GATE Electronics practice paper - 1

1)   Which process plays a crucial role in transforming the pattern or layout on the working mask of silicon wafer in an IC fabrication mechanism? (Marks : 01)

a. Wafer Cleaning
b. Mask Making
c. Epitaxy
d. Photo-lithography
Answer  Explanation 

ANSWER: Photo-lithography

Photo-lithography basically deals with the photo-engraving technique where the silicon wafer is coated with a photo-resist along with an exposure to UV light.

However, the exposed portions of resist are completely removed by keeping the unexposed areas at an intact or an integral level

2)   The ratio of collector current to emitter current by maintaining collector to base voltage at a constant level  is usually  termed as ___________ (Marks : 01)

a. Common Emitter Amplification Factor
b. Common Collector Amplification Factor
c. Common Base Amplification Factor
d. None of the above
Answer  Explanation 

ANSWER: Common Base Amplification Factor

The point of operation that moves on the characteristic curve for AC operation is basically represented as,
α AC = Δ Ic / Δ IE ( VCB = constant)
where, α AC is expressed as common base short amplification factor.
In DC mode of operation, collector current and emitter current are specified levels of current on the basis of majority carriers & hence can be relatively expressed as,
α AC = Ic / IE

3)   Which phenomenon in BJT is responsible for reduction in the effective base-width due to reverse-biasing of base-collector junction? (Marks : 01)

a. Hall Effect
b. Early Effect
c. Fermi-Level Effect
d. All of the above
Answer  Explanation 

ANSWER: Early Effect

The effective base width decreases as compared to metallurgical base-width because the collector junction is in reverse-biased mode.
This effect is also renowned as base -width modulation since effective base width exhibits variations in accordance to biasing conditions.

4)   Consider the below mentioned assertions :

A1 : Increase in doping level of p-type moves EF towards the centre
A2 : Increase in doping level of p-type moves EF away from the centre
A3: Increase in doping level of p-type results in downward shifting in EF
A4 : Increase in doping level of p-type results in an upward shifting in EF

Which among them is/are correct in accordance to the existence of fermi-level effect in P-type semiconductor?
(Marks : 02)

a. A1 & A3
b. A2 & A4
c. A1 & A4
d. A2 & A3
Answer  Explanation 


Fermi-Level in P-type semiconductor occurs exactly above the acceptor energy level. However, by increasing the addition of impurity during the existence of Fermi-level effect results in the downward shifting of p-type in fermi-level energy (EF) .Besides these, it also moves towards the centre with the rise in temperature level.

5)   Consider the below mentioned statements.

A1. Reduction in channel width & cross-sectional area
A2. Reduction in current density of channel

Which among them are the possible consequences in JFET upon the application of drain-to-source voltage (VDS)? (Marks : 02)

a. Only A1 is true
b. Both A1 & A2 are true but A2 is not a reason for A1
c. Both A1 & A2 are true but A2 is a reason for A1
d. Both A1 & A2 are false
Answer  Explanation 

ANSWER: Only A1 is true

JFET comprises a wedge-shaped channel & gate to source operates only under the revere biased condition. The reverse biasing of gate to source junction increases the input resistance of JFET.
Hence, the channel width cross-sectional area get reduced upon the application of drain to source voltage. This ultimately increases the channel current density.

6)   Consider the assertions S1,S2,S3 & S4

S1 : SiO2  acts as an isolation layer between the junctions in IC fabrication process
S2 : SiO2  acts as an isolation equipment/ material  between the  different devices
S3: SiO2   acts as a passivation layer by preventing undesired impurities over the silicon surface.
S4 : SiO2  acts  as a di-electric between poly-silicon gate and the channel of semiconductor

Which among them is/ are precise functions of silicon dioxide in an ion implantation  process?(Marks : 01)

a. S1: Correct, S2: Correct, S3:Correct , S4: Correct
b. S1: Correct, S2: Incorrect, S3: Correct , S4 : Correct
c. S1: Correct, S2: Correct, S3 :Incorrect , S4 : Correct
d. S1: Correct, S2: Correct, S3 : Correct, S4 : Incorrect
Answer  Explanation 

ANSWER: S1: Correct, S2: Correct, S3:Correct , S4: Correct

SiO2 performs the major functions associated with an ion implantation process in IC fabrication process. It serves to be a dielectric, isolation as well as passivation layer depending upon the type of application.
It also allows the precise doping level of windows between SiO2 with greater proficiency at ion implantation process.

