In lanthanide series, the element well known to exhibit +4 oxidation state is

Which among the following is used in detergents?

Identify the most suitable reagents (I) and (II) for the following sequence of reactions

The bond order of which of the following two species is same?

The minimum number of quantum numbers required to specify an orbital in an atom is

At \(27^{\circ} \mathrm{C}\) in a \(10 \mathrm{~L}\) flask \(4.0 \mathrm{~g}\) of an ideal gaseous mixture containing. He (molar mass \(4.0 \mathrm{~g} \mathrm{~mol}^{-1}\) ) and \(\mathrm{Ne}\) (molar mass \(\left.20 \mathrm{~g} \mathrm{~mol}^{-1}\right)\) has a pres sure of \(1.23 \mathrm{~atm}\). What is the mass \(\%\) of neon ? \(\left(R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)

What is the shape of \(\mathrm{I}_3^{-}\)ion?

For a positive real number \(\lambda\), if the vector \(\hat{\mathrm{a}}=\lambda \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}\) satisfies the equation \([\hat{\mathrm{i}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{i}})+\hat{\mathrm{j}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{j}})+\hat{\mathrm{k}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{k}})]^2=440\), then \(\lambda=\)

From the following data
\[
\begin{aligned}
& \mathrm{CH}_3 \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \\
& \Delta_r H^{\circ}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(l) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-393 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
&
\end{aligned}
\]
The standard enthalpy of formation of \(\mathrm{CH}_3 \mathrm{OH}(l)\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is

. Displacement ' \(s\) ' of a particle, in meters, at any time ' \(t\) ' \(s\) in expressed as \(s=\frac{t^3}{3}-6 t\). Find the acceleration at a time when the velocity vanishes,

Starting from rest, the time taken by a body sliding down on a rough inclined plane at \(45^{\circ}\) with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is

For a prism, the angle of the prism is \(60^{\circ}\) and the refractive index is \(\sqrt{\frac{7}{3}}\). The minimum possible angle of incidence so that the light ray is refracted from the second surface is

A launching vehicle carrying an artificial satellite of mass \(m\) is set for launch on the surface of the earth of mass \(M\) and radius \(R\). If the satellite is intended to move in a circular orbit of radius \(7 R\), the minimum energy required to be spent by the launching vehicle on the satellite is
\((\) Gravitational constant \(=G\) )