At \(298 \mathrm{~K}\), the limiting molar conductivity of a weak monobasic acid is \(4 \times 10^{2} \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\). At \(298 \mathrm{~K}\), for an aqueous solution of the acid the degree of dissociation is \(\boldsymbol{\alpha}\) and the molar conductivity is \(\mathbf{y} \times 10^{2} \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\). At \(298 \mathrm{~K}\), upon 20 times dilution with water, the molar conductivity of the solution becomes \(3 \mathbf{y} \times 10^{2} \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\)
The value of $\mathrm{\alpha }$ is _______ .

Using the data provided, calculate the multiple bond energy \(\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\) of a \(\mathrm{C} \equiv \mathrm{C}\) bond in \(\mathrm{C}_{2} \mathrm{H}_{2}\). That energy is (take the bond energy of a \(\mathrm{C}-\mathrm{H}\) bond as \(350 \mathrm{~kJ} \mathrm{~mol}^{-1}\) ) \(2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HC}=\mathrm{CH}(\mathrm{g}) ; \Delta \mathrm{H}=\) \(225 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) ; \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}(\mathrm{g}) ; \Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Match each set of hybrid orbitals from LIST-I with complex (es) given in LIST-II.

	LIST -I		LIST -II
A)	$ds{p}^2$	P)	${\left[Fe{F}_6\right]}^{4-}$
B)	$s{p}^3$	Q)	$\left[Ti{\left(H_{2}O\right)}_{3}C{l}_3\right]$
C)	$s{p}^3{d}^2$	R)	${\left[Cr{\left(N{H}_3\right)}_6\right]}^{3+}$
D)	$d^{2}s{p}^3$	S)	${\left[FeC{l}_4\right]}^{2-}$
		T)	$Ni{\left(CO\right)}_4$
		U)	${\left[Ni{\left(CN\right)}_4\right]}^{2-}$

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

The compound(s) formed upon combustion of sodium metal in excess air is (are)

Based on VSEPR theory, the number of 90 degree \(\mathrm{F}-\mathrm{Br}-\mathrm{F}\) angles in \(\mathrm{BrF}_5\) is

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The reaction of \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with freshly prepared \(\mathrm{FeSO}_{4}\) solution produces a dark blue precipitate called Turnbull's blue. Reaction of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with the \(\mathrm{FeSO}_{4}\) solution in complete absence of air produces a white precipitate \(\mathbf{X}\), which turns blue in air. Mixing the \(\mathrm{FeSO}_{4}\) solution with \(\mathrm{NaNO}_{3}\), followed by a slow addition of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) through the side of the test tube produces a brown ring.
Question:
Among the following, the brown ring is due to the formation of

A charged shell of radius $\mathrm{R}$ carries a total charge $\mathrm{Q}.$ Given $\mathrm{\Phi }$ as the flux of electric field through a closed cylindrical surface of height $\mathrm{h},$ radius $\mathrm{r}$ and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct? [ ${\in }_0$ is the permittivity of free space]

Let P be the point on the parabola $y^2=4x$ which is at the shortest distance from the center S of the circle $x^2+y^2-4x-16y+64=0.$ Let Q be the point on the circle dividing the line segment SP internally. Then -

The centres of two circles \(C_1\) and \(C_2\) each of unit radius are at a distance of 6 units from each other. Let \(P\) be the mid-point of the line segment joining the centres of \(C_1\) and \(C_2\) and \(C\) be a circle touching circles \(C_1\) and \(C_2\) externally. If a common tangents to \(C_1\) and \(C\) passing through \(P\) is also a common tangent to \(C_2\) and \(C\), then the radius of the circle \(C\) is

The correct stability order for the following species is

The correct statement about the following disaccharide is

Let S be the set of all twice differentiable functions f from $\mathrm{ℝ}$ to $\mathrm{ℝ}$ such that $\frac{d^{2}f}{d{x}^2}\left(x\right)>0$ for all $x\in \left(-1,1\right)$. For $f\in S$, let $X_f$ be the number of points $x\in \left(-1,1\right)$ for which $f\left(x\right)=x$. Then which of the following statements is(are) true?