GATE Instrumentation

Suresh said, “I did it yesterday.” Which one of the following options is the correct form of this sentence in indirect speech?

To continue the sequence of tiles shown, the tile indicated by the question mark should be

Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the w...

The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?

A coin with heads facing up is shown as H and a coin with tails facing up is shown as T . Six coins are placed in the Starting Arrangement, as shown in the figure below. A "step" i...

Exacerbate : Mitigate :: ________ : ________ Choose the option with the correct pair of words to fill the blank.

A paper shown in Panel I is folded along the dashed lines (---) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes...

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high chol...

Four people P, Q, R, and S, of different ages, make the following observations. P - I am younger than S. Q - I am neither the youngest nor the oldest. R - P is older than me. Based...

Circles C1, C2, and C3, with centers O1, O2, and O3, and radii r1, r2, and r3, respectively, touch each other as shown in the following figure. Given r1 = 2 cm, r2 = 1 cm and the a...

A matrix P∈ R^3x3 satisfies P^3 – 4P^2 + 5P − 2I = 0 where I is a 3 × 3 identity matrix. The set of all possible eigenvalues of matrix P is ______.

Which one among the following statements is true for the function f(x) = x|x| ?

Consider a function f(z) = z² + z + 1 where z ∈ C is a complex variable. A simple closed contour γ in z-plane encloses the point z = 1 + 0j. The value of integral ∮_γ (f(z))/(z-1)...

Consider a matrix $A = \begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & 0 \\ 0 & 1 & 2 \end{bmatrix}$ Let $b = \begin{bmatrix} 1 \\ 3 \\ 0 \end{bmatrix}$ and $x = \begin{bmatrix} x_1 \\ x_2 \...

An electric field has a potential of V(x,y,z) = $\sqrt{x^2 + y^2 + z^2}$ V. A charge of 1 coulomb placed at $(\hat{i} + \hat{j} + \hat{k})$ experiences a force of $\vec{F} = (a\hat...

The RLC filter shown below acts as a _________.

A single phase step-down transformer has a high voltage primary winding and a low voltage secondary winding. The secondary winding is connected to a load impedance Z2. The impedanc...

A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter with cut-off frequency of 21 kHz. The output signal is a _________.

Given $x(t) = 4 \sin(15\pi t) + 7 \cos(4\pi t)$, where $t$ is in seconds. The fundamental period of $x(t)$ is ________ seconds.

Among the following, the differential equation(s) not representative of a linear dynamical system is/are ______. (i) $\frac{d^2x}{dt^2} + 2t \frac{dx}{dt} + x(t) = u(t)$ (ii) $(\fr...

A common gate amplifier represents a ____________.

In the circuit shown, the BJT has a β of 100. The base-emitter junction voltage is 0.65 V. The quiescent collector current, Ic is ________ mA.

The maximum signal to quantization noise ratio (SQNR) for a 16-bit analog-to-digital converter is approximately ________ dB.

The Kelvin double bridge is used to measure ________ valued resistances and has ________ resistors in its construction.

Active strain gauges are connected in a half-bridge configuration to measure strain in a cantilever element. When powered by a voltage source of 10 V, the voltage at the output of...

A glass pH electrode behaves linearly with an output change of 60 mV per unit change in pH. The measurement reference is set such that a solution of pH 6 produces an output of 60 m...

An analog speech signal contains signals from 200 Hz to 2400 Hz. It is sampled at 6 kHz and quantized with 512 levels for pulse code modulation (PCM). The bit rate will be ______ k...

The slope efficiency of a laser diode is 0.5 W/A, and the output optical power at a current of 100 mA is 30 mW. Assuming piece-wise linear characteristics of the laser diode, the t...

In a linear element, the measured current is 100 mA ± 2.5% and the measured voltage is 5 V ± 5%. Which of the following options show(s) the consumed power?

Which of the following statements is/are correct for a thermocouple?

