GATE 2021 Electronics and Communication Engineering Previous Year Paper

Q.1	The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
(A)	9,92,500
(B)	9,95,006
(C)	10,00,000
(D)	12,51,506

Q.2
(A)	3
(B)	7
(C)	9
(D)	11
Q.3	The least number of squares that must be added so that the line P-Q becomes the line of symmetry is _________
(A)	4
(B)	3
(C)	6
(D)	7

Q.4	Nostalgia is to anticipation as is to________ Which one of the following options maintains a similar logical relation in the above sentence?
(A)	Present, past
(B)	Future, past
(C)	Past, future
(D)	Future, present

Q.5	Consider the following sentences:I woke up from sleep.I woked up from sleep.I was woken up from sleep.I was wokened up from sleep.Which of the above sentences are grammatically CORRECT?
(A)	(i) and (ii)
(B)	(i) and (iii)
(C)	(ii) and (iii)
(D)	(i) and (iv)

Q.6	Given below are two statements and two conclusions. Statement 1: All purple are green. Statement 2: All black are green. Conclusion I: Some black are purple. Conclusion II: No black is purple. Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A)	Only conclusion I is correct.
(B)	Only conclusion II is correct.
(C)	Either conclusion I or II is correct.
(D)	Both conclusion I and II are correct.

Q.7	Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.Which of the following can be deduced from the above passage?Nowadays, computers are present in almost all places.Computers cannot be used for solving problems in engineering.For humans, there are both positive and negative effects of using computers.Artificial intelligence can be done without data.
(A)	(ii) and (iii)
(B)	(ii) and (iv)
(C)	(i), (iii) and (iv)
(D)	(i) and (iii)

Q.8	Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is__________
(A)	𝜋/3
(B)	2𝜋/3
(C)	3𝜋 / 2
(D)	3π

Q.9	The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
(A)	4
(B)	5
(C)	6
(D)	7

Q.10	Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
(A)	2 : 3
(B)	3 : 4
(C)	4 : 5
(D)	5 : 6

Q.1	The vector function 𝐅 (𝐫) = −𝒙 𝒊̂ + 𝒚 𝖩̂ is defined over a circular arc C shown in the figure. The line integral of ∫_𝑪𝐅 (𝐫) 𝒅𝐫 is.
(A)	1/2
(B)	1/4
(C)	1/6
(D)	1/3

Q.2	Consider the differential equation given below. The integrating factor of the differential equation is
(A)	(1 − 𝑥²)^−3⁄4
(B)	(1 − 𝑥²)^−1⁄4
(C)	(1 − 𝑥²)^−3⁄2
(D)	(1 − 𝑥²)^−1⁄2

Q.3	Two continuous random variables 𝑿 and 𝒀 are related as 𝒀 = 𝟐𝑿 + 𝟑 Let 𝝈^𝟐_𝑿 and 𝝈^𝟐_𝒀 denote the variances of 𝑿 and 𝒀, respectively. The variances are related as
(A)	𝜎²_𝑌 = 2 𝜎²_𝑋
(B)	𝜎²_𝑌 = 4 𝜎²_𝑋
(C)	𝜎² _𝑌 = 5 𝜎²_𝑋
(D)	𝜎²_𝑌 = 25 𝜎²_𝑋

Q.4	Consider a real-valued base-band signal (𝒕), band limited to 𝟏𝟎 kHz. The Nyquist rate for the signal 𝒚(𝒕) = 𝒙(𝒕) 𝒙 ( 𝟏 + t/2) is
(A)	15 kHz
(B)	30 kHz
(C)	60 kHz
(D)	20 kHz

Q.5	Consider two 𝟏𝟔-point sequences [𝒏] and 𝒉[𝒏]. Let the linear convolution of 𝒙[𝒏] and 𝒉[𝒏] be denoted by 𝒚[𝒏], while 𝒛[𝒏] denotes the 𝟏𝟔-point inverse discrete Fourier transform (IDFT) of the product of the 𝟏𝟔-point DFTs of [𝒏] and 𝒉[𝒏]. The value(s) of 𝒌 for which 𝒛[𝒌] = 𝒚[𝒌] is/are
(A)	𝑘 = 0, 1, 2, … , 15
(B)	𝑘 = 0
(C)	𝑘 = 15
(D)	𝑘 = 0 and 𝑘 = 15

Q.6	A bar of silicon is doped with boron concentration of 𝟏𝟎^𝟏𝟔 𝐜𝐦^−𝟑 and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of 𝟏𝟎^𝟐𝟎 𝐜𝐦^−𝟑𝐬^−𝟏. If the recombination lifetime is 𝟏𝟎𝟎 µs, intrinsic carrier concentration of silicon is 𝟏𝟎^𝟏𝟎 𝐜𝐦^−𝟑 and assuming 𝟏𝟎𝟎% ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is
(A)	10²⁰_cm−6
(B)	2 × 10²⁰ cm⁻⁶
(C)	10³² _cm−6
(D)	2 × 10³² cm⁻⁶

Q.9	For the circuit with an ideal OPAMP shown in the figure, VREF is fixed. If VOUT = 𝟏 volt for VIN = 𝟎. 𝟏 volt and VOUT = 𝟔 volt for VIN = 𝟏 volt, where VOUT is measured across RL connected at the output of this OPAMP, the value of 𝐑_𝐅⁄𝐑_𝐈𝐍 is
(A)	3.285
(B)	2.860
(C)	3.825
(D)	5.555

Q.10	Consider the circuit with an ideal OPAMP shown in the figure. Assuming \|𝐕_𝐈𝐍\| ≪ \|𝐕_𝐂𝐂\| and \|𝐕_𝐑𝐄𝐅\| ≪ \|𝐕_𝐂𝐂\|, the condition at which VOUT equals to zero is
(A)	V_IN ⁼V_REF
(B)	V_IN = 0.5 V_REF
(C)	V_IN ⁼2 V_REF
(D)	V_IN = 2 + V_REF

Q.11	If (𝟏𝟐𝟑𝟓)_𝒙 = (𝟑𝟎𝟑𝟑)_𝒚, where 𝒙 and 𝒚 indicate the bases of the corresponding numbers, then
(A)	𝑥 = 7 and 𝑦 = 5
(B)	𝑥 = 8 and 𝑦 = 6
(C)	𝑥 = 6 and 𝑦 = 4
(D)	𝑥 = 9 and 𝑦 = 7

Q.12	Addressing of a 𝟑𝟐K × 𝟏𝟔 memory is realized using a single decoder. The minimum number of AND gates required for the decoder is
(A)	2₈
(B)	2₃₂
(C)	2₁₅
(D)	2₁₉

Q.14	The complete Nyquist plot of the open-loop transfer function (𝒔)𝑯(𝒔) of a feedback control system is shown in the figure. If 𝑮(𝒔)𝑯(𝒔) has one zero in the right-half of the 𝒔-plane, the number of poles that the closed-loop system will have in the right-half of the 𝒔-plane is
(A)	0
(B)	1
(C)	4
(D)	3

Q.15	Consider a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. A plane wave traveling in the region 𝒛 ≥ 𝟎 with electric field vector 𝐄 = 𝟏𝟎 𝐜𝐨(𝟐 × 𝟏𝟎^𝟖𝒕 + 𝖰𝒛)𝐚_𝒚 is incident normally on the plane at 𝒛 = 𝟎, where β is the phase constant. The region 𝒛 ≥ 𝟎 is in free space and the region 𝒛 < 𝟎 is filled with a lossless medium (permittivity 𝗌 = 𝗌_𝟎, permeability 𝝁 = 𝟒𝝁_𝟎, where 𝗌_𝟎 = 𝟖. 𝟖𝟓 × 𝟏𝟎^−𝟏𝟐 F/m and 𝝁_𝟎 = 𝟒𝝅 ×𝟏𝟎^−𝟕 H/m). The value of the reflection coefficient is
(A)	1/3
(B)	3/5
(C)	2/5
(D)	2/3

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).


