Consider the following reduction processes:
\(Al^{3+} + 3e^{-} \rightarrow Al(s), E^{\circ} = -1.66 V\)
\(Fe^{3+} + e^{-} \rightarrow Fe^{2+}, E^{\circ} = +0.77 V\)
\(Co^{3+} + e^{-} \rightarrow Co^{2+}, E^{\circ} = +1.81 V\)
\(Cr^{3+} + 3e^{-} \rightarrow Cr(s), E^{\circ} = -0.74 V\)
The tendency to act as reducing agent decreases in the order:

If a substance ' \(A\) ' dissolves in solution of a mixture of ' \(B\) ' and ' \(C\) ' with their respective number of moles as \(n_A, n_B\) and \(n_C\), mole fraction of ' \(C\) ' in the solution is _______.

Given below are two statements, one is labeled as Assertion \((A)\) and other is labeled as Reason \((R).\) Assertion \((A):\) Gabriel phthalimide synthesis cannot be used to prepare aromatic primary amines. Reason \((R) :\) Aryl halides do not undergo nucleophilic substitution reaction. In the light of the above statements, choose the correct answer form the options given below.

The radius of the second Bohr orbit for hydrogen atom is  .......... \(\mathop A\limits^o \) (Plank's const. \( h = 6. \times 10^{-34}\, Js\,;\) mass of electron \(= 9.1091 \times 10^{-31}\, kg\,;\) charge of electron \(e= 1.60210 \times 10^{-19}\, C\,;\) permittivity of vaccum \(\epsilon _0 = 8.854185 \times 10^{-12} \,kg^{-1} \,m^{-3} A^2\))

Which of the following is a set of green house gases ?

Among \(\mathrm{SO}_2, \mathrm{NF}_3, \mathrm{NH}_3, \mathrm{XeF}_2, \mathrm{ClF}_3\) and \(\mathrm{SF}_4\), the hybridization of the molecule with non-zero dipole moment and highest number of lone-pairs of electrons on the central atom is _______.

Match \(List-I\) with \(List-II\).

\(List-I\)	\(List-II\)
\((A)\) \(\Psi_{ MO }=\Psi_{ A }-\Psi_{ B }\)	\((I)\) Dipole moment
\((B)\) \(\mu=Q \times I\)	\((II)\) Bonding molecular orbital
\((C)\) \(\frac{N_{b}-N_{a}}{2}\)	\((III)\) Anti-bonding molecualr orbital
\((D)\) \(\Psi_{ MO }=\Psi_{ A }+\Psi_{ B }\)	\((IV)\) Bond order

 

What would be the electrode potential for the given half cell reaction at \(pH = 5\) ? ........... \(\mathrm{V}\) \(2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{O}_{2}+4 \mathrm{H}^{\oplus}+4 \mathrm{e}^{-} ; \mathrm{E}_{\mathrm{red}}^{0}=1.23 \mathrm{V}\) \((\mathrm{R}=8.314 \;\mathrm{J} \mathrm{mol}^{-1} \mathrm{K}^{-1} ; \text { Temperature }=298 \;\mathrm{K} ;\) oxygen under std. atm. pressure of \(1 \;bar\))

\(1\,L,0.02\,M\) solution of \(\left[ Co \left( NH _3\right)_5 SO _4\right] Br\) is mixed with \(1\,L,0.02\,M\) solution of \(\left[ Co \left( NH _3\right)_5 Br _3\right] SO _4\). The resulting solution is divided into two equal parts (X) and treated with excess \(AgNO _3\) solution and \(BaCl _2\) solution respectively as shown below: \(1\,L\) Solution \(( X )+ AgNO _3\) solution (excess) \(\rightarrow Y\) \(1\,L\) Solution \(( X )+ BaCl _2\) solution (excess) \(\rightarrow Z\) The number of moles of \(Y\) and \(Z\) respectively are

Electricity is passed through an acidic solution of \( Cu^{2+} \) till all the \( Cu^{2+} \) was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is ______ mL.
(Nearest integer)
[Given :
\(Cu ^{2+}( aq )+2 e ^{-} \rightarrow Cu ( s ) E _{\text {red }}^0=+0.34 V\)
\(O _2(g)+4 H ^{+}+4 e ^{-} \rightarrow 2 H _2 O E _{ red }^0=+1.23 V\)
Molar mass of \(Cu =63.54~g~mol ^{-1}\)
Molar mass of \(O _2=32~g~mol ^{-1}\)
Faraday Constant \(=96500~C~mol ^{-1}\)
Molar volume at \(S T P=22.4 L\) ]

Let C be the circle \(\mathrm{x}^2+(\mathrm{y}-1)^2=2, \mathrm{E}_1\) and \(\mathrm{E}_2\) be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line \(x+y=3\) touch the curves \(C\), \(E_1\) and \(E_2\) at \(P\left(x_1, y_1\right), Q\left(x_2, y_2\right)\) and \(R\left(x_3, y_3\right)\) respectively. Given that \(P\) is the mid-point of the line segment \(Q R\) and \(P Q=\frac{2 \sqrt{2}}{3}\), the value of \(9\left(x_1 y_1+x_2 y_2+x_3 y_3\right)\) is equal to ______ .

The Born-Haber cycle for \(\mathrm{KCl}\) is evaluated with the following data : \(\Delta_{f} \mathrm{H}^{\ominus}\) for \(\mathrm{KCl}=-436.7 \,\mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {sub }} \mathrm{H}^{\ominus}\) for \(\mathrm{K}=89.2 \,\mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {ionization }} \,\mathrm{H}^{-}\) for \(\mathrm{K}=419.0\, \mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {electron gain }} \mathrm{H}^{\ominus}\) for \(\mathrm{Cl}_{(\text {e) }}=-348.6 \,\mathrm{~kJ} \,\mathrm{~mol}^{-1}\) \(\Delta_{\mathrm{bond}} \mathrm{H}^{-}\) for \(\mathrm{Cl}_{2}=243.0 \,\mathrm{~kJ} \,\mathrm{~mol}^{-1}\) The magnitude of lattice enthalpy of \(\mathrm{KCl}\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is ..... . (Nearest integer)

If the image of the point \((-4,5)\) in the line \(x+2 y=2\) lies on the circle \((x+4)^2+(y-3)^2=r^2\), then \(r\) is equal lo: