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QUESTION: 1

The strategies that the company ________ to sell its products _________ house-to-house marketing.

Solution:

The strategies that the company uses to sell its products include house to house marketing.

QUESTION: 2

The boat arrived _______ dawn.

Solution:

The boat arrived at down

QUESTION: 3

Five different books (P, Q, S, R, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is ___________.

Solution:

As the positions of book R & S are fixed. The books P, Q and T can be arranged in 3! = 6 ways

QUESTION: 4

When he did not come home, she _______ him lying dead on the roadside somewhere.

Solution:

When he did not come home, she pictured him lying dead on the roadside somewhere.

QUESTION: 5

It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is __________ hours.

Solution:

Let t be the time taken by the machines when they work simultaneously.

QUESTION: 6

The bar graph in Panel (a) shows the proportion of male and female iliterates in 2001 and 2011. The proportions of males and females in 2001 and 2011 are given in Panel (b) and (c), respectively. The total population did not change during this period. The percentage increase in the total number of litertes from 2001 to 2011 is

Solution:

Given is the % of illiterates

So % of literates will be

Let total population in both the years as T.

So total literate in 2001 will be 0.4 × 0.4 + 0.5 × 0.6 = 0.46T

And total literate in 2011 will be 0.5 × 0.6 + 0.5 × 0.6 = 0.6T

∴ Increase = 0.6T – 0.46T = 0.14T

QUESTION: 7

Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is an engineer, one is a doctor, one a teacher and another a dancer. You are told that :

1. Mathew is not standing next to Seema

2. There are two people standing between Lohit and the engineer

3. Rahul is not a doctor

4. The teacher and the dancer are standing next to each other

5. Seema is turning to her right to speak to the doctor standing next to her

Q. Who among them is an engineer?

Solution:

QUESTION: 8

“Indian history was written by British historians – extremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subservient to the glory of the Union Jack. Latter-day Indian scholars presented a contrary picture.”From the text above, we can infer that :Indian history written by British historians _________

Solution:

As first line says Indian history was written by British historians was extremely well

documented and researched, but not always impartial.

So option (C) can be interfered from given passage.

QUESTION: 9

Two design consultants, P and Q started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no teabreaks. The market rate for consultants isUSD 200 per hour and breaks are not paid.After paying the consultants, the clientshall have USD ________ remaining in thebudget.

Solution:

∴ paid working hours = 7 hrs + 8 hrs – 30 minutes – 20 minutes

= 14 hrs 10 minutes

∴ Paid = 2833.33

∴ Budget left = 3000 – 2833.33 = 166.67

QUESTION: 10

Five people P, Q, R, S and T work in a bank. P and Q don’t like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, who is currently sharing an office with T wants to move to the adjacent office with S, the handsome new intern. Given the floor plan, what is the current location of Q, R and T? (O = Office, WR = Washroom)

Solution:

As it is given that R is sharing an office with T. So only option (D) is correct.

QUESTION: 11

Which one of the following functions is analystic over the entire complex plane?

Solution:

A function F(z) is said to be analytic at a point z = a then F(z) has a derivative at z = a and derivative

exists at each neighbouring point of z = a in domain D.

But cos z exists for all values of z so it is analytic over the entire complex plane.

QUESTION: 12

Which one of the following options describes correctly the equilibrium band diagram at T = 300 K of a Silicon pnn^{+}p^{++ }configuration shown in the figure?

Solution:

As no supply is connected hence fermi level will be constant.

In P type semiconductor Fermi level should be closer to EV.

In N type semiconductor Fermi level should be closer to EC.

In P++ type semiconductor due to large doping Fermi level enters into valance band.

Hence answer is (B).

QUESTION: 13

Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure).

Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?

Solution:

By reciprocity theorem,

∴ I = 1A

QUESTION: 14

In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?

Solution:

let output of NAND gate is M and output of NOR gate is N

When E_{N} = 0

M = 1 and N = 0

So both PMOS and NMOS will be OFF

So F will be at high impedance

When E_{N} = 1

So this CMOS will act as not gate

∴ F will be D

∴ Option (A) is correct.

