If the lines x + y = a and x – y = b touch the curve y = x² – 3x + 2 at the points where the curve intersects the x–axis, then bais equal to ...

The coefficient of x⁴ in the expansion of (1 + x + x² + x³)⁶ in powers of x, is .

23.

$$\begin{gathered} \mathrm{Let} \mathrm{A} = \left\{\mathrm{a}, \mathrm{b}, \mathrm{c}\right\} \mathrm{and} \mathrm{B} = \left\{1, 2, 3, 4\right\}.\mathrm{Then} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{elements} \mathrm{in} \mathrm{the} \mathrm{set} \\ \mathrm{C}=\left\{\mathrm{f} : \mathrm{A} \to \mathrm{B}|2 \in \mathrm{f}(\mathrm{A}) \mathrm{and} \mathrm{f} \mathrm{is} \mathrm{not} \mathrm{one}–\mathrm{one}\right\}\mathrm{is}... \end{gathered}$$

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is ....

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{vectors}\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{c}} \mathrm{be} \mathrm{such} \mathrm{that} \left|\overrightarrow{\mathrm{a}}\right| = 2, \left|\overrightarrow{\mathrm{b}}\right| = 4 \mathrm{and} \left|\overrightarrow{\mathrm{c}}\right| = 4. \mathrm{If} \mathrm{the} \mathrm{projection} \mathrm{of} \\ \overrightarrow{\mathrm{b}} \mathrm{on} \overrightarrow{\mathrm{a}} \mathrm{is} \mathrm{equal} \mathrm{to} \mathrm{the} \mathrm{projection} \mathrm{of} \overrightarrow{\mathrm{c}}\mathrm{on} \overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}} \mathrm{is} \mathrm{perpendicular} \mathrm{to} \overrightarrow{\mathrm{c}}, \\ \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} \left|\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}}\right|\mathrm{is} ....... \end{gathered}$$