Let $$\overrightarrow a $$ = 2$$\widehat i$$ $$-$$ 3$$\widehat j$$ + 4$$\widehat k$$ and $$\overrightarrow b $$ = 7$$\widehat i$$ + $$\widehat j$$ $$-$$ 6$$\widehat k$$.

If $$\overrightarrow r $$ $$\times$$ $$\overrightarrow a $$ = $$\overrightarrow r $$ $$\times$$ $$\overrightarrow b $$, $$\overrightarrow r $$ . ($$\widehat i$$ + 2$$\widehat j$$ + $$\widehat k$$) = $$-$$3, then $$\overrightarrow r $$ . (2$$\widehat i$$ $$-$$ 3$$\widehat j$$ + $$\widehat k$$) is equal to :

Which of the following is true for y(x) that satisfies the differential equation

$${{dy} \over {dx}}$$ = xy $$-$$ 1 + x $$-$$ y; y(0) = 0 :

The sum of possible values of x for

tan^$$-$$1(x + 1) + cot^$$-$$1$$\left( {{1 \over {x - 1}}} \right)$$ = tan^$$-$$1$$\left( {{8 \over {31}}} \right)$$ is :

The line 2x $$-$$ y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x $$-$$ 2y = 4. Then, the radius of the circle is :