*Answer can only contain numeric values

QUESTION: 15

The number of distinct eigenvalues of the matrix

is equal to __________.

Solution:

Since it is a upper triangular matrix eigen values will bee 2, 1, 3, 2

∴ distinct eigen values are three

QUESTION: 16

The families of curves represented by the solution of the equation

for n = - 1 and n = + 1, respectively, are

Solution:

When n = –1

∴lny = – ln(x) + ln(c)

∴ ln(xy) = ln(c)

∴xy = c

This represents rectangular hyperbola.

Now for n = +1

∴ydy = –x dx

∴ x2 + y2 = 2c

This represents family of circles.

QUESTION: 17

Let H(z) be the z-transform of a realvalued discrete-time signal h[n]. If P(z) = H(z) has a zero at and

P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?

Solution:

*Answer can only contain numeric values

QUESTION: 18

The value of the integral is equal to __________.

Solution:

By changing order of integration

*Answer can only contain numeric values

QUESTION: 19

Radiation resistance of a small dipole current element of length l at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation resistance, rounded off to two decimal places, is _________%.

Solution:

Now frequency is constant

QUESTION: 20

Let Y(s) be the unit-step response of a causal system having a transfer function

that is, The forced response of the system is

Solution:

y(s) is unit step response

QUESTION: 21

The correct circuit representation of the structure shown in the figure is

Solution:

QUESTION: 22

What is the electric flux through a quarter-cylinder of height H (as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of Q?

Solution:

If we consider a total cylinder then by gauss law

But Qenclosed = Q · H

And we are considering only th of the cylinder

QUESTION: 23

In the circuit shown, A and B are the inputs and F is the output. What is the functionality of the circuit?

Solution:

By rearranging the circuit,

Truth table:

So it is XNOR gate.

*Answer can only contain numeric values

QUESTION: 24

In the circuit shown, Vs is a square wave of period T with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and R_{1} = R_{2} = 50 Ω.

The average value of VL is _________ volts (rounded off to 1 decimal place).

Solution:

When VS is +ve

Diode will be reserve biased

When V_{S} is –ve

Diode will be forward biased

∴ VL = VS = –10V …(ii)

From (i) and (ii)

∴ Average value = –3

*Answer can only contain numeric values

QUESTION: 25

If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] = _________.

Solution:

We know that

E[AX + BY] = AE[X] + BE[Y]

∴ E[2X + Y] = 2E[X] + E[Y] = 0 …(i)

And E[X + 2Y] = E[X] + 2E[Y] = 33 …(ii)

Adding (i) and (ii)

3E[X] + 3E[Y] = 33

∴ E[X] + E[Y] = 11

QUESTION: 26

A standard CMOS inverter is designed with equal rise and fall times (βn = βp). If the width of the pMOS transistor in the inverter is increased, what would be the effect on the LOW noise margin (NML) and the HIGH noise margin NMH?

Solution:

We know that

QUESTION: 27

In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side.

Solution:

This is Gauss law

This is faraday law of electromagnetic induction

This is Gauss law in magnetostatics which states magnetic monopole does not exists.

This is modified form of ampere’s circuital law.

QUESTION: 28

For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles N_{p} and the number of system zeros N_{z} in the frequency range 1 Hz ≤ f ≤ 10^{7} Hz is

Solution:

at F = 10 Hz we have one pole

At F = 102 Hz we can see two more poles are added as slope is decreased by 40 dB/decade

At F = 10^{3} Hz we have a zero

At F = 10^{4} Hz we have two zero’s

At F = 10^{5} Hz we have two pole’s

At F = 10^{6} we have one pole

∴ Total poles N_{P} = 6

And total zeros N_{Z} = 3

*Answer can only contain numeric values

QUESTION: 29

The baseband signal m(t) shown in the figure is phase-modulated to generate the PM signal φ(t) = cos (2πf_{c}t + k m(t)). The time t on the x-axis in the figure is in milliseconds. If the carrier frequency is f_{c} = 50 kHz and k = 10π, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _________ (rounded off to 2 decimal places).

