If $\alpha, \beta, \gamma$ are roots of $x^3 - 2x^2 + 3x - 2 = 0$,then the value of $\left( \frac{\alpha \beta}{\alpha + \beta} + \frac{\alpha \gamma}{\alpha + \gamma} + \frac{\beta \gamma}{\beta + \gamma} \right)$ is

For the equation $2x^2 - 2(m^2 + 1)x + m^4 + m^2 + 1 = 0$,if $\alpha$ and $\beta$ are the roots,then $\alpha^2 + \beta^2 = \dots$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-ax^2+bx-c=0$,then $\Sigma \alpha^2(\beta+\gamma) = $

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + x^2 + x + 1 = 0$,then match the items of List-$I$ with those of List-$II$:
List-$I$:
$(i)$ $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$
(ii) $\alpha^3 + \beta^3 + \gamma^3$
(iii) $\alpha^4 + \beta^4 + \gamma^4$
(iv) $(\alpha - \beta)^2 + (\beta - \gamma)^2 + (\gamma - \alpha)^2$
List-$II$:
$(A)$ $-1$
$(B)$ $-4$
$(C)$ $1$
$(D)$ $3$
$(E)$ $0$

If $\operatorname{cosec} \theta$ and $\cot \theta$ are the roots of $cx^2+bx+a=0$ $(bc \neq 0)$,then $b^2(b^2-4ac)=$

If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be