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QUESTION: 1

A rectangular waveguide, in dominant TE mode, has dimensions 10 *cm* x 15 *cm*. The cut off frequency is

Solution:

QUESTION: 2

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

sentence.

The principal presented the chief guest with a ________, as token of appreciation.

Solution:

QUESTION: 3

Choose the appropriate word/phrase, out of the four options given below, to complete the

following sentence:

Frogs__________.

Solution:

QUESTION: 4

Choose the word most similar in meaning to the given word: ( educe)

Solution:

QUESTION: 5

If log_{x} (5/7) = –1/3, then the value of x is

Solution:

QUESTION: 6

**Q. 6 -10 Carry Two mark each**

**Q.**

A cube of side 3 units is formed using a set of smaller cubes of side 1 unit; Find the proportion of

the number of faces of the smaller cubes visible to those which are NOT visible.

Solution:

QUESTION: 7

The following question presents a sentence, part of which is underlined. Beneath the sentence you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence.

Tuberculosis, together with its effects, "__ranks one of the leading causes of death"__ in India.

Solution:

QUESTION: 8

Humpty Dumpty sits on a every day while having lunch. The wall sometimes breaks. A person

sitting on the wall falls if the wall breaks.

Which one of the statements below is logically valid and can be inferred from the above

sentences?

Solution:

*Answer can only contain numeric values

QUESTION: 9

Find the missing Value:

Solution:

QUESTION: 10

Read the following paragraph and choose the correct statement.

Climate change has reduced human security and threatened human well being. An ignored reality

of human progress is that human security largely depends upon environmental security. But on the

contrary, human progress seems contradictory to environment security. To keep up both at the

required level is a challenge to be addressed by one and all. One of the ways to curb the climate

change may be suitable scientific innovations, while the other may be the Gandhian perspective on

small scale progress with focus on sustainability.

Solution:

QUESTION: 11

**Q. No. 11 – 35 Carry One Mark Each**

**Q.**

A region of negative differential resistance is observed in the current voltage characteristics

of a silicon PN junction if

Solution:

*Answer can only contain numeric values

QUESTION: 12

A silicon sample is uniformly doped with donor type impurities with a concentration of

10^{16} / cm^{3} . The electron and hole mobilities in the sample are

1200cm^{3} / V-s and 400cm^{2} / V-s respectively. Assume complete ionization of impurities.

The charge of an electron is 1.6x 10^{-19} C. The resistivity of the sample (in ?- cm) is _____________.

Solution:

*Answer can only contain numeric values

QUESTION: 13

A unity negative feedback system has the open-loop transfer function

The value of the gain K (>0) at which the root locus crosses the imaginary axis is

_________________.

Solution:

By using Routh Table, s^{1} row should be zero. For poles to be on imaginary axis

QUESTION: 14

Suppose A and B are two independent events with probabilities be their complements. Which one of the following statements is FALSE?

Solution:

We know that A and B are independent

then

*Answer can only contain numeric values

QUESTION: 15

The waveform of a periodic signal x(t) is shown in the figure

A signal g(t) is defined by . The average power of g(t) is

__________________.

Solution:

The average power of x(t) and g(t) is same because the signal g(t) is scaled and shifted

version of x(t).

*Answer can only contain numeric values

QUESTION: 16

In the network shown in the figure, all resistors are identical with R = 300?. The resistance

R_{ab} (in ?) of the network is___________.

Solution:

*Answer can only contain numeric values

QUESTION: 17

Consider a system of linear equations:

x − 2 y + 3z = −1,

x − 3y + 4z = 1, and

−2x + 4 y − 6z = k.

The value of k for which the system has infinitely many solutions is ______.

Solution:

x-2y+3z = -1

x-3y+4z = 1

-2x+4y-6z = k

The system will have infinitely many solutions if p(A/B) = p(A) = r < number of variables

k-2 = 0

k = 2

QUESTION: 18

The polar plot of the <transfer function for 0 ω < ∞ will be in the

Solution:

QUESTION: 19

Let z = x + iy be a complex variable. Consider that contour integration is performed along

the unit circle in anticlockwise direction. Which one of the following statements is NOT

TRUE?

