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If $\alpha, \beta$ are the roots of $x^2 - px + q = 0$ and $\alpha', \beta'$ are the roots of $x^2 - p'x + q' = 0$,then find the value of $(\alpha - \alpha')^2 + (\beta - \alpha')^2 + (\alpha - \beta')^2 + (\beta - \beta')^2$.

If the tangent to the curve $y = \frac{x}{x^2 - 3}$,$x \in R$,$(x \neq \pm \sqrt{3})$ at a point $(\alpha, \beta) \neq (0, 0)$ on it is parallel to the line $2x + 6y - 11 = 0$,then:

The area of the triangle $ABC$ is $10 \sqrt{3} \text{ cm}^2$,angle $B$ is $60^{\circ}$ and its perimeter is $20 \text{ cm}$,then $\ell(AC) = $ (in $text{ cm}$)

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures $200\,^{\circ}C$ and $20\,^{\circ}C$,respectively. The temperature of junction $B$ will be ......... $^{\circ}C$.

What is formed when $PCl_3$ reacts with water?

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