7)   Which control systems basically exhibit their output dependency upon input as well as the previous output stages? (Marks : 01)

a. Open-loop Control System
b. Closed-loop Control System
c. Both a & b
d. None of the above
Answer  Explanation 

ANSWER: Closed-loop Control System

In an open-loop system, the control characteristics are totally independent of the system output & hence are generally stable, while the output relies on the controlling action (input) along with the previous output
in a closed-loop control system. As a result, closed loop systems may sometimes become unstable.

8)   Which among the below specified block reduction techniques deal with an algebraic addition of block for the evaluation of transfer function? (Marks : 01)

a. Associative Law
b. Blocks in Series
c. Blocks in Parallel
d. Summing Point Shift (behind the block)
Answer  Explanation 

ANSWER: Blocks in Parallel

According to the drawing procedure of block diagram, sequential block reduction priorities are assigned for those connected in series , parallel,minor feedback loops and then summing point shift.
However, the transfer function of the serially connected blocks is evaluated on the basis of multiplication while the transfer function of the blocks connected in parallel combination is evaluated on the basis of an algebraic addition.
Associative law is only applicable when two or more directly connected summing points are interchangeable.

9)   Which term associated with the signal flow theory is also renowned as 'Transfer Function'? (Marks : 01)

a. Transmittance
b. Admittance
c. Reluctance
d. Inductance
Answer  Explanation 

ANSWER: Transmittance

Basically, signal flow graph is a graphical representation of a set associated with simultaneous equations & applicable for linear time invariant systems by reducing the time required for block reduction techniques.
Sine the transmittance is normally represented or written on the branch near the arrow by specifying the input-output relationship, it is also referred as a transfer function.

10)   What action should be performed in accordance to the rule of signal flow theory, if the summing point is located after the take-off point in the direction of signal flow? (Marks : 02)

a. Only Summing Point should be represented by a single node
b. Only Summing Point should be represented by separate node
c. Summing & Take-off Points should be represented by a single node
d. Summing & Take-off Points should be represented by separate nodes
Answer  Explanation 

ANSWER: Summing & Take-off Points should be represented by separate nodes

According to the construction rule of signal flow graph, all summing & take-off points are absolutely represented by nodes.
Therefore, a single node is sufficient to represent the summing and take-off points,if the position of summing point is before the take-off point.
But, if the position of summing point lies after the take-off point, then both of them are represented with the assistance of separate nodes connected by a branch possessing unit value of transmittances.

11)   What does the term/value 'ΔK' represents in an equation of Mason's Gain Formula? (Marks : 02)

a. Path Factor
b. Forward Path Transmittance of kth path
c. Loop Gain
d. Graph Determinant
Answer  Explanation 

ANSWER: Path Factor

Mason's Gain Formula is used to evaluate an overall transmittance (gain), which can be expressed as,

T = k=1∑n PK ΔK / Δ
where, Pk = forward path transmittance of kth path
Δ = graph determinant comprising closed loop transmittances & mutual interactions between non-touching loops.
ΔK = path factor consisting of all isolated closed loops from the forward path in the graph.

12)   Which among the below stated conditions is/are precise for non-minimum phase function? (Marks : 02)

a. It consists of at least one pole or zero at RHS of an imaginary axis
b. It consists of symmetric poles and zeros about imaginary axis in s-plane
c. It consists of at least one symmetric pair of pole & zero at RHS of real axis
d. It does not contain any poles or zeros in the RHS of an imaginary axis
Answer  Explanation 

ANSWER: It consists of at least one pole or zero at RHS of an imaginary axis

If the transfer function possesses at least one pole or zero at RHS of an imaginary axis, then the system is said to be in ' Non-minimum Phase while options (b) &(d) represent the conditions of all-pass and minimum phase systems/transfer functions respectively

13)   Consider the statements given below:

A. Beginning of root locus with an open-loop pole at k = 0
B. Location of root locus about the real axis

C. Determination of the branches of root
D. Estimation of an angle of asymptote
E. Monitors the liability for the existence of real axis
F. Termination of root locus either on open-loop zero or at infinity

