If $$\mathop {\lim }\limits_{x \to 0} {{ax - ({e^{4x}} - 1)} \over {ax({e^{4x}} - 1)}}$$ exists and is equal to b, then the value of a $$-$$ 2b is __________.

If the curve, y = y(x) represented by the solution of the differential equation (2xy² $$-$$ y)dx + xdy = 0, passes through the intersection of the lines, 2x $$-$$ 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to _________.

An LCR circuit contains resistance of 110$$\Omega$$ and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45$$^\circ$$. If on the other hand, only inductor is removed the current leads by 45$$^\circ$$ with the applied voltage. The rms current flowing in the circuit will be :

An electron with kinetic energy K₁ enters between parallel plates of a capacitor at an angle '$$\alpha$$' with the plates. It leaves the plates at angle '$$\beta$$' with kinetic energy K₂. Then the ratio of kinetic energies K₁ : K₂ will be :