A data set is given to be [1, 2, 0, -1, -3, 1, 2, 0, 1]. The median of the data set is _______. (rounded off to the nearest integer)

The potential difference between nodes A and B in a circuit is V_A - V_B = 5 V. The work done in moving a charge of 1 coulomb from point B to A is _______ J. (answer in integer)

In a series RL circuit shown in the figure, the current through the resistor lags the AC source voltage by 45°. Let R = 100π Ω and L = 2 H. The frequency of the source is _______ H...

In the circuit below the maximum value of V_out is _______ V. (rounded off to the nearest integer)

The minimum number of comparators required in a 6-bit flash analog-to-digital converter is _______ (answer in integer)

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is ______.

An electric field in free space is $\vec{E} = (2x + 5y + 6z)\hat{i} + (5x + 4y + 10z)\hat{j} + (6x + 10y + 2z)\hat{k}$ V/m. The charge density is _______ C/m³. ($\epsilon_0$ is the...

A straight thin wire carrying a current of I = 1 A in the direction $\hat{n} = \frac{1}{\sqrt{6}}\hat{i} + \frac{2}{\sqrt{6}}\hat{j} + \frac{1}{\sqrt{6}}\hat{k}$ is placed inside a...

A two-port network has z-parameters Z11 = Z22 = 10 Ω, and Z12 = Z21 = 5 Ω. The value of RL such that maximum power is transferred to RL is ________ Ω.

In the circuit shown below, the value of the output voltage V₀ is ____ V.

A signal x(t) is shown below. The plot of y(t) = 1 - x(4-t) is shown in ________.

In the table shown below, List-I are the system responses to input x(t) and List-II are the system properties. The correct matching is ______.

Given two signals: x(t) = u(t − 2) – u(t - 3), and y(t) = e^(-4t)u(t). If z(t) = x(t) * y(t), then Z(s) is _________.

A linear time invariant (LTI) system is described by: $\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -10 & -7 \end{bmatrix} \begin{bmatrix} x_1 \\...

In the circuit shown below, R is 1 kΩ and Rf is 10 kΩ. If Vin is 100 mV and the op-amps have supply voltages of ±15 V, then Vout is ________ V.

In the following active filter circuit with ideal op-amps, R is 1 kΩ, C is 1 µF, and Vin has an amplitude of 1 V at 1000 rad/s. The amplitude of Vout is _________ V.

The initial state of Q3Q2Q1Q0 in the digital circuit shown below is 1011. The new value of Q3Q2Q1Q0 after two rising edges of the clock (CLK) will be ________.

A closed Lissajous pattern observed on an oscilloscope in the X - Y mode has three horizontal tangencies and two vertical tangencies in steady state. If the signal-frequency on cha...

If the definition of SI unit 'X' is required to define SI unit 'Y', the dependency is indicated as X → Y. A valid order of dependencies, as per present convention, is ________.

A parallel plate capacitive displacement sensor has a plate area of 2 cm². The air gap between the plates is decreased by 0.1 mm from an initial value of 0.5 mm. The percentage cha...

The emitted radiant energy from a piece of metal was measured using a pyrometer. The temperature was calculated to be 1000 °C, assuming a surface emissivity of 0.8. It was later fo...

An amplitude modulated voltage signal x(t) drives a load of 1 Ω. x(t) = K cos(300π t) + L cos(240π t) + L cos(360π t). If the efficiency is 60% and the carrier power is 50 W, the v...

Given f(x, y) = x² – 2xy + y² The complete contour of the equation f(x, y) = 1 is described by the option(s) ______.

Given a differential equation $\frac{d^2x}{dt^2} + x = 0$ with $x(0) \neq 0$. Which of the following statements is/are true?

Which of the following functions represent(s) the output of the CMOS logic-gate shown in the circuit below?

A 16-bit processor has 16-bit wide instructions and a few internal registers. Every 16-bit instruction is encoded in a fixed format with one operation code of 7 bits and up to thre...

Let $f(t) = \begin{cases} 1, & t \in [0,2] \\ -t + 3, & t \in [2,3] \\ 0, & \text{otherwise} \end{cases}$ Then $\int_{-\infty}^{\infty} f(\tau)d\tau = \text{______}$. (rounded off...