Which is the correct chronological order of sequential steps obligatory for the construction of root loci? (Marks : 02)

a. A, D, E,B,C, F
b. A, B, C, D, E, F
c. B, A, F, C, E, D
d. B, F, A, D, E, C
Answer  Explanation 

ANSWER: B, A, F, C, E, D

Root locus is a graphical mechanism which is concerned to the plotting of roots of the characteristic equation in s-plane for several parameter values. It is mandatory to determine the root locus properly in proper sequential steps specified in option (c) so as to estimate the presence or location of any point on it by verifying the roots of characteristic equation with the assistance of angle and magnitude criteria.

14)   What values of resistance are offered by an ideal diode in forward and reverse biased conditions respectively?(Marks : 01)

a. zero & infinity
b. infinity & zero
c. zero & unity
d. unity & infinity
Answer  Explanation 

ANSWER: zero & infinity

Ideally, the diode operates in forward-biased condition .This is so because the current flows in forward-biased direction only when the resistance across the voltage is zero. Without any form of obstruction in the flow of current, diodes operates in forward-biasing.
On the contrary, the diode has to pass through an infinite resistance in reverse-biasing mode, which ultimately prevent it from conduction.
However, these both operating conditions of an ideal diode enable it to act as a perfect switch.

15)   Which current acts as a constant form of current source in an active region of BJT amplifiers? (Marks : 01)

a. Collector Current
b. Emitter Current
c. Base Current
d. All of the above
Answer  Explanation 

ANSWER: Collector Current

Collector current is independent of collector voltage and depends only on the emitter current in the active region of BJT.
Therefore, the magnitude of collector current is slightly less than that of emitter current because the value of αDC is less than one but, in fact, almost equal to unity.
These reasons enable the collector current to act as a constant form of current source in an active region of BJT

16)   What is the possible form of output generation in the secondary by the centre-tapped primary of push-pull amplifier due to combination of two collector currents? (Marks : 01)

a. sine wave
b. square wave
c. cosine wave wave
d. triangular wave
Answer  Explanation 

ANSWER: sine wave

In accordance to the configuration arrangement of push-pull amplifier, the centre-tapped secondary winding of transformer provides equal and opposite voltage to base circuits of the two transistors.
Thus , the supply voltage is connected between bases and centre tap. Transistor T1 provides amplification to every half cycle of the signal by leading it to appear in the upper half of the primary winding of output transformer by the ultimate result of combining two collector currents.
This eventually generates the output in the form of sine wave.

17)   Consider the following statements. Which of them represents the precise condition of clipper circuits  that clips the input voltage above a reference voltage?

A. If VR> Vi , then diode is supposed to be reversed-biased & hence V0= Vi
B. If Vi> VR , then diode is supposed to be forward-biased & hence V0 = Vi (Marks : 02)

a. A is false and B is true
b. A is true and B is false
c. Both A & B are true
d. Both A &B are false
Answer  Explanation 

ANSWER: A is true and B is false

Clipper circuits are applicable for selecting that portion of input wave which is located above or below the reference levels.
For the clipper circuit that clips the input voltage above the reference voltage , the necessary operational conditions are

1) If Vi < VR, then diode is reverse-biased & does not operate or conduct Thus, V0= Vi &
2) If Vi>VR , then diode operates in forward biased condition & hence Vo = VR

18)   Which reasons prohibit /reduce the probability of recombining of charge carriers in the base region of bi-polar junction transistor amplifier? (Marks : 02)

a. Increase in collector voltage increases the space charge width & decreases base width
b. Increase in emitter voltage increases the space charge width & decreases base width
c. Increase in emitter voltage decrease the space charge width & increases base width
d. Increase in collector voltage decreases the space charge width & increases base width
Answer  Explanation 

ANSWER: Increase in collector voltage increases the space charge width & decreases base width

Due to the phenomenon of early effect, the collector current increases slightly with voltage. This results in the reduction of base current.
However, increase in collector voltage also increases the space charge but reduces effective base-width. Therefore, there is less possibility for recombination within the base region.

19)   What kind of current sources are applicable for replacing large resistors so as to  prevent them from occupying copious areas on IC chip in the voltage regulator circuits? (Marks : 02)

a. Simple Current Sources
b. Widlar Current Sources
c. Wilson Current Sources
d. Mirror Current Sources
Answer  Explanation 

ANSWER: Widlar Current Sources

Generally, it is mandatory for large resistors to maintain small currents of few micro ampere. Therefore, large areas are occupied by these large resistors on the IC chip. However, Widler current sources are preferred for replacing these large resistors.

20)   Which is the correct truth-table for J-K flip-flop? (Marks : 01)





Answer  Explanation 


J-K Flipflop has an ability to overcome the drawbacks of S-R flipflops .
When both the inputs of JK flipflop are zero, the output is Qn while when both the inputs are 1, the output is the complement of Qn i.e (Q
When the inputs are in the form of '0' , '1' & '1','0' respectively, then the outputs are generated in accordance to the J input value; i.e, outputs are '0' & '1' respectively for both the conditions.

21)   It the input clock frequency of eight flip-flops is 768kHz, then what would be the value of its output frequency? (Marks : 01)

a. 2 kHz
b. 3 kHz
c. 6 kHz
d. 18 kHz
Answer  Explanation 


Input frequency = 768 kHz
The output frequency of eight flipflops = (1 / 28) x Input frequency
= (1 / 28 ) x 768
= 768 / 256
= 3 kHz

22)   What is the crucial function of Emitter-Coupled Logic (ECL) ? (Marks : 01)

a. Least Power Consumption
b. Saturated Logic Operation
c. Highest Packing Density
d. Maximum Power Consumption
Answer  Explanation 

ANSWER: Maximum Power Consumption

Transistors of ECL always operates in an active or cut-off regions & never goes in saturation region thereby eliminating the storage time.
ECL comprises difference amplifiers in addition to emitter followers. These emitter followers are utilized at the output of difference amplifiers for shifting the DC level by consuming maximum power at the requisite level.

23)   Which is the correct chronological order of the steps adopted in Quine-Mc Cluskey Method ?

A. Listing of primary implicants

B. Listing of all given minterms in binary equivalent form

C. Arrangement of minterms in accordance to number of '1's

D.  Selection of minimum number of primes which covers all the minterms

E. Comparison of each binary number with every term in higher next category at adjacent position. If the difference exists by one position,then check mark is assigned and written in the next column.

F. Repetition of  step E for resultant column & continuation of cycle until the occurrence of no further elimination in variables (Marks : 02)

a. A, B, C, D, E, F
b. C, A, B, F, A, D
c. B , C , E, F, A, D
d. B, A, C,D, E, F
Answer  Explanation 

ANSWER: B , C , E, F, A, D

When the number of variables increases beyond six or multiple form, it becomes very arduous to form the group and simplify the boolean expression.
However, it is possible to overcome this predicament by using Quine-Mc Clusky method for the simplification purpose of the boolean expression.
Therefore, Option (c) specifies the precise sequential order of the steps that are followed or undertaken in this method.

24)   Choose the incorrect statement(s) from the following:

A. MROM does not allow the storage of user specified data  to the manufacturer of the memory
B. PROM can be reprogrammed again and again at any number of times
C. EPROM allows to erase the stored content by direct exposure of chip to UV radiations every time before reprogramming
D. E2 PROM allows erasing in an electrical manner despite the exposure of chip to UV rays. (Marks : 02)

a. A & B
b. C & D
c. Only C
d. B & D
Answer  Explanation 


From the given statements, C & D are correct while A & B are incorrect ones. This is so because

In MROM, the user specified data is absolutely stored to the manufacturer of the memory, while PROM allows the data pattern to be programmed on electrical basis with an assistance of a special device called as PROM programmer. Once the data is programmed in PROM, it cannot be changed.