Solution:

QUESTION: 20

Consider the signal where mˆ t denotes the Hilbert

transform of m(t) and the bandwidth of m(t) is very small compared to f_{c} . The signal s(t) is a

Solution:

Given s(t) is the equation for single side band modulation (lower side band).

Thus it is a Band pass signal.

QUESTION: 21

For the circuit with ideal diodes shown in the figure, the shape of the output (vout) for the

given sine wave input (v_{in}) will be

Solution:

The circuit can be re drawn as

During positive pulse, both diodes are forward biased. So output pulse of +ve polarity is

produced. As polarity at ‘d’ and ‘c’ is given opposite to input terminals, hence +ve pulse is

inverted. During negative pulse, both diodes are reverse biased. So, V0 = 0V

QUESTION: 22

The result of the convolution x(-t) *δ(-t-t_{0}) is

Solution:

*Answer can only contain numeric values

QUESTION: 23

The value of p such that the vector is an eigenvector of the matrix is

Solution:

QUESTION: 24

In the given circuit, the values of V_{1} and V_{2} respectively are

Solution:

QUESTION: 25

In an 8085 microprocessor, the shift registers which store the result of an addition and the

overflow bit are, respectively

Solution:

In an 8085 microprocessor, after performing the addition, result is stored in accumulator and if any carry (overflow bit) is generated it updates flags.

QUESTION: 26

Negative feedback in a closed-loop control system DOES NOT

Solution:

Negative feedback in a closed loop

(i) Increases bandwidth

(ii) Reduces gain

(iii) Improve distance rejection

*Answer can only contain numeric values

QUESTION: 27

A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one

(number of rows is equal to the number of columns). The minimum number of address lines

needed for the row decoder is ___________________.

Solution:

Generally the structure of a memory chip = Number of Row × Number of column

= M×N

→ The number of address line required for row decoder is n where M = 2n or

n = log2M

→ As per information given in question : M = N

So M×N = M×M = M2 = 16k = 24×210

M2 = 214

M = 128

→ n = log2128 = 7

QUESTION: 28

A function f(x) = 1- x^{2}+x^{3}is defined in the closed interval [-1, 1]. The value of x, in the

open interval (-1, 1) for which the mean value theorem is satisfied, is

Solution:

By Lagrange’s mean value theorem

*Answer can only contain numeric values

QUESTION: 29

The electric field component of a plane wave traveling in a lossless dielectric medium is

given by

The wavelength (in m) for the wave is

Solution:

QUESTION: 30

In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The energy (in μJ) taken from the 3V source to charge the 0.1μF capacitor from 0V to 3V is

Solution:

So the capacitor in initially uncharged i.e. VC(0) = 0

→ The capacitor will be charged to supply voltage 3V when the switch is in position B

for ∞ time.

→ So we need to find capacitor voltage

*Answer can only contain numeric values

QUESTION: 31

In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6V. The output

voltage V_{0} (in volts) is ________________.

Solution:

Zener is not Breakdown

Hence

V_{0 }=10x (1/2) =5V

*Answer can only contain numeric values

QUESTION: 32

Consider a four bit D to A converter. The analog value corresponding to digital signals of values 0000 and 0001 are 0V and 0.0625V respectively. The analog value (in Volts) corresponding to the digital signal 1111 is ___________.

Solution:

Analog output = [Resolution] × [Decimal equivalent of Binary]

= (0.0615) (15) = 0.9225V

*Answer can only contain numeric values

QUESTION: 33

In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across

the capacitor is ___________________.

Solution:

QUESTION: 34

A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and

step-size Δ of the delta modulator are 20,000 samples per second and 0.1V, respectively. To

prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

Solution:

QUESTION: 35

Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one

of the following plots (in linear scale) qualitatively represents the dependence of on r,

where is the magnitude of the azimuthal component of magnetic field outside the

conductor and r is the radial distance from the conductor?