Q.16	If the vectors (𝟏. 𝟎, −𝟏. 𝟎, 𝟐. 𝟎), (𝟕. 𝟎, 𝟑. 𝟎, 𝒙) and (𝟐. 𝟎, 𝟑. 𝟎, 𝟏. 𝟎) in ℝ^𝟑are linearly dependent, the value of 𝒙 is ______________

Q.17	Consider the vector field 𝐅 = 𝐚_x(𝟒𝒚 − 𝒄_𝟏𝒛) + 𝐚_𝒚(𝟒𝒙 + 𝟐𝒛) + 𝐚_𝒛(𝟐𝒚 + 𝒛) in a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. If the field F is irrotational (conservative), then the constant 𝒄_𝟏 (in integer) is___________


Q.18	Consider the circuit shown in the figure. The current I flowing through the 7 Ω resistor between P and Q (rounded off to one decimal place) is _________A.

Q.19

Consider the circuit shown in the figure.

The value of v0 (rounded off to one decimal place) is _________ V.

Q.20

An 𝟖-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 𝟎 V to 𝟕. 𝟔𝟖 V. If the digital input code is 10010110 (the leftmost bit is MSB), then the analog output voltage of the DAC (rounded off to one decimal place) is _______V.

Q.21	The autocorrelation function 𝑹(𝑟) of a wide-sense stationary random process 𝑿(𝒕) is shown in the figure. The average power of 𝑿(𝒕) is_______

Q.22	Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 𝟓𝟎%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is __________________

Q.23	A speech signal, band limited to 𝟒 kHz, is sampled at 𝟏. 𝟐𝟓 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range −𝟓 V to +𝟓 V, are subsequently quantized in an 𝟖-bit uniform quantizer and then transmitted over a voice- grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 𝟐𝟔 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is ___________ kHz.

Q.24	A 𝟒 kHz sinusoidal message signal having amplitude 𝟒 V is fed to a delta modulator (DM) operating at a sampling rate of 𝟑𝟐 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is ____________V.

Q.25	The refractive indices of the core and cladding of an optical fiber are 𝟏. 𝟓𝟎 and 𝟏. 𝟒𝟖, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is ____________________ degree.

Q.27	A box contains the following three coins. I. A fair coin with head on one face and tail on the other face. II. A coin with heads on both the faces. III.A coin with tails on both the faces.A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is
(A)	2/5
(B)	1/3
(C)	1/2
(D)	2/3

Q.29	Consider the two-port network shown in the figure. The admittance parameters, in siemens, are
(A)	𝑦₁₁ = 2, 𝑦₁₂ = −4, 𝑦₂₁ = −4, 𝑦₂₂ = 2
(B)	𝑦₁₁ = 1, 𝑦₁₂ = −2, 𝑦₂₁ = −1, 𝑦₂₂ = 3
(C)	𝑦₁₁ = 2, 𝑦₁₂ = −4, 𝑦₂₁ = −1, 𝑦₂₂ = 2
(D)	𝑦₁₁ = 2, 𝑦₁₂ = −4, 𝑦₂₁ = −4, 𝑦₂₂ = 3

Q.30	For an n-channel silicon MOSFET with 𝟏𝟎 nm gate oxide thickness, the substrate sensitivity (𝝏𝑽_𝑻⁄𝝏\|𝑽_𝑩𝑺\|) is found to be 𝟓𝟎 mV/V at a substrate voltage\|𝑽_𝑩𝑺\| = 𝟐 𝑽, where 𝑽_𝑻 is the threshold voltage of the MOSFET. Assume that, \|𝑽_𝑩𝑺\| ≫ 𝟐𝚽_𝑩, where 𝐪𝚽_𝑩 is the separation between the Fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given areElectron charge (q) = 𝟏. 𝟔 × 𝟏𝟎^−𝟏𝟗 CVacuum permittivity (𝗌_𝟎) = 𝟖. 𝟖𝟓 × 𝟏𝟎^−𝟏𝟐 F/m Relative permittivity of silicon (𝗌_𝐒𝐢) = 𝟏𝟐 Relative permittivity of oxide (𝗌_𝐨𝐱) = 𝟒The doping concentration of the substrate is
(A)	7.37 × 10¹⁵ cm⁻³
(B)	4.37 × 10¹⁵ cm⁻³
(C)	2.37 × 10¹⁵ cm⁻³
(D)	9.37 × 10¹⁵ cm⁻³

