GATE IN 2014 Question Paper (02-Feb-2014) (Shift 2)

Consider the control system shown in figure with feed forward action for rejection of a measurable disturbance d(t). The value of k, for which the disturbance response at the output y(t) is zero mean, is

A mixture contains two mutually inert solutions ‘X’ and ‘Y’ in equal volumes. The mixture is examined in a spectrophotometer using a cuvette. It is observed that the transmittance is 0.40. With only the solution ‘X’ in the same cuvette, the transmittance is 0.20. With only solution ‘Y’ in the cuvette the transmittance is___________.

Monochromatic light from a step index (n 1 = 1.500; n 2 = 1.485), multimode optical fiber of core diameter 100 μm is incident through air (n = 1.000) onto a linear photo-detector array placed at 1 mm distance from the tip of the fiber. The tip of the fiber is polished and its exit plane is perpendicular to the axis of the fiber. The detector array is oriented parallel to the exit plane of the tip. The array consists of photo-detector elements each of 5 μm diameter. The distance between the edges of two adjacent elements can be assumed to be zero. The number of elements illuminated by the light coming out of the fiber is___________.

An image of the chest of a patient is taken with an X-ray machine on a photographic film. The Hurter-Driffield (HD) curve of the film is shown in the figure. The highly absorbing parts of the body (e.g. bones), show up as low exposure regions(mapped near A) and the less absorbing parts (e.g. muscles) show up as high exposure regions(mapped near B).



If the exposure time is increased 10 times, while keeping the voltages and currents in the X-ray machine constant, in the image

For the given low-pass circuit shown in the figure, the cutoff frequency in Hz will be ___________.