The rate constant, k of a zero order reaction \(2 \mathrm{NH}_3(\mathrm{~g})\) \(\underset{1130 \mathrm{~K}}{\stackrel{\mathrm{Pt}}{\longrightarrow}} \mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g})\) is \(\mathrm{y} \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\). The rate of formation of hydrogen (in \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\) ) is

Calculated magnetic moment value for \(\mathrm{Fe}^{2+}\) ion in \(\mathrm{BM}\) is

In a Freundlich adsorption isotherm, if the slope is unity and k is 0.1, the extent of adsorption at 2 atm is \((\log 2=0.30)\)

At \(\mathrm{T}(\mathrm{K}), \mathrm{K}_{\mathrm{c}}\) value of \(\mathrm{AO}_2(\mathrm{~g})+\mathrm{BO}_2(\mathrm{~g}) \rightleftharpoons \mathrm{AO}_3(\mathrm{~g})+\mathrm{BO}(\mathrm{g})\) is 16. In a closed 1 L flask, one mole each of \(\mathrm{AO}_2, \mathrm{BO}_2, \mathrm{AO}_3\) and BO are taken and heated to \(\mathrm{T}(\mathrm{K})\). Identify the correct statements about this equilibrium.
I) Total number of moles at equilibrium is 4
II) At equilibrium, the ratio of moles of \(\mathrm{AO}_2\) and \(\mathrm{AO}_3\) is \(1: 4\)
III) Total number of moles of \(\mathrm{AO}_2\) and \(\mathrm{BO}_2\) at equilibrium is 0.8

5 moles of a gas is allowed to pass through a series of changes as shown in the graph, in a cyclic process. The processes \(\mathrm{C} \rightarrow \mathrm{A}, \mathrm{B} \rightarrow \mathrm{C}\) and \(\mathrm{A} \rightarrow \mathrm{B}\) respectively are

Which one of the following is correct order of second ionisation potential of \(\mathrm{Na}, \mathrm{Ne}, \mathrm{Mg}\) and \(\mathrm{Al}\) ?

$\mathrm{x}\%\left(\mathrm{w}/\mathrm{v}\right)$ solution of urea is isotonic with $4\%\left(\mathrm{w}/\mathrm{v}\right)$ solution of a non-volatile solute of molar mass $120 \mathrm{g} {\mathrm{mol}}^{-1}$. The value of $\mathrm{x}$ is

\(\int_{-1 / 24}^{1 / 24} \sec x \log \left(\frac{1-x}{1+x}\right) d x=\)

The coefficient of static friction between the road and tyres of a car is 0.4 . The maximum permissible speed of the car is \(10 \mathrm{~ms}^{-1}\) on curved unbanked road. Then the maximum radius of curvature of the road is
(acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

The perpendicular distance from the point \((-1,1,0)\) to the line joining the points \((0,2,4)\) and \((3,0,1)\) is

If \(I_1=\int_0^{\pi / 2} \frac{x}{\sin x} d x\), and \(I_2=\int_0^1 \frac{\tan ^{-1} x}{x} d x\), then \(I_1: I_2\) is

If \(A X=D\) represents the system of simultaneous linear equations \(x+y+z=6\), \(5 x-y+2 z=3\) and \(2 x+y-z=-5\), then \((\operatorname{Adj} A) D=\)

The equation of a common tangent to the circle \(x^2+y^2=16\) and to the ellipse \(\frac{x^2}{49}+\frac{y^2}{4}=1\) is