GATE IN 2015 Question Paper (01-Feb-2015) (Shift 2)

A system is represented in state-space is X = Ax + Bu,where A = ≤ft[ {*20c 1&2\\ α &6 } ]andB = ≤ft[ {*20c 1\\ 1 } ]. The value of α for which the system is not controllable is _______.

A liquid level measurement system employing a radio-isotope is mounted on a tank as shown in the figure. The absorption coefficient of water for the radiation is 7.7 m${}^{\text{–}1}$. If the height of water in the tank is reduced from 100 mm to 90 mm, the percentage change in the radiation intensity received by the detector, neglecting absorption of the radiation by air, is __________ %.

The figure shows a spot of light of uniform intensity 50 W/m² and size 10 mm × 10 mm incident at the exact center of a photo-detector, comprising two identical photo-diodes D₁ and D₂. Each diode has a sensitivity of 0.4 A/W and is operated in the photoconductive mode. If the spot of light is displaced upwards by 100 μm, the resulting difference between the photocurrents generated by D₁ and D₂ in micro amperes, is __________ μA.

A beam of monochromatic light passes through two glass slabs of the same geometrical thickness at normal incidence. The refractive index of the first slab is 1.5 and that of the second, 2.0. The ratio of the time of passage of the beam through the first to the second slab is __________ .

The resolving power of a spectrometer consisting of a collimator, a grating and a telescope can be increased by