Figure 1. electron


Figure 2. wave function for 2s orbital
Which of the following point in Figure 2 mostaccurately represents the nodal surface as shown in Figure 1 ?

The first transition series metal ' M ' has the highest enthalpy of atomisation in its series. One of its aquated ion \(\left(\mathrm{M}^{\mathrm{n} \dagger}\right)\) exists in green colour. The nature of the oxide formed by the above \(\mathrm{M}^{\mathrm{n}-}\) ion is _______.

The number of incorrect statements from the following is \(A.\) The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy. \(B.\) \(E _{\text {cell }}^0\) is dependent on the pressure \(C.\) \(\frac{ dE ^0 \text { cell }}{ dT }=\frac{\Delta_{ r } S ^0}{ nF }\) \(D.\) A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

When 1 g each of compounds AB and \(\mathrm{AB}_2\) are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in amu) is ____ \(\times 10^{-1}\) (Nearest integer)
(Given : Molal boiling point elevation constant is \(\left.0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)

A litre of buffer solution contains \(0.1\) mole of each of \(NH _3\) and \(NH _4 Cl\). On the addition of \(0.02\,mole\) of \(HCl\) by dissolving gaseous \(HCl\), the \(pH\) of the solution is found to be \(......\times 10^{-3}(\) Nearest integer) \(\left[\right.\) Given : \(pK _{ b }\left( NH _3\right)=4.745\) \(\log 2=0.301\) \(\log 3=0.477\) \(T =298\,K ]\)

A solution containing \(10 \mathrm{~g}\) of an electrolyte \(\mathrm{AB}_2\) in \(100 \mathrm{~g}\) of water boils at \(100.52^{\circ} \mathrm{C}\). The degree of ionization of the electrolyte \((\alpha)\) is _______ \(\times 10^{-1}\). (nearest integer) [Given : Molar mass of \(\mathrm{AB}_2=200 \mathrm{~g} \mathrm{~mol}^{-1} \cdot \mathrm{K}_{\mathrm{b}}\) (molal boiling point elevation const. of water) \(=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\), boiling point of water \(=100^{\circ} \mathrm{C}\); \(\mathrm{AB}_2\) ionises as \(\left.\mathrm{AB}_2 \rightarrow \mathrm{A}^{2+}+2 \mathrm{~B}^{-}\right]\)

The compound with molecular formula \(\mathrm{C}_6 \mathrm{H}_6\), which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has ________ \(=\) electrons.

Let \(\alpha=\frac{-1+i \sqrt{3}}{2} .\) If \(a=(1+\alpha) \sum\limits_{k=0}^{100} \alpha^{2 k}\) and \(\mathrm{b}=\sum\limits_{\mathrm{k}=0}^{100} \alpha^{3 \mathrm{k}},\) then a and \(\mathrm{b}\) are the roots of the quadratic equation

The wave number of the first emission line in the Balmer series of \(H-\) Spectrum is ( \(R =\) Rydberg constant)

Combustion of \(1\) mole of benzene is expressed at \(\mathrm{C}_6 \mathrm{H}_6(1)+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(1) \text {. }\) The standard enthalpy of combustion of \(2 \mathrm{~mol}\) of benzene is - ' \(x\) ' \(k J\). \(\mathrm{x}=\) _______ \((1)\) standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{C}_6 \mathrm{H}_6(1)\), for the reaction \(6 \mathrm{C}\) (graphite) \(+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{C}_6 \mathrm{H}_n(1)\) is \(48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((2)\) Standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{CO}_2(\mathrm{~g})\), for the reaction \(\mathrm{C}\) (graphite) \(+\mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_2(\mathrm{~g})\) is \(-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((3)\) Standard and Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{H}_2 \mathrm{O}(1)\), for the reaction \(\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(1)\) is \(-286 \mathrm{~kJ} \mathrm{~mol}^{-1}\).

If \(S\) is the set of distinct values of \('b'\) for which the following system of linear equations \(x + y + z = 1;x + ay + z = 1;ax + by + z = 0\) has no solution , then \(S\) is :

The equilibrium \(\mathrm{Cr}_2 \mathrm{O}_7^{2-} \rightleftharpoons 2 \mathrm{CrO}_4^{2-}\) is shifted to the right in _______.

Let a point A lie between the parallel lines \( L_{1} \) and \( L_{2} \) such that its distances from \( L_{1} \) and \( L_{2} \) are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC, where the points B and C lie on the lines \( L_{1} \) and \( L_{2} \) respectively, is: