Let y = y(x) be the solution curve of the differential equation,

$$\left( {{y^2} - x} \right){{dy} \over {dx}} = 1$$, satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is :

Let $$\alpha $$ and $$\beta $$ be the roots of the equation x² - x - 1 = 0.
If p_k = $${\left( \alpha \right)^k} + {\left( \beta \right)^k}$$ , k $$ \ge $$ 1, then which one of the following statements is not true?

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is $$\mu $$ = 0.4, the maximum possible value of 100 × $${b \over a}$$ for box not to topple before moving is .......

The sum of two forces $$\overrightarrow P $$ and $$\overrightarrow Q $$ is $$\overrightarrow R $$ such that $$\left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right|$$ . The angle $$\theta $$ (in degrees) that the resultant of 2$${\overrightarrow P }$$ and $${\overrightarrow Q }$$ will make with $${\overrightarrow Q }$$ is , ..............