Q.31	The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are 4ns, 2 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied simultaneously and held constant, the maximum propagation delay of the circuit is
(A)	3 ns
(B)	5 ns
(C)	6 ns
(D)	7 ns

Q.32	The content of the registers are R1 = 𝟐𝟓H, R2 = 𝟑𝟎H and R3 = 𝟒𝟎H. The following machine instructions are executed.PUSH{R1} PUSH{R2} PUSH{R3} POP{R1} POP{R2} POP{R3}After execution, the content of registers R1, R2, R3 are
(A)	R₁ = 40H, R₂ = 30H, R₃ = 25H
(B)	R₁ = 25H, R₂ = 30H, R₃ = 40H
(C)	R₁ = 30H, R₂ = 40H, R₃ = 25H
(D)	R₁ = 40H, R₂ = 25H, R₃ = 30H

Q.33	The electrical system shown in the figure converts input source current 𝒊_𝒔(𝒕) to output voltage v_o (t). Current i_L (t ) in the inductor and voltage v_C (t )across the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e., i_L (0)= 0 and v_C (0) = 0. The system is
(A)	completely state controllable as well as completely observable
(B)	completely state controllable but not observable
(C)	completely observable but not state controllable
(D)	neither state controllable nor observable

Q.34	A digital transmission system uses a (𝟕, 𝟒) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code ( 𝐦_𝒊 ; 𝐜_𝒊 ), where 𝐜_𝒊 is the codeword corresponding to the i^thmessage 𝐦_𝒊, are known to be ( 𝟏 𝟏 𝟎 𝟎 ; 𝟎 𝟏 𝟎 𝟏 𝟏 𝟎 𝟎 ), ( 𝟏 𝟏 𝟏 𝟎 ; 𝟎 𝟎 𝟏 𝟏 𝟏 𝟏 𝟎 ) and (𝟎 𝟏 𝟏 𝟎 ; 𝟏 𝟎 𝟎 𝟎 𝟏 𝟏 𝟎 ), then which of the following is a valid codeword in this code?
(A)	1 1 0 1 0 0 1
(B)	1 0 1 1 0 1 0
(C)	0 0 0 1 0 1 1
(D)	0 1 1 0 1 0 0

Q.35	The impedance matching network shown in the figure is to match a lossless line having characteristic impedance 𝒁_𝟎 = 𝟓𝟎 Ω with a load impedance 𝒁_𝐋. A quarter-wave line having a characteristic impedance 𝒁_𝟏 = 𝟕𝟓 Ω is connected to 𝒁_𝐋. Two stubs having characteristic impedance of 𝟕𝟓 Ω each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length 𝟎. 𝟐𝟓𝝀 connected across PQ and the other one is an open-circuited (O.C.) stub of length 𝟎. 𝟓𝝀 connected across RS.The impedance matching is achieved when the real part of 𝒁_𝐋 is
(A)	112.5 Ω
(B)	75.0 Ω
(C)	50.0 Ω
(D)	33.3 Ω

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).


Q.36	A real 𝟐 × 𝟐 non-singular matrix 𝐀 with repeated eigenvalue is given as where 𝒙 is a real positive number. The value of 𝒙 (rounded off to one decimal place) is ____________

Q.37	For a vector field 𝐃 = 𝝆 𝐜𝐨𝐬^𝟐 𝝋 𝐚_𝝆 + 𝒛^𝟐 𝐬𝐢𝐧^𝟐 𝝋 𝐚_𝝋 in a cylindrical coordinate system (𝝆, 𝝋, 𝒛) with unit vectors 𝐚_𝝆, 𝐚_𝝋 𝐚𝐧𝐝 𝐚_𝒛, the net flux of 𝐃 leaving the closed surface of the cylinder (𝝆 = 𝟑, 𝟎 ≤ 𝒛 ≤ 𝟐) (rounded off to two decimal places) is_____________

Q.38	In the circuit shown in the figure, the switch is closed at time 𝒕 = 𝟎, while the capacitor is initially charged to −𝟓 V(i.e., vc(𝟎) = −𝟓 V). The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is_____________ms.

