Two coherent sources of light interfere. The intensity ratio of two sources is $$1: 4$$. For this interference pattern if the value of $$\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }}$$ is equal to $$\frac{2 \alpha+1}{\beta+3}$$, then $$\frac{\alpha}{\beta}$$ will be :

With reference to the observations in photo-electric effect, identify the correct statements from below :

(A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light.

(B) The value of saturation current increases on moving the source of light away from the metal surface.

(C) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light.

(D) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves.

(E) Existence of threshold wavelength can not be explained by wave nature of light/ electromagnetic waves.

Choose the correct answer from the options given below :

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 ______________ $$\mathrm{cm}$$.