If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is

A tetrapeptide has -COOH group on alanine. This produces glycine (Gly), Valine (Val), Phenyl alanine (Phe) and Alanine (Ala) on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with -NH₂ group attached to a chiral center is 

Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is
\(\begin{array}{llll}
\mathrm{KCN} & \mathrm{K}_2 \mathrm{SO}_4 & \left(\mathrm{NH}_4\right)_2 \mathrm{C}_2 \mathrm{O}_4 & \mathrm{NaCl} \\
\mathrm{Zn}\left(\mathrm{NO}_3\right)_2 & \mathrm{FeCl}_3 & \mathrm{~K}_2 \mathrm{CO}_3 & \mathrm{NH}_4 \mathrm{NO}_3 \\
\mathrm{LiCN} & & &
\end{array}\)

Among the following metal carbonyls, the \(\mathrm{C}-\mathrm{O}\) bond order is lowest in

Paragraph:
Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately \(6.023 \times 10^{23}\) ) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.
A \(4.0\) molar aqueous solution of \(\mathrm{NaCl}\) is prepared and \(500 \mathrm{~mL}\) of this solution is electrolysed. This leads to the evolution of chlorine gas at one of electrodes (atomic mass: \(\mathrm{Na}=23, \mathrm{Hg}=200 ; 1\) faraday \(=96500\) coulombs).
Question:
If the cathode is a Hg electrode, the maximum weight \((g)\) of amalgam formed from this solution is

The compound that does NOT liberate CO₂, on treatment with aqueous sodium bicarbonate solution, is 

Fusion of $\mathrm{M}\mathrm{n}{\mathrm{O}}_2$ with $\mathrm{K}\mathrm{O}\mathrm{H}$ in presence of ${\mathrm{O}}_2$ produces a salt $\mathrm{W}.$ Alkaline solution of $\mathrm{W}$ upon electrolytic oxidation yields another salt $\mathrm{X}.$ The manganese containing ions present in $\mathrm{W}$ and $\mathrm{X},$ respectively, are $\mathrm{Y}$ and $\mathrm{Z}.$ Correct statement(s) is (are)

A spherical body of radius $\mathrm{R}$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $\mathrm{P}\left(\mathrm{r}\right)$ is the pressure at $\mathrm{r}(\mathrm{r}<\mathrm{R})$ , then the correct option(s) is (are)

A hydrogen atom in its ground state is irradiated by light of wavelength $970 Å.$ Taking hc/e = $1.237\times {10}^{-6} eV$ m and the ground state energy of hydrogen atom as $-13.6 eV$ , the number of lines present in the emission spectrum is

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500 Hz$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length $50.7 cm and 83.9 cm$ . Which of the following statements is (are) true?

Let \(\alpha, \beta\) and \(\gamma\) be real numbers such that the system of linear equations
\[
\begin{array}{c}
x+2 y+3 z=\alpha \\
4 x+5 y+6 z=\beta \\
7 x+8 y+9 z=\gamma-1
\end{array}
\]
is consistent. Let \(|M|\) represent the determinant of the matrix
\[
M=\left[\begin{array}{ccc}
\alpha & 2 & \gamma \\
\beta & 1 & 0 \\
-1 & 0 & 1
\end{array}\right]
\]
Let \(P\) be the plane containing all those \((\alpha, \beta, \gamma)\) for which the above system of linear equations is consistent, and \(D\) be the square of the distance of the point \((0,1,0)\) from the plane \(P\).
The value of $\left|M\right|$ is

Let $E_1$ and $E_2$ be two ellipse whose centers are at the origin. The major axes of $E_{1}and E_2$ lie along the x - axis and the y - axis, respectively. Let S be the circle $x^2+{\left(y-1\right)}^2=2.$ The straight line $x+y=3$ touches the curves $S, E_1$ and $E_2$ at $P, Q$ and $R,$ respectively. Suppose that $PQ=PR= \frac{2\sqrt{2}}{3}.$ If$e_1$ and $e_2$ are the eccentricities of $E_1$ and $E_2,$respectively, then the correct expression(s) is(are)

Addition of excess aqueous ammonia to a pink coloured aqueous solution of $MC{l}_2.6H_{2}O \left(X\right)$ and $N{H}_{4}Cl$ gives an octahedral complex Y in the presence of air. In aqueous solution, complex Y behaves as 1 : 3 electrolyte. The reaction of X with excess HCl at room temperature results in the formation of a blue coloured complex Z. The calculated spin only magnetic moment of X and Z is 3.87 B.M., whereas it is zero for complex Y.
Among the following options, which statement(s) is(are) correct ?