\(\mathrm{A}_{(\mathrm{g})} \rightleftharpoons \mathrm{B}_{(\mathrm{g})}+\frac{\mathrm{C}}{2}(\mathrm{~g})\) The correct relationship between \(K_P, \alpha\) and equilibrium pressure \(P\) is _______.

Given below are two statements: Statement \((I)\) : In the Lanthanoids, the formation of \(\mathrm{Ce}^{+4}\) is favoured by its noble gas configuration. Statement \((II)\) : \(\mathrm{Ce}^{+4}\) is a strong oxidant reverting to the common \(+3\) state. In the light of the above statements, choose the most appropriate answer from the options given below:

The Crystal Field Stabilization Energy \((CFSE)\) and magnetic moment (spin-only) of an octahedral aqua complex of a metal ion \(\left(\mathrm{M}^{2+}\right)\) are \(-0.8\, \Delta_{0}\) and \(3.87\, \mathrm{BM}\), respectively. Identify \(\left(\mathrm{M}^{Z+}\right):\)

The number of interhalogens from the following having square pyramidal structure is. \(ClF _{3}, IF _{7}, BrF _{5}, BrF _{3}, I _{2} Cl _{6}, IF _{5}, ClF , ClF _{5}\)

A liquid when kept inside a thermally insulated closed vessel at \(25^{\circ} \mathrm{C}\) was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ?

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). Assertion \((A)\) : \(\mathrm{NH}_3\) and \(\mathrm{NF}_3\) molecule have pyramidal shape with a lone pair of electrons on nitrogen atom. The resultant dipole moment of \(\mathrm{NH}_3\) is greater than that of \(\mathrm{NF}_3\). Reason \((R)\) : In \(\mathrm{NH}_3\), the orbital dipole due to lone pair is in the same direction as the resultant dipole moment of the \(\mathrm{N}-\mathrm{H}\) bonds. \(\mathrm{F}\) is the most electronegative element. In the light of the above statements, choose the correct answer from the options given below:

Identify from the following species in which \(\mathrm{d}^2 \mathrm{sp}^3\) hybridization is shown by central atom:

In the expansion of \(\left(9x-\dfrac{1}{3\sqrt{x}}\right)^{18}\), \(x>0\), if the term independent of \(x\) is \((221)k\), then \(k\) is equal to:

The number of natural numbers less than \(7,000\) which can be formed by using the digits \(0, 1, 3, 7, 9\) (repetition of digits allowed) is equal to

An electric power line having total resistance of 2 Ω, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line is: __________ .

At \(298\,K\), the equilibrium constant is \(2 \times 10^{15}\) for the reaction. \(Cu ( s )+2 Ag ^{+}( aq ) \rightleftharpoons Cu ^{2+}( aq )+2 Ag ( s )\) The equilibrium constant for the reaction.\(\frac{1}{2} Cu ^{2+}( aq )+ Ag ( s ) \rightleftharpoons \frac{1}{2} Cu ( s )+ Ag ^{+}( aq )\) is \(x \times 10^{-8}\). The value of \(x\) is (Nearest Integer)

The number of chiral centres present in \([ B ]\) is

The value of current in the \(6 \,\Omega\) resistance is \(....\,A\)