25)   What is the probability of output generation when the inputs are '1' &  '0' respectively in S-R clocked flipflop? (Marks : 02)

a. 1,1 & output remains undefined because outputs try to become '1'
b. 1,0 & flip-flop is reset
c. 0,1 & flip-flop is set
d. 0,0 & output remains unchanged
Answer  Explanation 

ANSWER: 0,1 & flip-flop is set

Set & Reset actions of S-R clocked flipflop are performed only on the basis of a clock pulse. So, when
S=0 & R =0, outputs are 1,1 ( output remains unchanged)
S=0 & R = 1, outputs are 1,0 ( Reset action of flipflop)
S= 1 & R=0, outputs are 0,1 ( Set action of flipflop)
S= 1 & R=1, outputs are 0,0 (output remains undefined since they ought to be 1)

26)   What will  be the value of largest MOD ripple counter that can be implemented in order to operate upto 16 MHz  using J-K flipflops with tnd = 10 ns?
(Marks : 02)

a. 8
b. 10
c. 32
d. 64
Answer  Explanation 


According to the given data,

tnd = 10 ns & f = 16 MHz
Assume that 'n' number of flipflops are connected . Hence, the frequency can be expressed as,
f = 1 / n. td
16 x 106 = 1 / (n x 10 x 10 -9 )

n = 1 / 16 x 106 x 10 x 10-9
= 1 / 16 x 10-2
n = 6.25 ≈ 6
Thus, number of flipflops = 6
Number of MOD ripple counters = 2n = (2) 6 = 64

27)   Which element of graph theory specifies a  subgraph of a graph by allowing the incidence of exactly two branches at each node? (Marks : 01)

a. Twig
b. Path
c. Loop
d. Link
Answer  Explanation 


According to the properties of a loop, it ensures the presence of at least two branches in addition to exactly two paths between any pair of nodes in it .Besides these, the number of branches are always equal to the number of nodes and hence, the two branches are exactly incident at each node.

28)   How many number of trees are possible for a network possessing 'n' nodes? (Marks : 01)

a. 2n-1
b. 2n+2
c. n[1/ n+2]
d. nn-2
Answer  Explanation 

ANSWER: nn-2

For any kind of network, the number of trees can be always determined on the basis of its branches and nodes. This can be implied as,
No. of trees = nn-2
where, n represents the nodes & n-2 represents the number of branches in a tree

29)   Which two-port device has a provision to simulate the equivalent values of  inductance? (Marks : 01)

a. Inductor
b. Capacitor
c. Transformer
d. Gyrator
Answer  Explanation 

ANSWER: Gyrator

Gyrator is a four terminal device whose coefficient value is dependent on the Op-amp parameters as well as externally connected R,C values.
It exhibits a unique feature of impedance inversion phenomenon due to which the input impedance is capacitive for an inductive load impedance and vice-versa. In addition to this, simulation of equivalent inductance values is also a major function performed by a gyrator

30)   Which statements represent the properties of a tree according to the  network graph theory ?

A1 : There exists only a single path between any pair of nodes.
A2 : The rank of a tree is similar to the rank of graph
A3: A tree does not contain any node on the graph
A4 : A tree comprises all closed paths
(Marks : 02)

a. A1 & A2
b. A3 & A4
c. A1, A2 , A 3 & A4
d. None of the above
Answer  Explanation 


Only the statements A1 & A2 satisfy the properties of a tree. The statements A3 & A4 are not precise because a tree contains all the nodes on the graph and does not contain any closed path.

31)   What will be the value of time constant for the network shown below?

(Marks : 02)

a. 5RC
b. 4RC
c. (4/5) RC
d. RC /5
Answer  Explanation 

ANSWER: (4/5) RC

By replacing the voltage source in terms of internal impedance, the equivalent circuit is shown below.

From the above equivalent network, it is obvious that

Req = (R x 4R) / 5R
= 4R /5
Also, the time constant (τ) = Req x C
= (4 /5) RC

32)   What is the function of dependent source in the circuit diagram shown below?
(Marks : 02)

a. It delivers 256 W
b. It absorbs 256 W
c. It delivers 512 W
d. It absorbs 512 W
Answer  Explanation 

ANSWER: It absorbs 512 W

From the given network,
Power = V x I
= (2 Ix) x Ix
= 2 I2x

Since Ix = 16A

P = 2 x (16)2
= 512 W (absorption)
Hence, the total power of about 512W is absorbed in the given circuit.

33)   Which theorems do not support the similarity of handling dependent and independent current and voltage sources ?

A. Thevenin's & Norton's Theorems
B. Superposition & Norton's Theorems
C. Maximum Power transfer & Reciprocity Theorems
D. Millman's & Tellegen's Theorem
Manipulation of independent and dependent voltage and current sources is almost similar in almost all types of theorems except Thevenin's , Norton's and superpositon theorems especially for the calculation of equivalent impedances.
(Marks : 02)

a. A & B
b. C & D
c. A & C
d. B & D
Answer  Explanation 


No explanation is available for this question!

34)   Any signal that exhibits symmetry on Y-axis is called as _______ (Marks : 01)

a. odd signal
b. even signal
c. periodic signal
d. exponential signal
Answer  Explanation 

ANSWER: even signal

A signal can be said to be symmetric on Y-axis only when the symmetrical nature of curve obtained from the signal exhibits two equal portions of the curve exactly similar to each other over the Y-axis.
Since this kind of symmetry is shown by the signal has even (equal) form of distributions in terms of curve portions,amplitudes & time instants, they are generally referred as 'Even Signals'

35)   Which among the below specified notations exhibit an odd signal? (Marks : 01)

a. x(-t) = -x(t) & x[-n] = -x[n]
b. x(-t) = x(t) & x[-n] = x[n]
c. x(-t) = -x(-t) & x[-n] = -x[-n]
d. x(t) = x(-t) & x[n] = x[-n]
Answer  Explanation 

ANSWER: x(-t) = -x(t) & x[-n] = -x[n]

The necessary condition of an odd signal is that it must be zero at t=o or n=o . Thus, it can be expressed as x(-t) = -x(t) & x[-n] = -x[n].
This implies that negative value of time instants are equal to the negativity of an entire term in an odd signal, while the negative value of time instants are equal to the positive values of an entire term in an even signal.
However, sin t is an odd signal while cos t is an even signal

36)   Which Fourier Dirichlet conditions for transform existence specify the necessity of possessing finite values of the signal at any instant over a finite interval of time (T) ? (Marks : 02)

a. Single Valued Property
b. Finite-discontinuities
c. Finite Peaks
d. Absolute Integration
Answer  Explanation 

ANSWER: Single Valued Property

The conditions which provide chances to the periodic function to get expanded in a convergent Fourier series , are renowned as Dirichlet Conditions.
Thus, the very first Dirichlet condition states that, the signal should have only the finite values over any time instant for a finite interval of time so the signal can be considered to be fourier transformable.
This condition implies the single-valued property that does not change or tend to increase over the infinite time intervals.

37)   Y1 : It is not mandatory for every signal to be even or odd
Y2 : : Any signal which is neither even nor odd can be expressed as the difference of even and odd signals
(Marks : 02)

a. Y1 only
b. Y2 only
c. Both Y1 & Y2 are correct but Y2 is not a reason for Y1
d. Both Y1 & Y2 are correct but Y2 is definitely a reason of Y1
Answer  Explanation 

ANSWER: Y1 only

The statement Y1 is only precise because every signal should not be necessarily even or odd. It can also belong to some other category of signals. Also, the signal which is neither odd nor even odd is basically expressed as the addition (sum) of even and odd signals.

38)   Consider the following assertions:

A: x(t) or x[n] is assumed to be an energy signal  if and only if 0>E>∞  and P=1
B: x(t) or x[n] is assumed to be a power signal only if 0>P> ∞ and E=1
C: x(t) or x[n] is assumed to be a power signal only if  0 < P < ∞ and E= ∞
D:  x(t) or x[n] is assumed to be an energy signal  if and only if 0
Which among them are correct in accordance to energy and power signals?
(Marks : 02)

a. A & B
b. C & D
c. A & C
d. B & D
Answer  Explanation 


According to the property of energy and power signals, a signal is said to be an energy signal only when the value of normalized energy lies within zero and infinity i.e. normalized energy should be greater than zero but less than infinity.
Similarly, Power signals lie within the same range of zero and infinity. This implies that , a signal is known as a power signal only if the value of normalized average power is greater than zero but less than infinity.
Signals which do not satisfy any of these properties are generally known as neither energy signals nor power signals.

