The number of incorrect statements from the following is \(A.\) The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy. \(B.\) \(E _{\text {cell }}^0\) is dependent on the pressure \(C.\) \(\frac{ dE ^0 \text { cell }}{ dT }=\frac{\Delta_{ r } S ^0}{ nF }\) \(D.\) A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

The enthalpy change for the conversion of \(\frac{1}{2} Cl _2\) (g) to \(Cl ^{-}\)(aq) is \((-).......\) \(kJ\,mol ^{-1}\) (Nearest integer) Given : \(\Delta_{ dis } H _{ Cl _{2(g)}}^{\circ}=240\,kJ\,mol ^{-1}\). \(\Delta_{ eg } H _{ Cl _{(g)}}^{\circ}=-350\,kJ\,mol ^{-1}\), \(\Delta_{ hyd } H _{ Cl i _{( j )}^{\circ}}^{\circ}=-380\,kJ\,mol ^{-1}\)

The increasing order of the reactivity of the following with \(LiAlH_4\) is

Consider the following reaction occurring in the blast furnace:
\(\mathrm{Fe}_3 \mathrm{O}_{4(\mathrm{~s})}+4 \mathrm{CO}_{(\mathrm{g})} \rightarrow 3 \mathrm{Fe}_{(\mathrm{l})}+4 \mathrm{CO}_{2(\mathrm{~g})}\)
' \(x\) ' kg of iron is produced when \(2.32 \times 10^3 \mathrm{~kg} \mathrm{Fe}_3 \mathrm{O}_4\) and \(2.8 \times 10^2 \mathrm{~kg} \mathrm{CO}\) are brought together in the furnace. The value of ' \(x\) ' is _____. (nearest integer)
Given:
molar mass of \(\mathrm{Fe}_3 \mathrm{O}_4=232 \mathrm{~g} \mathrm{~mol}^{-1}\)
molar mass of \(\mathrm{CO}=28 \mathrm{~g} \mathrm{~mol}^{-1}\)
molar mass of \(\left.\mathrm{Fe}=56 \mathrm{~g} \mathrm{~mol}^{-1}\right\}\)

' \(X\) ' is the number of electrons in \(t_{2 g}\) orbitals of the most stable complex ion among \(\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_6\right]^{3+}\), \(\left[\mathrm{Fe}\left(\mathrm{Cl}_6\right)\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}\) and \(\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}\). The nature of oxide of vanadium of the type \(\mathrm{V}_2 \mathrm{O}_{\mathrm{X}}\) is _______.

An exothermic reaction \(X \rightarrow Y\) has an activation energy \(30\, kJ \,mol ^{-1}\). If energy change \(\Delta E\) during the reaction is \(-20\, kJ ,\) then the activation energy for the reverse reaction in \(kJ\) is \(...\).(Integer answer)

Given below are two statements
Statement I : The N-N single bond is weaker and longer than that of \(\mathrm{P}-\mathrm{P}\) single bond
Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.
In the light of above statements, choose the correct answer from the options given below

Which one among the following chemical tests is used to distinguish monosaccharide from disaccharide?

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........

The spin-only magnetic moment value of \(\mathrm{M}^{\mathrm{n+-}}\) ion formed among \(\mathrm{Ni}, \mathrm{Zn} \mathrm{Mn}\) and Cu that has the least enthalpy of atomisation is ________. (in nearest integer)
Here n is equal to the number of diamagnetic complexes among \(\mathrm{K}_2\left[\mathrm{NiCl}_4\right],\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2\),
\(\mathrm{K}_3\left[\mathrm{Mn}(\mathrm{CN})_6\right] \text { and }\left[\mathrm{Cu}\left(\mathrm{PPh}_3\right)_3 \mathrm{I}\right]\)

Match List \(I\) with List \(II\)

List \(I\) (Anion)	List \(II\) \((\)Gas evolved on reaction with dil \(H _{2} SO _{4})\)
\(A.\) \(CO _{3}^{2-}\)	\(I.\) Colourless gas which turns lead acetate paper black
\(B.\) \(S^{2-}\)	\(II.\) Colourless gas which turns acidified potassium dichromate solution green.
\(C.\) \(SO_{3}{ }^{2-}\)	\(III.\) Brown fumes which turns acidified KI solution containing starch blue.
\(D.\) \(NO _{2}^{-}\)	\(IV.\) Colourless gas evolved with brisk effervescence, which turns lime water milky.

Choose the correct answer from the options given below

Let \(\vec{a}=\hat{i}+\hat{j}+2 \hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\overrightarrow{ c }=\hat{ i }-\hat{ j }+\hat{ k }\) be three given vectors. Let \(\vec{v}\) be a vector in the plane of \(\vec{a}\) and \(\overrightarrow{ b }\) whose projection on \(\overrightarrow{ c }\) is \(\frac{2}{\sqrt{3}}\). If \(\overrightarrow{ v } . \hat{ j }=7\), then \(\overrightarrow{ v } \cdot(\hat{ i }+\hat{ k })\) is equal to

If \(f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R\), then