Let $$a_{1}, a_{2}, a_{3}, \ldots, a_{\mathrm{n}}$$ be $$\mathrm{n}$$ positive consecutive terms of an arithmetic progression. If $$\mathrm{d} > 0$$ is its common difference, then

$$\lim_\limits{n \rightarrow \infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots \ldots \ldots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}\right)$$ is

Statement $$\mathrm{(P \Rightarrow Q) \wedge(R \Rightarrow Q)}$$ is logically equivalent to :

If $${ }^{2 n} C_{3}:{ }^{n} C_{3}=10: 1$$, then the ratio $$\left(n^{2}+3 n\right):\left(n^{2}-3 n+4\right)$$ is :

The sum of all the roots of the equation $$\left|x^{2}-8 x+15\right|-2 x+7=0$$ is :