For a reaction, given below is the graph of \(\ln k\,v s \frac{1}{ T }\). The activation energy for the reaction is equal to \(......cal\) \(mol ^{-1}\). (Nearest integer). (Given : \(R =2\,cal\,K ^{-1}\,mol ^{-1}\) )

\(2.7 \mathrm{Kg}\) of each of water and acetic acid are mixed, The freezing point of the solution will be \(-\mathrm{x}^{\circ} \mathrm{C}\). Consider the acetic acid does not dimerise in water, nor dissociates in water \(\mathrm{x}=\) _______ (nearest integer) [Given : Molar mass of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\), acetic acid \(=60 \mathrm{~g} \mathrm{~mol}^{-1}\) ] \({ }^{\mathrm{K}_{\mathrm{f}}} \mathrm{H}_2 \mathrm{O}: 1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) \(\mathrm{K}_{\mathrm{r}}\) acetic acid : \(3.90 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) freezing point: \(\mathrm{H}_2 \mathrm{O}=273 \mathrm{~K}\), acetic acid \(=290 \mathrm{~K}\) ]

The incorrect statement regarding the geometrical isomers of \(2\)-butene is _______.

Given below are two statements :
Statement (I) : Dimethyl glyoxime forms a six membered covalent chelate when treated with \(NiCl _2\) solution in presence of \(NH _4 OH\).
Statement (II) : Prussian blue precipitate contains iron both in ( +2 ) and ( +3 ) oxidation states.
In the light of the above statements, choose the most appropriate answer from the options given below:

In a chemical reaction \(A + 2B \overset K  \rightleftharpoons  2C + D\), the initial concentration of \(B\) was \(1.5\) times of \(A\) but the equilibrium concentrations of \(A\) and \(B\) were found to be equal. The equilibrium, constant \((K)\) for the aforesaid chemical reaction is

The wave number of the first emission line in the Balmer series of \(H-\) Spectrum is ( \(R =\) Rydberg constant)

The species which does not undergo disproportionation reaction is _______.

The remainder when \((2021)^{2022}+(2022)^{ 2021 }\) is divided by \(7\) is.

The area (in sq. units) of the region \(\mathrm{S}=\{\mathrm{z} \in \mathbb{C} ;|\mathrm{z}-1| \leq 2 ;(\mathrm{z}+\overline{\mathrm{z}})+\mathrm{i}(\mathrm{z}-\overline{\mathrm{z}}) \leq 2, \operatorname{lm}(\mathrm{z}) \geq 0\}\) is

The set of all values of \(\lambda\) for which the system of linear  \(2{x_1} - 2{x_2} + {x_3} = \lambda {x_1}\;,\;2{x_1} - 3{x_2} + 2{x_3} = \lambda {x_2}\;\;,\)\(\;\; - {x_1} + 2{x_2} = \lambda {x_3}\) has a non-trivial solution

A particle executes simple harmonic motion. Its amplitude is \(8 \,cm\) and time period is \(6 \,s\). The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. \(s\)

Conside the following reactions: \(\mathrm{NaCl}+\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{Conc} .) \rightarrow(\mathrm{A})+\) Side products \((\mathrm{A})+\mathrm{NaOH} \rightarrow(\mathrm{B})+\) side product \((\mathrm{B})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{dilute})+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow(\mathrm{C})+\) Side product The sum of the total number of atoms in one molecule each of \((A), (B)\) and \((C)\) is

Given below are two statements :
Statement I : Ozonolysis followed by treatment with \(\mathrm{Zn}, \mathrm{H}_2 \mathrm{O}\) of cis-2-butene gives ethanal.Statement II : The production obtained by ozonolysis followed by treatment with \(\mathrm{Zn}, \mathrm{H}_2 \mathrm{O}\) of 3, 6-dimethyloct-4-ene has no chiral carbon atom.
In the light of the above statements, choose the correct answer from the options given below