Solution:

*Answer can only contain numeric values

QUESTION: 30

In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz. The frequency of the signal at Q2 is __________ kHz.

Solution:

As three states are there Frequency of output = Frequency of

QUESTION: 31

A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 100110, then the message 0010 is mapped to

Solution:

As it is given that it is linear hamming code addition of two codes will produce another code. (Here we are talking about mod 2 addition)

*Answer can only contain numeric values

QUESTION: 32

Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by

Then Pr(Z > 2 |Z > 1), rounded off to two decimal places, is equal to __________.

Solution:

Probability density function

*Answer can only contain numeric values

QUESTION: 33

Consider the signal f(t) = 1 + 2cos (πt) + 3 where t is in seconds. Its fundamental time period, in seconds, is ____________.

Solution:

DC value and phase shift does not affect time period of a signal.

So it is equivalent to find time period of

Now overall T = LCM (T_{1}, T_{2}, T_{3})

= LCM (2, 3, 4)

∴ overall T = 12 seconds

QUESTION: 34

The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points

Solution:

*Answer can only contain numeric values

QUESTION: 35

The value of the contour integral

evaluated over the unit circle |z| = 1 is ________.

Solution:

QUESTION: 36

The state transition diagram for the circuit shown is

Solution:

Let output of MUX is M

State Diagram:-

QUESTION: 37

In the circuits shown, the threshold voltage of each nMOS transistor is 0.6 V. Ignoring the effect of channel length modulation and body bias, the values of Vout 1 and Vout 2, respectively, in volts, are

Solution:

In figure (i)

Ever MOS transistor has same V_{G} = 3V

∴ V_{1} = V_{2} = Vout 2 = VG – VT

= 3 – 0.6

∴ Vout 2 = 2.4 V

QUESTION: 38

The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function

Solution:

*Answer can only contain numeric values

QUESTION: 39

A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise n is independent of X, and is uniformly distributed over the interval [-2, 2]. The receiver makes a decision

Where the threshold θ ∈ [-1, 1] is chosen so as to minimize the probability of error Pr The minimum probability of error, rounded off to 1 decimal place, is ______________.

Solution:

=0.05 – 0.5Vth + 0.2Vth + 0.2

P_{e} = 0.25 + 0.15Vth

For Vth = 0 → Pe = 0.25

For Vth = 1 → Pe = 0.4

For Vth = –1 → Pe = 0.1

∴ Minimum probability of error = 0.1

*Answer can only contain numeric values

QUESTION: 40

A germanium sample of dimensions 1 cm × 1 cm is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dixodieGermanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at 600 nm is 3 × 104 cm^{-1} and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is _________ μm.

Solution:

*Answer can only contain numeric values

QUESTION: 41

In the circuit shown, the threshold voltages of the pMOS (|V_{tp}|) and nMOS (V_{tn}) transistors are both equal to 1 V. All the transistors have the same output resistance r_{ds} of 6 MΩ. The other parameters are listed below.

Μ_{n} and μ_{p} are the carrier mobilites, and C_{ox} is the oxide capacitance per unit area. Ignoring the effect of channel length modulation and body bias, the gain of the circuit is ____________(rounded off to 1 decimal place).

Solution:

= –300 × 10^{–6} × 3 × 10^{6}

∴ AV = –900

QUESTION: 42

It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form

where c_{1} and c_{2} are arbitrary real numbers.

The desired three-tap filter is given by

h[0] = 1, h[1] = a, h[2] = b and h[n] = 0 for n < 0 or n > 2.

What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above?