A single phase transformer has a rating of 10 kVA, 50 Hz, 1100 V/ 220 V. In an open circuit test with the high voltage side open, the following are obtained: * Voltage applied to t...

A linear time invariant (LTI) system has a transfer function $G(s) = \frac{10(s + 1)}{s(s^2 + 2s + 5)}$ The system is placed in unity negative feedback configuration. For a unit ra...

The system $G(s) = \frac{K}{(s+1)^4}$ has a gain margin of 20 dB. The value of K is ________. (rounded off to two decimal places)

In the phase-locked-loop circuit shown below, the output of the VCO is a digital square wave. If the input is a square wave at 10 kHz, the steady state frequency of the output is _...

A digital counter increments its count every 0.1 μs. The counter is used in an instrument to measure frequency. The counter is operated for one period of the input signal to the in...

A current carrying semiconductor of thickness 0.7 mm is placed in a transverse magnetic field. The measured Hall voltage is 0.9 mV and the current is 6 mA. If the Hall coefficient...

For a fiber Bragg grating-based sensor, the shift in the Bragg wavelength gives information about the value of the measurand. For a Bragg wavelength of 1550 nm and effective index...

A photodiode has a responsivity 0.8 A/W. If the input optical power to the photodiode is 2 mW, the power delivered to a 50 Ω load is ________ μW. (rounded off to the nearest intege...

The angle between two vectors $${X_1} = {\left[ {\matrix{ 2 & 6 & {14} \cr } } \right]^T}$$ and $${X_2} = {\left[ {\matrix{ { - 12} & 8 & {16} \cr } } \right]^T}$$ in radian is ___...

Let $$z=x+iy$$ where $$i = \sqrt { - 1} .$$ Then $$\overline {\cos \,z} = $$

If $$V$$ is a non-zero vector of dimension $$3 \times 1,$$ then the matrix $$\,A = V{V^T}$$ has a rank $$=$$ ________

The eigen values of the matrix $$A = \left[ {\matrix{ 1 & { - 1} & 5 \cr 0 & 5 & 6 \cr 0 & { - 6} & 5 \cr } } \right]$$ are

The probability that a communication system will have high fidelity is $$0.81.$$ The probability that the system will have both high fidelity and high selectivity is $$0.18$$. The...

A straight line of the form $$y=mx+c$$ passes through the origin and the point $$(x, y)=(2,6).$$ The value of $$m$$ is

$$\mathop {\lim }\limits_{n \to \infty } \left( {\sqrt {{n^2} + n} - \sqrt {{n^2} + 1} } \right)\,\,$$ is ________.

Let $$\,\,f:\left[ { - 1, - } \right] \to R,\,\,$$ where $$\,f\left( x \right) = 2{x^3} - {x^4} - 10.$$ The minimum value of $$f(x)$$ is _______.

In the neighborhood of $$z=1,$$ the function $$f(z)$$ has a power series expansion of the form $$f\left( z \right) = 1 + \left( {1 - z} \right) + {\left( {1 - z} \right)^2} + ........

The value of the integral $${1 \over {2\pi j}}\int\limits_c {{{{z^2} + 1} \over {{z^2} - 1}}} dz$$ where $$z$$ is a complex number and $$C$$ is a unit circle with center at $$1+0j$...

Consider the matrix $$A = \left( {\matrix{ 2 & 1 & 1 \cr 2 & 3 & 4 \cr { - 1} & { - 1} & { - 2} \cr } } \right)$$ whose eigen values are $$1, -1$$ and $$3$$. Then trace of $$\left(...

An urn contains $$5$$ red and $$7$$ green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour....

The vector that is NOT perpendicular to the vectors $$\,\,\left( {i + j + k} \right)\,\,$$ and $$\,\left( {i + 2j + 3k} \right)\,\,$$ is _________.

The double integral $$\,\,\int_0^a {\int_0^y {f\left( {x,y} \right)\,dx\,dy\,\,\,} } $$ is equivalent to

The value of $$\oint\limits_c {{1 \over {{z^2}}}dz} $$ where the contour is the unit circle traversed clock - wise, is