Question 31. Two ammeters A1 and A2 measure the same current and provide readings I1 and I2 , respectively. The ammeter errors can be characterized as independent zero mean Gaussian random variables of standard deviations σ1 and σ2 , respectively. The value of the current is computed as : I = μ I1 + (1 - μ) I2 The value of μ which gives the lowest standard deviation of I is

Question 32. A tungsten wire used in a constant current hot wire anemometer has the following parameters : Resistance at 0° C is 10
Ω, Surface area is 10-4 m2, Linear temperature coefficient of resistance of the tungsten wire is 4.8 * 10-3 /°C, Convective heat transfer coefficient is 25.2W / m2 /°C, flowing air
temperature is 30°C, wire current is 100 mA, mass-specific heat product is 2.5 * 10-5 J /°CThe thermal time constant of the hot wire under flowing air condition in ms is

Question 33. A piezo-electric force sensor, connected by a cable to a voltage amplifier, has the following parameters : Crystal properties : Stiffness 109 N/m, Damping ratio 0.01, Natural frequency 105 rad/s, Force-to-Charge sensitivity 10-9 C/N, Capacitance 10-9 F with its loss angle assumed negligible Cable properties : Capacitance 2 × 10-9 F with its resistance assumed negligible Amplifier properties : Input impedance 1 MΩ
, Bandwidth 1MHz , Gain 3 The minimum frequency of a force signal in Hz within its useful mid-band range of measurement,
for which the gain amplitude is more than 0.95, approximately is,

Question 34. A tungsten wire used in a constant current hot wire anemometer has the following parameters : Resistance at 0° C is 10
Ω, Surface area is 10-4 m2, Linear temperature coefficient of resistance of the tungsten wire is 4.8 * 10-3 /°C, Convective heat transfer coefficient is 25.2W / m2 /°C, flowing air
temperature is 30°C, wire current is 100 mA, mass-specific heat product is 2.5 * 10-5 J /°CAt steady state, the resistance of the wire in Ω
is

Question 35. A piezo-electric force sensor, connected by a cable to a voltage amplifier, has the following parameters : Crystal properties : Stiffness 109 N/m, Damping ratio 0.01, Natural frequency 105 rad/s, Force-to-Charge sensitivity 10-9 C/N, Capacitance 10-9 F with its loss angle assumed negligible Cable properties : Capacitance 2 × 10-9 F with its resistance assumed negligible Amplifier properties : Input impedance 1 MΩ
, Bandwidth 1MHz , Gain 3 The maximum frequency of a force signal in Hz below the natural frequency within its useful midband range of measurement, for which the gain amplitude is less than 1.05, approximately is,

Question 36. The maximum value of the solution y (t) of the differential equation y(t) + ӱ(t) = 0 with initial conditions ӱ(0) = 1 and y(0) = 1, for t ≥ 0 is

Question 37. If x = √-1, then the value of xx is

Question 38. The unilateral Laplace transform of f (t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is

Question 39. With initial condition x(1)  0.5 , the solution of the differential equation, t dx/dt + x = t is

Question 40. Two independent random variables X and Y are uniformly distributed in the interval [“1, 1]. The
probability that max[X, Y] is less than 1/2 is