Instrumentation Engineering - IN 2014 GATE Paper (Practice Test) - GATE MCQ

In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years.

(Important - Enter only the numerical value in the answer)

The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? 

Q. 6 – 10 Carry Two Marks Each.

In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group?

Statements:

1. Shiv is younger to Riaz.

2. Shiv is elder to Som.

Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis.

From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier

The main point of the paragraph is:

The total exports and revenues from the exports of a country are given in the two pie charts below.

The pie chart for exports shows the quantity of each item as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram?

X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km?

10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _________.

Q.11 – 35 Carry One Mark Each.

Given

The x-y plot will be

Given that x is a random variable in the range [0, ∞] with a probability density 

 the value of the constant K is ___________.

(Important - Enter only the numerical value in the answer)

The figure shows the plot of y as a function of x

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is:

A vector is defined as  are unit vectors in Cartesian (x, y, z) coordinate system. 

The surface integral ? ??. ??s over the closed surface S of a cube with vertices having the following coordinates: (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1) is ___________ .

(Important - Enter only the numerical value in the answer)

The figure shows the schematic of a production process with machines A, B and C. An input job needs to be pre-processed either by A or by B before it is fed to C, from which the final finished product comes out. The probabilities of failure of the machines are given as: 

P_A=0.15, P_B=0.05, P_C=0.1

Assuming independence of failures of the machines, the probability that a given job is successfully processed (up to the third decimal place) is ___________.

The circuit shown in figure was at steady state for t < 0 with the switch at position 'A'. The switch is thrown to position 'B' at time t = 0. The voltage V(volts) across the 10Ω resistor at time t = 0⁺ is ___________.

(Important - Enter only the numerical value in the answer)

The average real power in watts delivered to a load impedance Z_L = (4 - j2) by an ideal current
source i(t) = 4sin(ωt + 20^o) A is __________ .

(Important - Enter only the numerical value in the answer)

Time domain expressions for the voltage v₁(t) and v₂(t) are given as

Which one of the following statements is TRUE?

A pHelectrode obeys Nernst equation and is being operated at 25^oC. The change in the open circuit voltage in millivolts across the electrode for a pH change from 6 to 8 is ___________.

(Important - Enter only the numerical value in the answer)

The pressure and velocity at the throat of a Venturi tube, measuring the flow of a liquid, are related to the upstream pressure and velocity, respectively, as follows:

Semiconductor strain gages typically have much higher gage factors than those of metallic strain gages, primarily due to:

For a rotameter, which one of the following statements is TRUE?

For the op-amp shown in the figure, the bias currents are I_b1 = 450 nA and I_b2 = 350 nA. The values of the input bias current (I_B) and the input offset current (I_f) are:

The amplifier in the figure has gain of −10 and input resistance of 50 kΩ. The values of Ri and

For the circuit shown in the figure assume ideal diodes with zero forward resistance and zero forward voltage drop. The current through the diode D₂ in mA is_________.

(Important - Enter only the numerical value in the answer)

The system function of an LTI system is given by

The above system can have stable inverse if the region of convergence of H(z) is defined as

The figure is a logic circuit with inputs A and B and output Y.V_ss = + 5 V. The circuit is of type

The impulses response of an LTI system is given as:

It represents an ideal

A discrete-time signal x[n] is obtained by sampling an analog signal at 10 kHz. The signal x[n] is filtered by a system with impulse response h[n] =  0.5{ δ[n] + δ[n - 1]}. The 3dB cutoff frequency of the filter is:

A full duplex binary FSK transmission is made through a channel of bandwidth 10 kHz. In each direction of transmission the two carriers used for the two states are separated by 2 kHz. The  maximum baud rate for this transmission is: