At $$298 \mathrm{~K}$$, the standard reduction potential for $$\mathrm{Cu}^{2+} / \mathrm{Cu}$$ electrode is $$0.34 \mathrm{~V}$$.

Given : $$\mathrm{K}_{\mathrm{sp}} \mathrm{Cu}(\mathrm{OH})_{2}=1 \times 10^{-20}$$

Take $$\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V}$$

The reduction potential at $$\mathrm{pH}=14$$ for the above couple is $$(-) x \times 10^{-2} \mathrm{~V}$$. The value of $$x$$ is ___________

20 mL of $$0.1 ~\mathrm{M} ~\mathrm{NaOH}$$ is added to $$50 \mathrm{~mL}$$ of $$0.1 ~\mathrm{M}$$ acetic acid solution. The $$\mathrm{pH}$$ of the resulting solution is ___________ $$\times 10^{-2}$$ (Nearest integer)

Given : $$\mathrm{pKa}\left(\mathrm{CH}_{3} \mathrm{COOH}\right)=4.76$$

$$\log 2=0.30$$

$$\log 3=0.48$$

Let a$$_1$$, a$$_2$$, a$$_3$$, .... be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3^rd and 5^th terms be $$\frac{1}{9}$$. Then $$6(a_2+a_4)(a_4+a_6)$$ is equal to

Let $$|\vec{a}|=2,|\vec{b}|=3$$ and the angle between the vectors $$\vec{a}$$ and $$\vec{b}$$ be $$\frac{\pi}{4}$$. Then $$|(\vec{a}+2 \vec{b}) \times(2 \vec{a}-3 \vec{b})|^{2}$$ is equal to :