Two reactions are given below: \(2 \mathrm{Fe}_{(\mathrm{s})}+\frac{3}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{Fe}_2 \mathrm{O}_{3(\mathrm{~s})}, \Delta \mathrm{H}^{\mathrm{o}}=-822 \mathrm{~kJ} / \mathrm{mol}\) \(\mathrm{C}_{(\mathrm{s})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_{(\mathrm{g})}, \Delta \mathrm{H}^{\mathrm{o}}=-110 \mathrm{~kJ} / \mathrm{mol}\) Then enthalpy change for following reaction \(3\mathrm{C}_{(\mathrm{s})}+\mathrm{Fe}_2 \mathrm{O}_{3(\mathrm{~s})} \rightarrow 2 \mathrm{Fe}_{(\mathrm{s})}+3 \mathrm{CO}_{(\mathrm{g})}\)

The reaction rate for the reaction \(\left[\mathrm{PtCl}_{4}\right]^{2-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right]^{-}+\mathrm{Cl}^{-}\) was measured as a function of concentrations of different species. It was observed that \(\frac{-\mathrm{d}\left[\left[\mathrm{PtCl}_{4}\right]^{2-}\right]}{\mathrm{dt}}=4.8 \times 10^{-5}\left[\left[\mathrm{PtCl}_{4}\right]^{2-}\right]-2.4 \times10^{-3}\)
\(\left[\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right]^{-}\right]\left[\mathrm{Cl}^{-}\right]\) where square brackets are used to denote molar concentrations. The equilibrium constant \(\mathrm{K}_{\mathrm{c}}=....\). (Nearest integer)

The correct order of spin only magnetic moments for the following complex ions is

A solution containing \(2.5 \times 10^{-3}\, kg\) of a solute dissolved in \(75 \times 10^{-3} \,kg\) of water boils at \(373.535\) \(K\). The molar mass of the solute is \(.....\,g\, mol ^{-1}\). [nearest integer] (Given: \(K _{ b }\left( H _{2} O \right)=0.52 \,K\, Kg\,mol ^{-1}\), boiling point of water \(=373.15 \,K\) )

Dissolving \(120\, g\) of a compound (mol. wt. \(60\)) in \(1000\, g\) of water gave a solution of density \(1.12\, g/mL\). The molarity of the solution is ............ \(\mathrm{M}\)

Decreasing order of reactivity towards electrophilie substitution for the following compounds is:

The decreasing order of reactivity towards dehydrohalogenation \((E_1)\) reaction of the following compounds is

Identify the correct statements about alkali metals.
A. The order of standard reduction potential \(\left( M ^{+} \mid M \right)\) for alkali metal ions is \(Na > Rb > Li\).
B. CsI is highly soluble in water.
C. Lithium carbonate is highly stable to heat.
D. Potassium dissolved in concentrated liquid ammonia is blue and paramagnetic.
E. All alkali metal hydrides are ionic solids.
Choose the correct answer from the options given below

A thin prism with angle \( 5^{\circ} \) of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is ___________.

A force acts on a \(2\,kg\) object so that its position is given as a function of time as \(x= 3t^2 + 5.\) What is the work done by this force in first \(5\,seconds\) ? ................ \(\mathrm{J}\)

When two soap bubbles of radii \(a\) and \(b ( b > a )\) coalesce, the radius of curvature of common surface is

Let \(\mathrm{E}_1: \frac{x^2}{9}+\frac{y^2}{4}=1\) be an ellipse. Ellipses \(\mathrm{E}_1\) 's are constructed such that their centres and eccentricities are same as that of \(E_1\), and the length of minor axis of \(E_i\) is the length of major axis of \(E_{i+1}(i \geq 1)\). If \(A_i\) is the area of the ellipse \(E_i\), then \(\frac{5}{\pi}\left(\sum_{i=1}^{\infty} A_i\right)\), is equal to

\(1\) mole of rigid diatomic gas performs a work of \(Q / 5\) when heat \(Q\) is supplied to it. The molar heat capacity of the gas during this transformation is \(\frac{ x R }{8},\) The value of \(x\) is \(\ldots \ldots \ldots .\) \([ K =\) universal gas constant \(]\)