In the electrolytic extraction of $Al$,molten cryolite $(Na_3AlF_6)$ is used because it .......
- Amakes alumina a good conductor of electricity
- Bacts as a reducing agent
- Cincreases the production of $Al$ at the anode
- Dprotects the anode
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The number of ways in which $6$ men and $5$ women can dine at a round table,if no two women are to sit together,is:
Two capacitors $C_1 = 2 \, \mu F$ and $C_2 = 4 \, \mu F$ are connected in a circuit as shown in the figure. The potential difference $(V_A - V_B)$ is.....$V$.
If $a = \frac{1-i \sqrt{3}}{2}$,then the correct matching of List-$I$ with List-$II$ is:
List-$I$ List-$II$ $(i) \ a \bar{a}$ $(A) -\frac{\pi}{3}$ $(ii) \ \arg \left(\frac{1}{\bar{a}}\right)$ $(B) -i \sqrt{3}$ $(iii) \ a-\bar{a}$ $(C) \frac{2i}{\sqrt{3}}$ $(iv) \ \operatorname{Im}\left(\frac{4}{3a}\right)$ $(D) 1$ $(E) \frac{\pi}{3}$ $(F) \frac{2}{\sqrt{3}}$
| List-$I$ | List-$II$ |
| $(i) \ a \bar{a}$ | $(A) -\frac{\pi}{3}$ |
| $(ii) \ \arg \left(\frac{1}{\bar{a}}\right)$ | $(B) -i \sqrt{3}$ |
| $(iii) \ a-\bar{a}$ | $(C) \frac{2i}{\sqrt{3}}$ |
| $(iv) \ \operatorname{Im}\left(\frac{4}{3a}\right)$ | $(D) 1$ |
| $(E) \frac{\pi}{3}$ | |
| $(F) \frac{2}{\sqrt{3}}$ |
If $3x^2-11xy+10y^2-7x+13y+k=0$ denotes a pair of straight lines,then the point of intersection of the lines is
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