Resistance of a conductivity cell (cell constant $$129 \mathrm{~m}^{-1}$$) filled with $$74.5 \,\mathrm{ppm}$$ solution of $$\mathrm{KCl}$$ is $$100 \,\Omega$$ (labelled as solution 1). When the same cell is filled with $$\mathrm{KCl}$$ solution of $$149 \,\mathrm{ppm}$$, the resistance is $$50 \,\Omega$$ (labelled as solution 2). The ratio of molar conductivity of solution 1 and solution 2 is i.e. $$\frac{\wedge_{1}}{\wedge_{2}}=x \times 10^{-3}$$. The value of $$x$$ is __________. (Nearest integer)

Given, molar mass of $$\mathrm{KCl}$$ is $$74.5 \mathrm{~g} \mathrm{~mol}^{-1}$$.

Ionic radii of cation $$\mathrm{A}^{+}$$ and anion $$\mathrm{B}^{-}$$ are 102 and $$181 \,\mathrm{pm}$$ respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for $$\mathrm{B}^{-}$$. $$\mathrm{A}^{+}$$ is present in all octahedral voids. The edge length of the unit cell of the crystal AB is __________ pm. (Nearest Integer)

The minimum uncertainty in the speed of an electron in an one dimensional region of length $$2 \mathrm{a}_{\mathrm{o}}$$ (Where $$\mathrm{a}_{\mathrm{o}}=$$ Bohr radius $$52.9 \,\mathrm{pm}$$) is _________ $$\mathrm{km} \,\mathrm{s}^{-1}$$.

(Given : Mass of electron = 9.1 $$\times$$ 10^$$-$$31 kg, Planck's constant h = 6.63 $$\times$$ 10^$$-$$34 Js)

When 600 mL of 0.2 M HNO₃ is mixed with $$400 \mathrm{~mL}$$ of 0.1 M NaOH solution in a flask, the rise in temperature of the flask is ___________ $$\times 10^{-2}{ }\,^{\circ} \mathrm{C}$$.

(Enthalpy of neutralisation $$=57 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and Specific heat of water $$=4.2 \,\mathrm{JK}^{-1} \mathrm{~g}^{-1}$$) (Neglect heat capacity of flask)