Q.39	The exponential Fourier series representation of a continuous-time periodic signal 𝒙(𝒕) is defined as ∞𝒙(𝒕) = ∑ 𝒂_𝒌 𝒆^{𝒋𝒌𝑚𝟎𝒕} 𝒌 = −∞where 𝑚_𝟎 is the fundamental angular frequency of 𝒙(𝒕) and the coefficients of the series are 𝒂_𝒌. The following information is given about (𝒕) and 𝒂_𝒌.𝒙(𝒕) is real and even, having a fundamental period of 𝟔The average value of 𝒙(𝒕) is 𝟐The average power of the signal 𝒙(𝒕) (rounded off to one decimal place) is___________

Q.40	For a unit step input [𝒏], a discrete-time LTI system produces an output signal ( 𝟐𝜹[𝒏 + 𝟏] + 𝜹[𝒏] + 𝜹[𝒏 − 𝟏] ). Let 𝒚[𝒏] be the output of the system for an input 𝒖[𝒏]). The value of 𝒚[𝟎] is_________

Q.41	Consider the signals [𝒏] = 𝟐^𝒏−𝟏 𝒖[−𝒏 + 𝟐] and 𝒚[𝒏] = 𝟐^−𝒏+𝟐 𝒖[𝒏 + 𝟏], where 𝒖[𝒏] is the unit step sequence. Let (𝒆^𝒋𝑚) and 𝒀(𝒆^𝒋𝑚) be the discrete- time Fourier transform of 𝒙[𝒏] and 𝒚[𝒏], respectively. The value of the integral (rounded off to one decimal place) is___________.

Q.42

A silicon P-N junction is shown in the figure. The doping in the P region is 𝟓 × 𝟏𝟎^𝟏𝟔 cm⁻³and doping in the N region is 𝟏𝟎 × 𝟏𝟎^𝟏𝟔 cm⁻³. The parameters given areBuilt-in voltage (𝚽_𝐛𝐢) = 0.8 V Electron charge (𝐪) = 𝟏. 𝟔 × 𝟏𝟎^−𝟏𝟗 CVacuum permittivity (𝗌_𝟎) = 𝟖. 𝟖𝟓 × 𝟏𝟎^−𝟏𝟐 F/m Relative permittivity of silicon (𝗌_𝐒𝐢) = 𝟏𝟐

The magnitude of reverse bias voltage that would completely deplete one of the two regions (P or N) prior to the other (rounded off to one decimal place) is__________ V.

Q.43	An asymmetrical periodic pulse train vin of 𝟏𝟎 V amplitude with on-time TON = 1 ms and off-time TOFF = 1 µs is applied to the circuit shown in the figure. The diode D1 is ideal.The difference between the maximum voltage and minimum voltage of the output waveform vo (in integer) is __________ V.

Q.44

For the transistor M1 in the circuit shown in the figure, µ_𝒏𝑪_𝐨𝐱 = 𝟏𝟎𝟎 µ𝐀/𝐕^𝟐 and (𝑾⁄𝑳) = 𝟏𝟎, where µ_𝒏 is the mobility of electron, 𝑪_𝐨𝐱 is the oxide capacitance per unit area, 𝑾 is the width and 𝑳 is the length.

The channel length modulation coefficient is ignored. If the gate-to-source voltage 𝑽_𝐆𝐒 is 1 V to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is ___________V.

Q.45

A circuit with an ideal OPAMP is shown in the figure. A pulse 𝐕_𝐈𝐍 of 𝟐𝟎 m𝐬 duration is applied to the input. The capacitors are initially uncharged.

The output voltage 𝐕_𝐎𝐔𝐓 of this circuit at 𝒕 = 𝟎⁺ (in integer) is______ V.

