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 line $3x - 2y + 6 = 0$ meets the $X$-axis and $Y$-axis at points $A$ and $B$ respectively,then the equation of the circle with radius $AB$ and center at $A$ is:

The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$ is:

$A$ whistle revolves in a circle with an angular speed of $20\, rad/s$ using a string of length $50\, cm$. If the frequency of sound from the whistle is $385\, Hz$,then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? (Speed of sound is $340\, m/s$)

The sum of the magnitudes of two forces acting at a point is $16 ~N$. If their resultant is normal to the smaller force and has a magnitude of $8 ~N$,then the forces are:

In the circuit shown below,the resistances are given in ohm and the battery is assumed ideal with $emf$ equal to $3\, V$. The voltage across the resistance $R_4$ is ................ $V$.