Select the option with correct property.

The sum of the total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is

Consider the following half cell reaction
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})\) \(\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
The reaction was conducted with the ratio of \(\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}\). The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
\(\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]\)

The ionic radii of \(O _{2}- F ^{-}, Na ^{+}\) and \(Mg ^{2+}\) are in the order :

Which of the following is least basic?

Assume carbon burns according to following equation : \(2 C _{( s )}+ O _{2( g )} \rightarrow 2 CO ( g )\) When \(12\,g\) carbon is burnt in \(48\,g\) of oxygen, the volume of carbon monoxide produced is \(......\times 10^{-1}\,L\) at STP [nearest integer] [Given : Assume \(CO\) as ideal gas, Mass of \(C\) is \(12\,g\,mol ^{-1}\), Mass of \(O\) is \(16\,g\,mol ^{-1}\) and molar volume of an ideal gas at STP is \(22.7\,L\, mol ^{-1}\) ]

Among the following organic acids, the acid present in rancid butter is

A \(20\,cm\) long metallic rod is rotated with \(210\,rpm\) about an axis normal to the rod passing through its one end. The order end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field \(0.2\,T\) parallel to the axis exists everywhere. The emf developed between the centre and the ring is \(.......\,mV\).Take \(\pi=\frac{22}{7}\)

A uniform heavy rod of mass \(20\,kg\). Cross sectional area \(0.4\,m ^{2}\) and length \(20\,m\) is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is \(x \times 10^{-9} m\). The value of \(x\) is (Given. Young's modulus \(Y =2 \times 10^{11} Nm ^{-2}\) અને \(\left.g=10\, ms ^{-2}\right)\)

\(200\, \mathrm{~mL}\) of \(0.2\, \mathrm{M} \mathrm{HCl}\) is mixed with \(300\, \mathrm{~mL}\) of \(0.1\, \mathrm{M} \mathrm{NaOH}\). The molar heat of neutralization of this reaction is \(-57.1 \,\mathrm{~kJ}\). The increase in temperature in \({ }^{\circ} \mathrm{C}\) of the system on mixing is \(\mathrm{x} \times 10^{-2}\). The value of \(\mathrm{x}\) is ....... . (Nearest integer) [Given : Specific heat of water \(=4.18\, \mathrm{~J} \,\mathrm{~g}^{-1}\, \mathrm{~K}^{-1}\) Density of water \(=1.00\, \mathrm{~g}\, \mathrm{~cm}^{-3}\) ] (Assume no volume change on mixing)

\(\Delta U\) is equal to

The energy required to remove the electron from a singly ionized Helium atom is \(2.2\, times\) the energy required to remove an electron from Helium atom . The total energy required to ionize the Helium atom completely is......\(eV\)

Let \(\alpha>0, \beta>0\) be such that \(\alpha^{3}+\beta^{2}=4 .\) If the maximum value of the term independent of \(x\) in the binomial expansion of \(\left(\alpha x^{\frac{1}{9}}+\beta x^{-\frac{1}{6}}\right)^{10}\) is \(10 k\) then \(\mathrm{k}\) is equal to