Solution:

*Answer can only contain numeric values

QUESTION: 36

**Q. No. 36 – 65 carry Two Marks Each**

**Q.**

The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ‘1’ was transmitted is ______________________.

Solution:

*Answer can only contain numeric values

QUESTION: 37

The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a

common bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total

bandwidth of the signal received by the base station of the cell will be at least (in kHz)

__________________.

Solution:

Since GSM requires 200 KHz and only 8 users can use it using TDMA, 9^{th} user needs

another 200 KHz.

9^{th}, 10^{th}, 11^{th}, 12^{th} user can use another 200 KHz bandwidth on time share basis.

Thus for 12 user we need 400 KHz bandwidth.

QUESTION: 38

For the discrete-time system shown in the figure, the poles of the system transfer function are

located at

Solution:

QUESTION: 39

The circuit shown in the figure has an ideal opamp. The oscillation frequency and the

condition to sustain the oscillations, respectively, are

Solution:

Frequency of Wein bridge oscillator is ω_{0 }=1/RC but in the question time constant is

doubled so, frequency becomes half.

QUESTION: 40

A source emits bit 0 with probability1/3 and bit 1 with probability 2/3. The emitted bits are

communicated to the receiver. The receiver decides for either 0 or 1 based on the received

value R. It is given that the conditional density functions of R are as

Solution:

QUESTION: 41

For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are

1 × 1017 cm^{-3} and 1 × 1015 cm^{-3}, respectively. The lifetimes of electrons in P region and holes in N

region are both 100 μs. The electron and hole diffusion coefficients are 49 cm^{2}/s and 36 cm^{2}/s,

respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 × 10^{10} cm^{-3}, and

q = 1.6 × 10^{-19} C. When a forward voltage of 208 mV is applied across the diode, the hole current

density (in nA/cm^{2}) injected from P region to N region is _____________.

Solution:

QUESTION: 42

For the NMOSFET in the circuit shown, the threshold voltage is V_{th} , where V_{th} > 0 . The

source voltage V_{ss} is varied from 0 to V_{DD} . Neglecting the channel length modulation, the

drain current I_{D} as a function V_{ss} is represented by.

Solution:

*Answer can only contain numeric values

QUESTION: 43

In the system shown in figure (a), m(t) is a low-pass signal with bandwidth W Hz. The

frequency response of the band-pass filter H(f) is shown in figure (b). If it is desired that the

output signal z(t) = 10x(t), the maximum value of W (in Hz) should be strictly less than

Solution:

m^{2} (t) →

2W<700

2400 - 2W >1700

w< 350

*Answer can only contain numeric values

QUESTION: 44

In the circuit shown, I_{1} =80mA and I_{2} = 4mA. Transistors T_{1} and T_{2} are identical. Assume

that the thermal voltage V_{T } is 26mV at 27^{o} C. At 50^{o} C , the value of the voltageV_{12} = V_{1} - V_{2} (in mV) is ________________.

Solution:

*Answer can only contain numeric values

QUESTION: 45

The electric field intensity of a plane wave traveling in free space is give by the following

expression

In this field, consider a square area 10cm x 10 cm on a plane x + y = 1. The total timeaveraged

power (in mW) passing through the square area is __________________.

Solution:

*Answer can only contain numeric values

QUESTION: 46

The maximum area (in square units) of a rectangle whose vertices lie on the ellipse

x^{2} + 4y^{2} =1 is ____________________.

