The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :

Let $$y=y(t)$$ be a solution of the differential equation $${{dy} \over {dt}} + \alpha y = \gamma {e^{ - \beta t}}$$ where, $$\alpha > 0,\beta > 0$$ and $$\gamma > 0$$. Then $$\mathop {\lim }\limits_{t \to \infty } y(t)$$

Let $$\overrightarrow a = - \widehat i - \widehat j + \widehat k,\overrightarrow a \,.\,\overrightarrow b = 1$$ and $$\overrightarrow a \times \overrightarrow b = \widehat i - \widehat j$$. Then $$\overrightarrow a - 6\overrightarrow b $$ is equal to :

If the four points, whose position vectors are $$3\widehat i - 4\widehat j + 2\widehat k,\widehat i + 2\widehat j - \widehat k, - 2\widehat i - \widehat j + 3\widehat k$$ and $$5\widehat i - 2\alpha \widehat j + 4\widehat k$$ are coplanar, then $$\alpha$$ is equal to :