MCQ
If $(a, b) = (x, y)$ then$............$
- A$a = x$
- B$a = y$
- C$a = y$ and $b = x$
- ✓$a = x$ and $b = y$
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$(a)$ reflection about the line $y=x$.
$(b)$ translation through $2$ units along the positive direction of $x$-axis.
$(c)$ rotation through angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.
If the co-ordinates of the final position of the point $P$ are $\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$, then the value of $2 a+b$ is equal to:
$\frac{3}{{1! + 2! + 3!}} + \frac{4}{{2! + 3! + 4!}} + \frac{5}{{3! + 4! + 5!}} + ...... + \frac{{2008}}{{\left( {2006} \right)! + \left( {2007} \right)! + \left( {2008} \right)!}}$ is equal to