Solution:

Let 2x, 2y be the length, breadth respectively of the rectangle inscribed in the ellipse

x^{2} + 4y^{2} =1, then

Area of the rectangle (2x) (2y) i.e., 4xy

*Answer can only contain numeric values

QUESTION: 47

In the given circuit, the maximum power (in Watts) that can be transferred to the load R_{L} is

___________________.

Solution:

*Answer can only contain numeric values

QUESTION: 48

A lead compensator network includes a parallel combination of R and C in the feed-forward

path. If the transfer function of the compensator is G_{C}(S) = s+2/s+4. the value of RC is

______________.

Solution:

*Answer can only contain numeric values

QUESTION: 49

A MOSFET in saturation has a drain current of 1mA for V_{DS} = 0.5V. If the channel length

modulation coefficient is 0.05 V^{-1} , the output resistance (in k?) of the MOSFET is

Solution:

*Answer can only contain numeric values

QUESTION: 50

The built-in potential of an abrupt p-n junction is 0.75V. If its junction capacitance ( C_{j}) at

a reverse bias ( V_{R}) of 1.25V is 5pF, the value of C_{j} in pF when V_{R }= 7.25V is ________________.

Solution:

*Answer can only contain numeric values

QUESTION: 51

In the circuit shown, assume that the opamp is ideal. The bridge output voltage V_{0} (in mV)

for δ= 0.05 is _______________________.

Solution:

QUESTION: 52

The damping ratio of a series RLC circuit can be expressed as

Solution:

*Answer can only contain numeric values

QUESTION: 53

In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value

of v_{c}(t) (in Volts) at t= 1 sec is ___________________.

Solution:

*Answer can only contain numeric values

QUESTION: 54

Consider a uniform plane wave with amplitude (E_{0}) of 10V/ m and 1.1GHz frequency

travelling in air, and incident normally on a dielectric medium with complex relative

permittivity (ε_{r }) and permeability (μr) as shown in the figure.

The magnitude of the transmitted electric field component (in V/m) after it has travelled a

distance of 10 cm inside the dielectric region is __________________.

Solution:

QUESTION: 55

A vector . Which one of the following statements

is TRUE?

Solution:

*Answer can only contain numeric values

QUESTION: 56

All the logic gates shown in the figure have a propagation delay of 20 ns. Let A=C=0 and

B=1 until time t=0. At t= 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that

state. For t > 0, output Z = 1 for a duration (in ns) of

Solution:

As per information given on question the waveforms of A, B, C are as follows

→The logic to solve this question is first obtain X, Y waveform and using this obtain Z.

→ To obtain X, initially assume delay of NOT gate is 0 and draw its waveform and finally

shift it by 20nsec to obtain actual X. Similar procedure to be followed for obtaining Y

and Z i.e., first draw waveform with 0 delay and at the end shift by the amount of delay

given in question.

Clearly we can say that output is high during 20 nsec to 60 nsec i.e. a duration of 40 nsec

QUESTION: 57

A plant transfer function is given as When the plant operates in a

unity feedback configuration, the condition for the stability of the closed loop system is

Solution:

QUESTION: 58

unity feedback configuration, the condition for the stability of the closed loop system is

Solution:

*Multiple options can be correct

QUESTION: 59

A 3-input majority gate is defined by the logic function M(a,b,c) = ab + bc + ca . Which one

of the following gates is represented by the function

Solution:

QUESTION: 60

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide

made of a perfect electric conductor is given by the following expression

The cross-sectional dimensions of the waveguide are given as a = 0.08m and b= 0.033m. The

mode of propagation inside the waveguide is

Solution:

*Answer can only contain numeric values

QUESTION: 61

The open-loop transfer function of a plant in a unity feedback configuration is given a

. The value of the gain K(>0) for which -1+ j2 lies on the root locus is _______________.

Solution:

QUESTION: 62

Two sequences [a, b, c] and [A, B, C] are related as,

then the relationship between the sequences [p, q, r] and [a, b, c] is

Solution:

QUESTION: 63

The solution of the differential equation

Solution:

QUESTION: 64

The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The

zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1,

we can conclude

Solution:

QUESTION: 65

Which one of the following graphs describes the function f(x) =e^{-x}(x^{2} + x + 1) ?

Solution:

f(1) = e^{-x} (x^{2}+x+1)

f(0) = 1

f(0.5) = 1.067

For positive values of x, function never goes negative.

QUESTION: 66

The Boolean expression converted into the

canonical product of sum (POS) form is

Solution:

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