If $\frac{1}{x(x + 1)(x + 2).....(x + n)} = \frac{A_0}{x} + \frac{A_1}{x + 1} + \frac{A_2}{x + 2} + ..... + \frac{A_n}{x + n}$,then $A_r = $

If the angular velocity of a disc depends on the angle rotated $\theta$ as $\omega = \theta^2 + 2\theta$,then its angular acceleration $\alpha$ at $\theta = 1 \ rad$ is ......... $rad/sec^2$.

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

If the angle between the pair of lines $2x^2 + 2hxy + 2y^2 - x + y - 1 = 0$ is $\tan^{-1}(3/4)$ and $h$ is a positive rational number,then the point of intersection of these two lines is

$AlCl_3$ is:

The work function of a metallic surface is $5.01 \ eV$. The photo-electrons are emitted when light of wavelength $2000 \ \mathring{A}$ falls on it. The potential difference applied to stop the fastest photo-electrons is .............. $volts$ $[h = 4.14 \times 10^{-15} \ eV \cdot s]$