39)   What is the obligatory sequence that need to be performed or executed in time shifting ,scaling and time reversal operational processes under the category of continuous time signals? (Marks : 02)

a. Time Shifting, Time Scaling & Time Reversal
b. Time Scaling, Time Reversal & Time Shifting
c. Time Shifting, Time Reversal & Time Scaling
d. Time Reversal, Time Scaling & Time Shifting
Answer  Explanation 

ANSWER: Time Shifting, Time Scaling & Time Reversal

In accordance to the properties of continuous time signals, when the stages of time shifting, scaling and reversal are to be performed,then it is always obligatory to initially perform time shifting, and then scaling and the reversal.
This is so because scaling can only be done after shifting the time signal. Time shifting property does not affect the amplitude of signal but it shows a slightly delayed version of original signal.
Eventually, once the signal undergoes time scaling, it can further undergo the time reversal phase, where the exact reflection of the time-scaled signal is generated about Y-axis.

40)   How is the distance defined  between two radical planes of the spheres at angles Ø and (Ø + dØ ) ? (Marks : 01)

a. r sin θ dФ
b. sin θ dФ
c. r dФ
d. r + sin θ dФ
Answer  Explanation 

ANSWER: r sin θ dФ

The locus of points which comprises similar powers corresponding to the two spheres is known as radical plane.
Therefore, the distance between two radical planes of the spheres is equal to the product of radius vector measured from Z-axis, sine angle between Z-axis & radius vector and the angle between X-axis and radius vector projection in XY plane.

41)   Which conditions are mandatory to get satisfied for the formation of a sphere ? (Marks : 01)

a. 0 ≤ θ ≤ π , 0 ≤ Ф ≤ 2 π & r = constant
b. Ф = change , r = change & θ = constant
c. r → ∞ , 0 ≤ θ ≤ 2π & Ф = constant
d. Ф → ∞ , 0 ≤ θ ≤ 2π & r= constant
Answer  Explanation 

ANSWER: 0 ≤ θ ≤ π , 0 ≤ Ф ≤ 2 π & r = constant

A sphere is formed only when the value of an angle vector originated due to Z-axis and radius vector lies between zero and π; and the value of angle vector between X-axis & radius vector projection over XY plane is greater than zero but less than or equal to 2π ,by keeping radius vector as a constant

42)   Which  among the below mentioned operators is supposed to be zero so as to justify the scalar field to be harmonic? (Marks : 01)

a. Gradient
b. Curl
c. Laplacian
d. Divergence
Answer  Explanation 

ANSWER: Laplacian

A function is said to be harmonic only when its laplacian operator value ▼2f is zero. Similarly, a scalar field is also said to be harmonic only when its laplacian operator becomes zero despite the other operators.

43)   How can the total charge enclosed by the closed or covered surface be expressed using Gauss's law ? (Marks : 02)

a. By the line integral of the charge density
b. By the surface integral of the charge density
c. By the Volume integral of the charge density
d. None of the above
Answer  Explanation 

ANSWER: By the Volume integral of the charge density

Guass's law states that the total flux over the outer closed surface is always equivalent to the total charge within the surface.
Similarly, Guass's law can also be defined in terms of volume integral which states that the total charge present over the closed surface is equal to the volume integral function of the charge density.

44)   Which among the below given statements are correct in accordance to the properties of a conductor?

A. The static electric field intensity at the surface of conductor is directed parallel to the surface.
B.  The static electric field intensity at the surface of conductor is directed perpendicular  to the surface.
(Marks : 02)

a. Only A is correct
b. Only B is correct
c. Both A & B are correct
d. Both A & B are incorrect
Answer  Explanation 

ANSWER: Only B is correct

Conductor develops an equal potential throughout the surface and the static electric field intensity within the inner portion of a conductor is zero. Thus, the properties of a conductor implies that the static electric field intensity over the surface of a conductor is directed equally and normal (perpendicular) to the surface.

45)   Which among the following statements is/are precise in accordance to distortionless line?

A. A lossless line is also a distortionless line
B. A distortionless line is not necessarily a lossless line
(Marks : 02)

a. A is true & B is false
b. A is false & Bis true
c. Both A & B are true
d. Both A & B are false
Answer  Explanation 

ANSWER: Both A & B are true

The conductors in the lossless line are perfect and the dielectric medium that separates them is absolutely lossless.
Besides this, a transmission line where the value of an attenuation constant is independent of frequency & phase constant is linearly dependent on frequency.
Hence, it is obvious that a lossless line can also be a distortionless line but a distortionless line cannot be essentially a lossless line.

46)   When can a random process is said to be an ergodic process? (Marks : 01)

a. Only when time averages are less than the ensemble averages
b. Only when time averages are equal to the ensemble averages
c. Only when time averages are greater than the ensemble averages
d. none of the above
Answer  Explanation 

ANSWER: Only when time averages are equal to the ensemble averages

Random Processes can be generally and completely specified on the basis of ensemble and the time statistics since only PDFs are insufficient to describe them completely.
So, any random process possessing the time averages exactly equal to averages [Probability Distribution Factor PDF (fx(t) (x)] which are derived from ensemble, then it is said to be an ergodic process.

47)   Consider the statements given below:

A. All SSS (Stationary in Strict Sense) processes are also WSS (Stationary in Wide Sense)

B. All the processes that are WSS  (Stationary in Wide Sense) are also absolutely  SSS (Stationary in Strict Sense)

Which of them are correct? (Marks : 01)

a. A is true & B is false
b. A is false & B is true
c. Both A & B are true
d. Both A & B are false
Answer  Explanation 

ANSWER: A is true & B is false

A random process is said to be Stationary in Strict Sense (SSS) if the joint probability distribution factor remains invariant to the translation of time origin. On the contrary, it is said to be Stationary in Wide Sense if mean value mx (t) is independent of time and the autocorrelation function Rx (tk, ti) depends only on the time difference (tk - ti).
Hence, it is obvious that all SSS are definitely WSS but all WSS are not necessarily SSS.

48)   Assume that super heterodyne receiver consumes an IF frequency of 350 kHz by high side tuning to a transmitter with a carrier frequency of 1200 kHz . What would be the value of an image frequency ? (Marks : 01)

a. 1550kHz
b. 8400 kHz
c. 1900 kHz
d. 1000kHz
Answer  Explanation 

ANSWER: 1900 kHz

Given data :
IF = 350 kHz
Carrier Frequency = fc = 1200 kHz

We know that,
Image Frequency = 2 IF + fc
= 2x 350 + 1200
= 1900 kHz

49)   A signal m(t) = 20cos (2π200t) along with carrier generates an FM signal x(t) = 40cos {2π x 106t  + 10 sin (2π 200t)}. What will be the value of approximate bandwidth of the frequency modulation? (Marks : 02)

a. 200 kHz
b. 2 kHz
c. 4.4 kHz
d. None of these
Answer  Explanation 

ANSWER: 4.4 kHz

Given data :
Frequency Deviation = Δf = 10 x ( 2π 200) rad
Deviation ratio = D = [10 x ( 2π 200)] / [( 2π 200)]
Therefore, D = 10

Bandwidth of Frequency Modulated Signal is given by,
B = 2 (D + 1) fm
= 2 (10 +1 ) x 200
= 2 (11) x 200
= 22 x 200
= 4400
= 4.4 kHz

50)   Which conditions justify the mutual orthogonality of two random signals X(t) & Y(t)?
(Marks : 02)

a. RXY , (t1, t2 ) = 0 for every t1 and t2
b. RXY , (t1, t2 ) = 1 for every t1 and t2
c. RXY = 0, (t1, t2 ) = 1 for t1 and t2 instants respectively
d. RXY = 1 , (t1, t2 ) = 0 for t1 and t2 instants respectively
Answer  Explanation 

ANSWER: RXY , (t1, t2 ) = 0 for every t1 and t2

Two random X(t) & Y(t) processes are usually said to be mutually orthogonal only and only if RXY, (t1,t2) becomes exactly equal to zero; where
t1 & t2 are the two time instants at which the processes are observed.

51)   How is the process of non-uniform quantization equivalently & combinationally  performed?

A. Passage of baseband signal through the compressor
B. Application of compressed signal to a uniform quantizer
C. Passage of passband signal through the compressor
D. Application of compressed signal to a non-uniform quantizer
(Marks : 02)

a. A & B
b. C & D
c. A & D
d. C & B
Answer  Explanation 


Non-uniform quantizer has has non-linear characteristics while the step-size consistently keeps on varying & depends on the amplitude of input signal.
This process of non-uniform quantization resemble to the mechanisms of passing the baseband signal through compressor and then eventually applying the compressed signal to a uniform quantizer.