The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula \(=\mathrm{C}_5 \mathrm{H}_{10}\) is

Statement I Alkali metals dissolve in liquid ammonia to give blue solutions. Statement II Alkali metals in liquid ammonia give solvated species of the type \(\left(M\left(\mathrm{NH}_3\right)_n\right]^{+}(M=\) alkali metals \()\).

A list of species having the formula XZ4 is given below.
\(\text{XeF} _4, \text{SF} _4, \text{SiF} _4, \text{BF} _4^{-}, \text{BrF} _4^{-},\left[\text{Cu} \left(\text{NH} _3\right)_4\right]^{2+},\) \(\left[\text{FeCl} _4\right]^{2-},\left[\text{CoCl} _4\right]^{2-}\) and \(\left[\text{PtCl} _4\right]^{2-}\)
Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is

With reference to aqua regia, choose the correct option(s).

An aqueous solution of hydrazine \(\left(\mathrm{N}_2 \mathrm{H}_4\right)\) is electrochemically oxidized by \(\mathrm{O}_2\), thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is \(\mathrm{N}_2(\mathrm{~g})\).
Choose the correct statement(s) about the above process :

The correct statement(s) about of the following reaction sequence is(are)

The dissociation constant of a substituted benzoic acid at \(25^{\circ} \mathrm{C}\) is \(1.0 \times 10^{-4}\). The \(\mathrm{pH}\) of \(0.01 \mathrm{M}\) solution of its sodium salt is

Let \(\omega\) be a complex cube root of unity with \(\omega \neq 1\). A fair die is thrown three times. If \(r_1, r_2\) and \(r_3\) are the numbers obtained on the die, then the probability that \(\omega^{r_1}+\omega^{r_2}+\omega^{r_3}=0\) is

In a one-litre flask, $6$ moles of $\mathrm{A}$ undergoes the reaction $\mathrm{A}( \mathrm{g})\rightleftharpoons \mathrm{P}( \mathrm{g})$. The progress of product formation at two temperatures (in Kelvin), ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, is shown in the figure: If ${\mathrm{T}}_1=2{\mathrm{T}}_2$ and$\left({\mathrm{\Delta G}}_2^{\mathrm{o}}-{\mathrm{\Delta G}}_1^{\mathrm{o}}\right)={\mathrm{RT}}_2\mathrm{lnx}$ , then the value of $\mathrm{x}$ is
[ ${\mathrm{\Delta G}}_1^{\mathrm{o}}$ and ${\mathrm{\Delta G}}_2^{\mathrm{o}}$ are standard Gibb's free energy change for the reaction at temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, respectively.]

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Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately \(6.023 \times 10^{23}\) ) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.
A \(4.0\) molar aqueous solution of \(\mathrm{NaCl}\) is prepared and \(500 \mathrm{~mL}\) of this solution is electrolysed. This leads to the evolution of chlorine gas at one of electrodes (atomic mass: \(\mathrm{Na}=23, \mathrm{Hg}=200 ; 1\) faraday \(=96500\) coulombs).
Question:
The total number of moles of chlorine gas evolved is

If \(f(x)=\min \left\{1, x^2, x^3\right\}\), then

Let $X$ be the set of all five digit numbers formed using $1,2,2,2,4,4,0$. For example, $22240$ is in $X$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of $20$ given that it is a multiple of $5$. Then the value of $38 p$ is equal to

A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is $1.95 \mathrm{eV}$. If the photoelectric threshold wavelength for the target metal is $310 \mathrm{nm}$, the value of $Z$ is _____.
[Given $hc=1240 \mathrm{eV}-\mathrm{nm}$ and $Rhc=13.6 \mathrm{eV}$, where $R$ is the Rydberg constant, $h$ is the Planck’s constant and $c$ is the speed of light in vacuum]