Q.46

The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns. The propagation delay of all the flip-flops is assumed to be zero. The clock (Clk) frequency provided to the circuit is 500 MHz.

Starting from the initial value of the flip-flop outputs 𝐐_𝟐𝐐_𝟏𝐐_𝟎 = 𝟏 𝟏 𝟏 with𝐃_𝟐 = 𝟏, the minimum number of triggering clock edges after which the flip- flop outputs 𝐐_𝟐𝐐_𝟏𝐐_𝟎 becomes 1 0 0 (in integer) is

Q.47

The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time𝒕 = 𝟎.

Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is_____A.

Q.48	A unity feedback system that uses proportional-integral (PI) control is shown in the figure. The stability of the overall system is controlled by tuning the PI control parameters 𝑲_𝑷 and 𝑲_𝑰. The maximum value of 𝑲_𝑰 that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is____________

Q.49	A sinusoidal message signal having root mean square value of 𝟒 V and frequency of 𝟏 kHz is fed to a phase modulator with phase deviation constant𝟐 rad/volt. If the carrier signal is 𝒄(𝒕) = 𝟐 𝐜𝐨𝐬(𝟐𝝅𝟏𝟎^𝟔𝒕), the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is _______Hz.

Q.50	Consider a superheterodyne receiver tuned to 𝟔𝟎𝟎 kHz. If the local oscillator feeds a 𝟏𝟎𝟎𝟎 kHz signal to the mixer, the image frequency (in integer) is_____________ kHz.

Q.51	In a high school having equal number of boy students and girl students, 𝟕𝟓% of the students study Science and the remaining 𝟐𝟓% students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is ___________bits.

Q.52

A message signal having peak-to-peak value of 2 V, root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of 50 kbps. Assuming that the quantization error is uniformly distributed, the maximum signal to quantization noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is________

Q.53	Consider a polar non-return to zero (NRZ) waveform, using +𝟐 V and −𝟐 V for representing binary ‘1’ and ‘0’ respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance 𝟎. 𝟒 V². If the a priori probability of transmission of a binary ‘1’ is 𝟎. 𝟒, the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is ______ V.

Q.54	A standard air-filled rectangular waveguide with dimensions 𝒂 = 𝟖 cm,𝒃 = 𝟒 cm, operates at 𝟑. 𝟒 GHz. For the dominant mode of wave propagation, the phase velocity of the signal is 𝒗_𝒑. The value (rounded off to two decimal places) of 𝒗_𝒑⁄𝒄, where 𝒄 denotes the velocity of light, is___________


Q.55	An antenna with a directive gain of 𝟔 dB is radiating a total power of 𝟏𝟔 kW. The amplitude of the electric field in free space at a distance of 𝟖 km from the antenna in the direction of 𝟔 dB gain (rounded off to three decimal places) is___________V/m.

Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans
1	C	1	A	11	B	21	2.0 to 2.0	31	C	41	7.9 to 8.1	51	3.320 to 3.325
2	B	2	B	12	C	22	94.2 to 94.6	32	A	42	8.1 to 8.4	52	30.00 to 34.00
3	C	3	B	13	C	23	9.24 to 9.28	33	D	43	10 to 10	53	0.03 to 0.05
4	C	4	B	14	D	24	2.80 to 3.20	34	C	44	0.5 to 0.5	54	1.15 to 1.25
5	B	5	C	15	A	25	9.30 to 9.44	35	A	45	-12 to -12	55	0.224 to 0.264
6	C	6	D	16	8.0 to 8.0	26	MTA	36	10.0 to 10.0	46	5 to 5
7	D	7	A	17	0 to 0	27	B	37	56.50 to 56.60	47	1.40 to 1.50
8	A	8	D	18	0.5 to 0.5	28	C	38	0.132 to 0.146	48	3.125 to 3.125
9	C	9	MTA	19	1.0 to 1.0	29	C	39	31.9 to 32.1	49	1011310.0 to 1011320.0
10	A	10	A	20	4.5 to 4.5	30	A	40	0.0 to 0.0	50	1400 to 1400