If $\frac{1-x+6x^2}{x-x^3} = \frac{A}{x} + \frac{B}{1-x} + \frac{C}{1+x}$,then $A$ is equal to

The shaded part of the given figure indicates the feasible region. Then the constraints are:

In an acute angled triangle,$\cot B \cot C + \cot A \cot C + \cot A \cot B$ is equal to

In the circuit shown,the reading of the Ammeter is doubled after the switch is closed. Each resistor has a resistance $1\,\Omega$ and the ideal cell has an $e.m.f.$ $10\,V$. Then,the Ammeter has a coil resistance equal to ............ $\Omega$

$A$ series $LCR$ circuit is connected across a source of alternating $emf$ of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance $(R)$ is increased by $1.4$ times,the resonant frequency now is

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2,$ respectively. If the maximum velocities during oscillations are equal,the ratio of amplitudes of $A$ and $B$ is