\(\Delta H\) and \(\Delta S\) were found to be both positive for a reversible reaction at temperature ' T '. If the equilibrium temperature is \(\mathrm{T}_{\mathrm{o}}\), the reaction will be spontaneous when

The \(\Delta\)G\(^o\) for the reaction, \(\text{Cd}^{2+}(aq) + \text{Zn}(s) \rightarrow \text{Zn}^{2+}(aq) + \text{Cd}(s)\) is:
\(\left[E^o_{\text{Cd}^{2+}/\text{Cd}} = -0.403,\ E^o_{\text{Zn}^{2+}/\text{Zn}} = -0.763\ V\right]\)

Choose the correct metal/ ion from the brackets which ..........
A. has chemical reactivity similar to that of the first few members of the Lanthanoids \((\mathrm{Zn}, \mathrm{Ca}, \mathrm{Fe}, \mathrm{Cu})\).
B. has stable \(4 \mathrm{f}^7\) electronic configuration, but acts as a strong reducing agent and converts to \(\mathrm{M}^{3+}\) state. \(\left(\mathrm{Eu}^{2+}, \mathrm{Ce}^{2+}, \mathrm{Pr}^{2+}, \mathrm{Dy}^{2+}\right)\)
C. is a colorless ion \(\left(\mathrm{Tm}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Gd}^{3+}, \mathrm{Sm}^{3+}\right)\).
D. shows stable +2 oxidation state and is diamagnetic \((\mathrm{Ce}, \mathrm{Sm}, \mathrm{Ho}, \mathrm{Yb})\)

The time required for \(100 \%\) completion of zero order reaction is

\(\mathrm{X} \rightarrow 2 \mathrm{Y}\) is a first order reaction where \(1.0 \mathrm{~mol} / \mathrm{L}\) of the reactant yields \(0.4 \mathrm{~mol} / \mathrm{L}\) of Y in 200 minutes. Calculate the half-life period of the reaction in minutes.

When, compared to \(\Delta G^{\circ}\) for the formation of \(\mathrm{Al}_{2} \mathrm{O}_{3}\), the \(\Delta G^{\circ}\) for the formation of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) is

Considering the reaction,
\(\mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+393.5 \mathrm{~kJ}\) The signs of \(\Delta H, \Delta \mathrm{S}\) and \(\Delta G\) respectively are \(\begin{array}{ll}\text { a. }-,+,- & \text { b. }-,-,- \\ \text { c. }-,+,+ & \text { d. }+,-,-\end{array}\)

Choose the correct statement from the options given

A straight wire of length \(2 \mathrm{~m}\) carries a current of \(10 \mathrm{~A}\). If this wire is placed in uniform magnetic field of \(0.15 \mathrm{~T}\) making an angle of \(45^{\circ}\) with the magnetic field, the applied force on the wire will be

A bob of a simple pendulum has a mass of 4 g and a charge of \(20 \mu \mathrm{C}\). If it is at rest in a uniform horizontal electric field of intensity \(1000 \mathrm{Vm}^{-1}\), the angle that the pendulum makes with the vertical at equilibrium is:

The multiplicative inverse of \(\frac{3+4 i}{4-5 i}\) is

The ratio of the speed of electron in the \(4^{\text {th }}\) orbit of \(\mathrm{Li}^{++}\)to the speed of electron in the ground state of hydrogen atom will be:

The correct condition for physical adsorption is