In a circuit $$L, C$$ and $$R$$ are connected in series with an alternating voltage source of frequency $$f$$. The current leads the voltage by $$45^{\circ}$$. The value of $$C$$ is
The graph between the energy log E of an electron and its de-Broglie wavelength log $$\lambda$$ will be




The half-life of a radioactive substance is $$20 \mathrm{~min}$$. The approximate time interval $$\left(t_2-t_1\right)$$ between the time $$t_2$$, when $$\frac{2}{3}$$ of it has decayed and time $$t_1$$ when $$\frac{1}{3}$$ of it had decayed is

In the figure, mass of a ball is $$\frac{9}{5}$$ times mass of the rod. Length of rod is $$1 \mathrm{~m}$$. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod.
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