In acidic medium one mole each of \(\mathrm{MnO}_4^{-}\)and \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}\) is reduced by \(x\) and \(y\) moles of ferrous ions. The sum of \(x\) and \(y\) is

The $\mathrm{IUPAC}$ name of the compound ${\left({\mathrm{NH}}_4\right)}_2\left[\mathrm{Ni}{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_2{\left({\mathrm{H}}_2\mathrm{O}\right)}_2\right]$ is

Among the following \(\mathrm{Cr}(\mathrm{III})\) complexes, which one will have the highest octahedral crystal field splitting?

The reaction conditions used for converting 1, 2-dibromo ethane to ethylene are

Which one of the following transitions of an electron in hydrogen atom emits radiation of the lowest wavelength?

Identify the correct statements from the folluwing (A) At 298 K, the potential of hydrogen electrode placed in a solution of \(\mathrm{pH}=10\), is -0.59 V (B) The limiting molar conductivity of \(\mathrm{Ca}^{2+}\) and \(\mathrm{Cl}^{-}\)is 119 and \(76 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\) respectively. The limiting molar conductivity of \(\mathrm{CaCl}_2\) is \(195 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-\frac{1}{2}}\) (C) The correct relationship between \(\mathrm{K}_{\mathrm{c}}\) and \(\mathrm{E}_{\text {cell }}^0\) is \(\mathrm{E}_{\mathrm{ccll}}^{-}=\frac{2.303 \mathrm{RT}}{\mathrm{nF}} \log \mathrm{~K}_{\mathrm{c}}\)

Identify \(X\) and \(Y\) in the following reaction sequence
\(X \stackrel{\mathrm{Zn}}{\longrightarrow} Y \underset{\mathrm{Zn}-\mathrm{H}_2 \mathrm{O}}{\stackrel{\mathrm{O}_3}{\longrightarrow}}\left(\mathrm{CH}_3\right)_2 \mathrm{CO}+\mathrm{CH}_2 \mathrm{O}\)
\(X \quad Y\)

The height of water level is a tank of uniform crosssection is 5 m . The volume of the water leaked in 5 s through a hole of area \(2.4 \mathrm{~mm}^2\) made at the bottom of the tank is (Assume the level of the water in the tank remains constant and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

If the point \(z=(1+i)(1+2 i)(1+3 i) \ldots\) \((1+10 i)\) lies on a circle with centre at origin and radius \(r\), then \(r^2\) is equal to

Propyne was subjected to a reaction with ${\mathrm{HgSO}}_4/$ dil. ${\mathrm{H}}_2{\mathrm{SO}}_4$, which resulted in a product $\mathrm{P}$. The product $\mathrm{P}$ was heated with $\mathrm{Ba}{\left(\mathrm{OH}\right)}_2$ to give the product $\mathrm{Q}$. The molecular formula of the product $\mathrm{Q}$ is

Two persons \(A\) and \(B\) are located in \(X-Y\) plane at the points \((0,0)\) and \((0,10)\) respectively. (The distances are measured in MKS unit). At a time \(t=0\), they start moving simultaneously with velocities \(\quad \overrightarrow{\mathbf{v}}_A=2 \mathbf{j} \mathrm{ms}^{-1} \quad\) and \(\quad \overrightarrow{\mathbf{v}}_B=2 \hat{\mathbf{i}} \mathrm{ms}^{-1}\) respectively. The time after which \(A\) and \(B\) are at their closest distance is

Two long straight parallel wires carry currents of 8 A and 10 A in opposite directions. If the distance of separation between the wires is 9 cm, then the net magnetic field at a point between the two wires, which is at a perpendicular distance of 4 cm from the wire carrying 8 A current is

A wire of cross-sectional area \(10^{-6} \mathrm{~m}^2\) is elongated by \(0.1 \%\) when the tension in it is 1000 N . The Young's modulus of the material of the wire is (Assume radius of the wire is constant)