The correct stability order of the following resonance structure is

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

A compound ${\mathrm{H}}_2\mathrm{X}$ with molar weight of 80g is dissolved in a solvent having density of $0.4\mathrm{ }\mathrm{g}\mathrm{m}{\mathrm{l}}^{–1}$ . Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is

Paragraph:
p-amino-N, N-dimethylaniline is added to a strongly acidic solution of \(X\). The resulting solution is treated with a few drops of aqueous solution of \(Y\) to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of \(Y\) with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of \(Y\) with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of \(Z\).
Question:
The compound \(X\), is

Mixture(s) showing positive deviation from Raoult's law at ${35}^{\mathrm{o}}\mathrm{C}$ is (are)

Hydrogen bonding plays a central role in the following phenomena:

According to kinetic theory of gases

A pendulum consists of a bob of mass \(m=0.1 \mathrm{~kg}\) and a massless inextensible string of length \(L=1.0 \mathrm{~m}\). It is suspended from a fixed point at height \(H=0.9 \mathrm{~m}\) above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse \(P=0.2 \mathrm{~kg}-\mathrm{m} / \mathrm{s}\) is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is \(J \mathrm{~kg}-\mathrm{m}^{2} / \mathrm{s}\). The kinetic energy of the pendulum just after the liftoff is \(K\) Joules.
The value of $K$ is ____.

One mole of an ideal gas at $900 \mathrm{K}$, undergoes two reversible processes, $\mathrm{I}$ followed by $\mathrm{II}$, as shown below. If the work done by the gas in the two processes are same, the value of $\ln \frac{{\mathrm{V}}_3}{{\mathrm{V}}_2}$ is ($\mathrm{U}$ : internal energy, $\mathrm{S}:$ entropy, $\mathrm{p}:$ pressure, $\mathrm{V}:$ volume, $\mathrm{R}$ : gas constant)  (Given: molar heat capacity at constant volume, ${\mathrm{C}}_{\mathrm{V},\mathrm{m}}$ of the gas is $\frac{5}{2}\mathrm{R}$)

Let M be a $2 \times 2$ symmetric matrix with integer entries. Then M is invertible if

Paragraph:
Let \(a\), b and \(c\) be three real numbers satisfying \(\left[\begin{array}{lll}a & b & c\end{array}\right]\left[\begin{array}{lll}1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]\)
Question:
Let \(\omega\) be a solution of \(x^3-1=0\) with \(\operatorname{Im}(\omega)>0\). If \(a=2\), with \(b\) and \(c\) satisfying Eq. (E), then the value of \(\frac{3}{\omega^a}+\frac{1}{\omega^b}+\frac{3}{\omega^c}\)

The correct order of acid strength of the following carboxylic acids is -

The equation of a plane passing through the line of intersection of the planes \(x+2 y+3 z=2\) and \(x-y+z=3\)

and at a distance \(\frac{2}{\sqrt{3}}\) from the point \((3,1,-1)\) is