The sum of the first $$20$$ terms of the series $$5+11+19+29+41+\ldots$$ is :

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $$\frac{k}{3^{11}}$$, then $$k$$ is equal to :

If the system of equations

$$x+y+a z=b$$

$$2 x+5 y+2 z=6$$

$$x+2 y+3 z=3$$

has infinitely many solutions, then $$2 a+3 b$$ is equal to :

The straight lines $$\mathrm{l_{1}}$$ and $$\mathrm{l_{2}}$$ pass through the origin and trisect the line segment of the line L : $$9 x+5 y=45$$ between the axes. If $$\mathrm{m}_{1}$$ and $$\mathrm{m}_{2}$$ are the slopes of the lines $$\mathrm{l_{1}}$$ and $$\mathrm{l_{2}}$$, then the point of intersection of the line $$\mathrm{y=\left(m_{1}+m_{2}\right)}x$$ with L lies on :