Solution:

Given that

h(0) = 1, h(1) = a, h(2) = b and h(n) = 0 otherwise

Now y(n) = 0 for all n

Both output (i) and (ii) will be zero if

a = 0, b = 1

*Answer can only contain numeric values

QUESTION: 43

Consider a long-channel MOSFET with a channel length 1 μm and width 10 μm. The device parameters are acceptor concentration NA = 5 × 10^{16} cm^{-3}, electron mobility μ_{n} = 800 cm^{2}/V-s, oxide capacitance/area C_{ox} = 3.45 × 10^{-7} F/cm2, threshold voltage V_{T} = 0.7 V. The drain saturation current (I_{Dsat}) for a gate voltage of 5 V is ____________ mA (rouonded off to two decimal places).

Solution:

*Answer can only contain numeric values

QUESTION: 44

In the circuit shown, V_{1} = 0 and V_{2} = V_{dd}. The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of I_{out} is ___________ mA (rounded off to 1 decimal place).

Solution:

Current through FET having

QUESTION: 45

The quantum efficiency (η) and responsivity (R) at wavelength λ (in μm) in a p-i-n photodetector are related by

Solution:

Quantum Efficiency

R_{e} = Corresponding Electron Rate (electrons/sec)

R_{p} = Incident Photon Rate (Photons/sec)

QUESTION: 46

In the circuit shown, if v(t) = 2 sin (1000 t) volts, R = 1 kΩ and C = 1 μF, then the steady-state current i(t), in milliamperes (mA), is

Solution:

Performing star to delta conversion

QUESTION: 47

In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are 20 V and 60 mA, respectively. The values of R1 and RL are 200 Ω and 1 kΩ, respectively. What is the range of Vi that will maintain the Zener diode in the ‘on’ state?

Solution:

As I_{Zmin} not given,

I_{Zmin} = 0 mA

Now I_{S} = I_{Z} + I_{L}

∴ I_{Smin} = I_{Zmin} + I_{L}

= 0 + 20 mA

∴ I_{Smin} = 20 mA

∴ V_{S} = 24V

Now I_{Smax} = I_{Zmax} + I_{L }

= 60 + 20

I_{Smax} = 80 mA

∴ V_{S} = 36 V

QUESTION: 48

Consider a differentiable function f(x) on the set of real numbers such that f(-1) = 0 and |f’(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x ∈ [-2, 2]?

Solution:

Magnetic field will be circular and can be find out by right hand rule

Both fields will add at middle region

∴ at dotted line

H = H_{1} + H_{2}

_{}

QUESTION: 49

Two identical copper wires W1 and W2, placed in parallel as shown in the figure, carry currents I and 2I, respectively, in opposite directions. If the two wires are separated by a distance of 4r, then the magnitude of the magnetic field B between the wires at a distance r from W1 is

Solution:

QUESTION: 50

The dispersion equation of a waveguide, which relates the wavenumber k to the frequency ω, is

where the speed of light c = 3 × 10^{8} m/s, and ω_{o} is a constant. If the group velocity is 2 × 10^{8} m/s, then the phase velocity is

Solution:

QUESTION: 51

Consider a causal second-order system with the transfer function with a unit-step as an input. Let C(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value rounded off to two decimal places, is

Solution:

∴ A(s + 1)^{2} + Bs(s + 1) + Cs = 1

∴ As^{2} + 2As + A + Bs^{2} + Bs + Cs = 1

∴ A + B = 0

∴ 2A + B + C = 0

∴ A = 1

So B = –1

And C = –1

At t → ∞ stedy state will occur

∴ C(∞) = 1

Now we are asked to find time at which 94% of the steady state value reached.

∴ C(t) = 1 – e–t – te–t = 0.94

∴ e–t + te–t = 0.06

∴ e–t (1 + t) = 0.06

Now from the given options try all option you will get t = 4.50 sec.

QUESTION: 52

Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[1] is shown in the figure. Let In the figure, what should be the values of the coefficients a_{1}, a_{2}, a_{3} in terms of W6 so that X[1] is obtained correctly?

Solution:

We are obtaining X(1) correctly

∴ k = 1

We know that

∴ comparing with given graph

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