm{MnO}_{2}\), a gas \(\mathbf{W}\) is formed. Excess amount of \(\mathbf{W}\) reacts with white phosphorus to give \(\mathbf{X}\). The reaction of \(\mathbf{X}\) with pure \(\mathrm{HNO}_{3}\) gives \(\mathbf{Y}\) and \(\mathbf{Z}\).
Question:
\(\mathbf{W}\) and \(\mathbf{X}\) are, respectively

A flat surface of a thin uniform disk $A$of radius$R$ is glued to a horizontal table. Another thin uniform disk$B$ of mass $M$and with the same radius $R$rolls without slipping on the circumference of $A$, as shown in the figure. A flat surface of $B$ also lies on the plane of the table. The center of mass of$B$ has fixed angular speed $\omega$about the vertical axis passing through the center of $A$. The angular momentum of $B$ is $nM\omega R^2$with respect to the center of $A$. Which of the following is the value of $n$?

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The reaction of \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with freshly prepared \(\mathrm{FeSO}_{4}\) solution produces a dark blue precipitate called Turnbull's blue. Reaction of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with the \(\mathrm{FeSO}_{4}\) solution in complete absence of air produces a white precipitate \(\mathbf{X}\), which turns blue in air. Mixing the \(\mathrm{FeSO}_{4}\) solution with \(\mathrm{NaNO}_{3}\), followed by a slow addition of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) through the side of the test tube produces a brown ring.
Question:
Among the following, the brown ring is due to the formation of

Let \(f(x)=x^4+a x^3+b x^2+c\) be a polynomial with real coefficients such that \(f(1)=-9\). Suppose that \(i \sqrt{3}\) is a root of the equation \(4 x^3+3 a x^2+2 b x=0\), where \(i=\sqrt{-1}\). If \(\alpha_1, \alpha_2, \alpha_3\), and \(\alpha_4\) are all the roots of the equation \(f(x)=0\), then \(\left|\alpha_1\right|^2+\left|\alpha_2\right|^2+\left|\alpha_3\right|^2+\left|\alpha_4\right|^2\) is equal to ________.

Monocyclic compounds \(\mathbf{P}, \mathbf{Q}, \mathbf{R}\) and \(\mathbf{S}\) are the major products formed in the reaction sequences given below.


The product having the highest number of unsaturated carbon atom(s) is-

The area enclosed by the curves $y=\sin x+\cos x$ and $\text{y}=\left|\text{cos x}-\text{sin x}\right|$ over the interval $\left[0\text{,}\frac{\pi }{2}\right]$ is

Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is