Following four solutions are prepared by mixing different volumes of \(NaOH\) and \(HCl\) of different concentrations, \(pH\) of which one of them will be equal to \(1\)?

\({image}\) The above reaction requires which of the following reaction conditions ?

\([\mathrm{Pd}(\mathrm{F})(\mathrm{Cl})(\mathrm{Br})(\mathrm{I})]^{2-}\) has \(n\) number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy \([CFSE]\) of \([Fe(CN)_6]^{\mathrm{n}-6},\) respectively, are [Note : Ignore the pairing energy]

Two positively charged particles \(m_{1}\) and \(m_{2}\) have been accelerated across the same potential difference of 200 keV as shown below.

[Given mass of \(m_{1} = 1 amu\) and \(m_{2} = 4 amu\)].
The deBroglie wavelength of \(m_{1}\) will be x times of \(m_{2}\). The value of x is __________ . (nearest integer)

\(IUPAC\) name of following hydrocarbon \((\mathrm{X})\) is _______.

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below \({O_3}(g)\, + \,C{l^ * }(g)\, \to \,{O_2}(g) + Cl{O^ * }(g)\) ..... \((i)\)               \([{K_i} = 5.2 \times {10^9}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) \(Cl{O^ * }(g) + {O^ * }(g)\, \to \,{O_2}(g) + \,C{l^ * }(g)\) ..... \((ii)\)                \([{K_{ii}} = 2.6 \times {10^{10}}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) The closest rate constant for the overall reaction  \({O_3}(g){\mkern 1mu}  + {\mkern 1mu} {O^*}(g){\mkern 1mu}  \to {\mkern 1mu} 2{O_2}(g)\) is  ........... \(L\,\,mo{l^{ - 1}}\,{s^{ - 1}}\)

The reason for double helical structure of \(DNA\) is the operation of

Let the ellipse \(\mathrm{E}_1: \frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1, \mathrm{a}\gt\mathrm{b}\) and \(\mathrm{E}_2: \frac{x^2}{\mathrm{~A}^2}+\frac{y^2}{\mathrm{~B}^2}=1, \mathrm{~A} \lt \mathrm{B}\) have same eccentricity \(\frac{1}{\sqrt{3}}\). Let the product of their lengths of latus rectums be \(\frac{32}{\sqrt{3}}\), and the distance between the foci of \(E_1\) be 4. If \(E_1\) and \(E_2\) meet at \(A, B, C\) and \(D\), then the area of the quadrilateral \(A B C D\) equals :

In some solutions, the concentration of \(H_3O^+\) remains constant even when small amounts of strong acid or strong base are added to them. These solutions are known as

Let the domain of the function \( f(x)=\log_{3}\log_{5}\log_{7}(9x-x^{2}-13) \) be the interval (m, n). Let the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) have eccentricity \( \frac{n}{3} \) and the length of the latus rectum \( \frac{8m}{3} \). Then \( b^{2}-a^{2} \) is equal to:

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{C_p}{C_v}\) for the gas is:

A plane electromagnetic wave propagating in \(\mathrm{x}\)-direction is described by \(\mathrm{E}_{\mathrm{y}}=\left(200\  \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 \mathrm{t}-0.05\  \mathrm{x}\right] \text {; }\) The intensity of the wave is :(Use \(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) )

The pair of metal ions that can give a spin-only magnetic moment of \(3.9\, BM\) for the complex \([M(H_2O)_6]Cl_2\) is