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 __________.

In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is $$40 \mathrm{~cm}$$. The balancing length, if the radius of the wire $$\mathrm{AB}$$ is doubled, will be ______________ $$\mathrm{cm}$$.

A thin prism of angle $$6^{\circ}$$ and refractive index for yellow light $$\left(\mathrm{n}_{\mathrm{Y}}\right) 1.5$$ is combined with another prism of angle $$5^{\circ}$$ and $$\mathrm{n}_{\mathrm{Y}}=1.55$$. The combination produces no dispersion. The net average deviation $$(\delta)$$ produced by the combination is $$\left(\frac{1}{x}\right)^{\circ}$$. The value of $$x$$ is ____________.

A conducting circular loop is placed in $$X-Y$$ plane in presence of magnetic field $$\overrightarrow{\mathrm{B}}=\left(3 \mathrm{t}^{3} \,\hat{j}+3 \mathrm{t}^{2}\, \hat{k}\right)$$ in SI unit. If the radius of the loop is $$1 \mathrm{~m}$$, the induced emf in the loop, at time, $$\mathrm{t}=2 \mathrm{~s}$$ is $$\mathrm{n} \pi \,\mathrm{V}$$. The value of $$\mathrm{n}$$ is ___________.