A student measures the focal length of a convex lens by putting an object pin at a distance $$'u'$$ from the lens and measuring the distance $$'v'$$ of the image pin. The graph between $$'u'$$ and $$'v'$$ plotted by the student should look like

In an experiment, electrons are made to pass through a narrow slit of width $$'d'$$ comparable to their de Broglie wavelength. They are detected on a screen at a distance $$'D'$$ from the slit (see figure).

Which of the following graphs can be expected to represent the number of electrons $$'N'$$ detected as a function of the detector position $$'y'\left( {y = 0} \right.$$ corresponds to the middle of the slit$$\left. \, \right)$$

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $$A=$$ $$10\,\,c{m^2}$$ and length $$=20$$ $$cm$$ . If one of the solenoid has $$300$$ turns and the other $$400$$ turns, their mutual inductance is
$$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,Tm\,{A^{ - 1}}} \right)$$