The activity of a radioactive material is $$6.4 \times 10^{-4}$$ curie. Its half life is 5 days. The activity will become $$5 \times 10^{-6}$$ curie after :

For a constant collector-emitter voltage of $$8 \mathrm{~V}$$, the collector current of a transistor reached to the value of $$6 \mathrm{~mA}$$ from $$4 \mathrm{~mA}$$, whereas base current changed from $$20 \,\mu \mathrm{A}$$ to $$25 \,\mu \mathrm{A}$$ value. If transistor is in active state, small signal current gain (current amplification factor) will be :

A square wave of the modulating signal is shown in the figure. The carrier wave is given by $$C(t)=5 \sin (8 \pi t)$$ Volt. The modulation index is :

In an experiment to determine the Young's modulus, steel wires of five different lengths $$(1,2,3,4$$, and $$5 \mathrm{~m})$$ but of same cross section $$\left(2 \mathrm{~mm}^{2}\right)$$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $$x \times 10^{11} \,\mathrm{Nm}^{-2}$$, then the value of $$x$$ is __________.