If the system of equations $$x+4 y-z=\lambda, 7 x+9 y+\mu z=-3,5 x+y+2 z=-1$$ has infinitely many solutions, then $$(2 \mu+3 \lambda)$$ is equal to :

Let $$f(x)=\left\{\begin{array}{ccc}-\mathrm{a} & \text { if } & -\mathrm{a} \leq x \leq 0 \\ x+\mathrm{a} & \text { if } & 0< x \leq \mathrm{a}\end{array}\right.$$ where $$\mathrm{a}> 0$$ and $$\mathrm{g}(x)=(f(|x|)-|f(x)|) / 2$$. Then the function $$g:[-a, a] \rightarrow[-a, a]$$ is

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $$\frac{70}{3}$$ and the product of the third and fifth terms is 49. Then the sum of the $$4^{\text {th }}, 6^{\text {th }}$$ and $$8^{\text {th }}$$ terms is equal to:

For $$\mathrm{a}, \mathrm{b}>0$$, let $$f(x)= \begin{cases}\frac{\tan ((\mathrm{a}+1) x)+\mathrm{b} \tan x}{x}, & x< 0 \\ 3, & x=0 \\ \frac{\sqrt{\mathrm{a} x+\mathrm{b}^2 x^2}-\sqrt{\mathrm{a} x}}{\mathrm{~b} \sqrt{\mathrm{a}} x \sqrt{x}}, & x> 0\end{cases}$$ be a continuous function at $$x=0$$. Then $$\frac{\mathrm{b}}{\mathrm{a}}$$ is equal to :