Instrumentation Engineering - IN 2012 GATE Paper (Practice Test) - GATE

Which one of the following options is the closest in meaning to the word given below?

Latitude

Choose the most appropriate word from the options given below to complete the following sentence:

Given the seriousness of the situation that he had to face, his ___ was impressive.

Q. 6 - Q. 10 carry two marks each.

Q. Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total
money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them.

Which one of the following statements best sums up the meaning of the above passage?

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

The data given in the following table summarizes the monthly budget of an average household.

The approximate percentage of the monthly budget NOT spent on savings is

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is

Q. 1 – Q. 25 carry one mark each.

Q. If , then the value of x^x is

With initial condition x(1) = 0.5 , the solution of the differential equation,

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

The unilateral Laplace transform of f (t) is  . The unilateral Laplace transform of  tf(t) is

Given
 . If C is a counterclockwise path in the z-plane such that |z +1| =1, the value of
 is

The average power delivered to an impedance (4 - j3)? by a current 5cos(100πt +100) A is

In the circuit shown below, the current through the inductor is

I n the following figure, C₁ and C₂ are ideal capacitors. C₁ has been charged to 12 V before the ideal
switch S is closed at t = 0. The current i(t) for all t is

T he impedance looking into nodes 1 and 2 in the given circuit is

T he i-v characteristics of the diode in the circuit given below are

The current in the circuit is

A system with transfer function

is excited by sin(ω t) . The steady-state output of the system is zero at

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is

In the sum of products function , the prime implicants are

Consider the given circuit.

In this circuit, the race around

If , then the region of convergence (ROC) of its Z-transform in the Z-plane will be

A capacitive motion transducer circuit is shown. The gap d between the parallel plates of the capacitor is varied as . If the value of the capacitance is 2pF at
t = 0 ms, the output voltage V_o at t = 2 ms is

A psychrometric chart is used to determine

A strain gauge is attached on a cantilever beam as shown. If the base of the cantilever vibrates according to the equation , then the output of the strain gauge is proportional to

T he transfer function of a Zero-Order-Hold system with sampling interval T is

A n LED emitting at 1 μm with a spectral width of 50 nm is used in a Michelson interferometer. To
obtain a sustained interference, the maximum optical path difference between the two arms of the
interferometer is

L ight of wavelength 630 nm in vacuum, falling normally on a biological specimen of thickness 10 μm, splits into two beams that are polarized at right angles. The refractive index of the tissue for the two polarizations are 1.32 and 1.333. When the two beams emerge, they are out of phase by

The responsivity of the PIN photodiode shown is 0.9 A/W. To obtain V_out of –1 V for an incident optical power of 1 mW, the value of R to be used is

A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil (PMMC) meter connected across the same load reads

For the circuit shown in the figure, the voltage and current expressions are

The average power measured by the Wattmeter is

The bridge method commonly used for finding mutual inductance is

Q. 36 - Q 65 carry two marks each:

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

Given that

the value of A³ is

The direction of vector A is radially outward from the origin, with |A| = krⁿ where 

The maximum value of

Consider the differential equation

If 

A ssuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

The voltage gain A_v of the circuit shown below is

The state variable description of an LTI system is given by

where y is the output and u is the input. The system is controllable for

The state transition diagram for the logic circuit shown is

The Fourier transform of a signal is

L et y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)ⁿ u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

The feedback system shown below oscillates at 2 rad/s when

The circuit shown is a

The input x(t) and output y(t) of a system are related as  The system is

A double convex lens is used to couple a laser beam of diameter 5 mm into an optical fiber with a numerical aperture of 0.5. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is

A n analog voltmeter uses external multiplier settings. With a multiplier setting of 20 kilo-ohms it reads
440 V and with a multiplier setting of 80 kilo-ohms it reads 352 V. For a multiplier setting of 40 kilo-ohms the
voltmeter reads

The open loop transfer function of a unity negative feedback control system is given by .The gain margin of the system is 

A dynamometer arm makes contact with the piezoelectric load cell as shown. The g-constant of the piezoelectric material is 50 x 10^-3Vm/N and the surface area of the load cell is 4 cm². If a torque τ =20 Nm is applied to the dynamometer, the output voltage V_o of the load cell is

Water (density: 1000 kgm^–3) stored in a cylindrical drum of diameter 1 m is emptied through a horizontal pipe of diameter 0.05 m. A pitot-static tube is placed inside the pipe facing the flow. At the time when the difference between the stagnation and static pressures measured by the pitotstatic tube is 10 kPa, the rate of reduction in water level in the drum is,

A U-tube manometer of tube diameter D is filled with a liquid of zero viscosity. If the volume of the liquid filled is V, the natural frequency of oscillations in the liquid level about its mean position, due to small perturbations, is

The open loop transfer function of a unity gain negative feedback control system is given by
 . The angle θ , at which the root locus approaches the zeros of the system,
satisfies

Common Data Questions

Common Data for Questions 58 and 59:

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following
were observed:

(i) 1 ohm connected at port B draws a current of 3 A

(ii) 2.5 ohm connected at port B draws a current of 2 A

Q. With 10 V dc connected at port A, the current drawn by 7 ohm connected at port B is

Common Data Questions

Common Data for Questions 58 and 59:

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following
were observed:

(i) 1 ohm connected at port B draws a current of 3 A

(ii) 2.5 ohm connected at port B draws a current of 2 A

Q. For the same network, with 6 V dc connected at port A, 1 ohm connected at port B draws 7/3 A.
If 8 V dc is connected to port A, the open circuit voltage at port B is

Common Data for Questions 60 and 61:

The deflection profile y (x) of a cantilever beam due to application of a point force F (in Newton), as a
function of distance x from its base, is given by  . The angular deformation θ at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure.

Q. The translation S of the spot of laser light on the photodetector when a force of F =1 N is applied
to the cantilever is

Common Data for Questions 60 and 61:

The deflection profile y (x) of a cantilever beam due to application of a point force F (in Newton), as a
function of distance x from its base, is given by  . The angular deformation θ at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure.

If linear variable differential transformers (LVDTs) are mounted at x = 1/2 m and x = 1/4 m on the
cantilever to measure the effect of time varying forces, the ratio of their outputs is

Linked Answer Questions

Statement for Linked Answer Questions 62 and 63:

The transfer function of a compensator is given as

Q. G_c(s) is a lead compensator if

Linked Answer Questions

Statement for Linked Answer Questions 62 and 63:

The transfer function of a compensator is given as

Q. The phase of the above lead compensator is maximum at

Statement for Linked Answer Questions 64 and 65:

In the circuit shown, the three voltmeter readings are 

Q. The power factor of the load is

Statement for Linked Answer Questions 64 and 65:

In the circuit shown, the three voltmeter readings are 

Q. If R_L = 5 ohm , the approximate power consumption in the load is