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QUESTION: 1

**Q. No. 1 – 5 Carry One Mark Each**

**Q.**

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

sentence.

Communication and interpersonal skills are_____ important in their own ways.

Solution:

QUESTION: 2

Which of the options given below best completes the following sentence?

She will feel much better if she ________________.

Solution:

QUESTION: 3

Choose the most appropriate pair of words from the options given below to complete the

following sentence.

She could not _____ the thought of _________ the election to her bitter rival.

Solution:

QUESTION: 4

A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of

throws show the following frequencies of occurrence: 1→0.167; 2→0.167; 3→0.152; 4→

0.166; 5→0.168; 6 →0.180. We call this die

Solution:

For a very large number of throws, the frequency should be same for unbiased throw. As it not same, then the die is baised.

*Answer can only contain numeric values

QUESTION: 5

Fill in the missing number in the series.

2 3 6 15 ___ 15 7.5 630

Solution:

2nd number/ Ist number

is in increasing order as shown above

QUESTION: 6

**Q. No. 6 – 10 Carry One Mark Each**

**Q.**

Find the odd one in the following group

Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X

Solution:

QUESTION: 7

Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the

ladder there are two lights. If one of the lights is red, the other light on that step will always

be blue. If one of the lights on a step is green, the other light on that step will always be

yellow. Which of the following statements is not necessarily correct?

Solution:

*Answer can only contain numeric values

QUESTION: 8

sum of eight consecutive odd numbers is 656. The average of four consecutive even

numbers is 87. What is the sum of the smallest odd number and second largest even number?

Solution:

Eight consecutive odd number =656

a-6, a-1, a-2, a ,a+2 ,a+4, a+6

a+8=656

a=81

Smallest m=75 … (1)

Average consecutive even numbers

(a-2+a+a+2+a+4)/4=87

a=86

Second largest number =88

1+2=163

QUESTION: 9

The total exports and revenues from the exports of a country are given in the two charts

shown below. The pie chart for exports shows the quantity of each item exported as a

percentage of the total quantity of exports. The pie chart for the revenues shows the

percentage of the total revenue generated through export of each item. The total quantity of

exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees.

Which item among the following has generated the maximum revenue per kg?

Solution:

QUESTION: 10

It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to

simultaneously pump water into the half-full tank while draining it. What is the rate at which

water has to be pumped in so that it gets fully filled in 10 minutes?

Solution:

V_{half}= 30(s) drawing rate = s

Total volume =60 S tank

(s^{1} )(10)- (s)10= 30s

s^{1} (s) -s= 3s

s1= 4s

s^{1}= 4drawing rate

*Answer can only contain numeric values

QUESTION: 11

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

**Q.**

**The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of
matrix AB is ________.**

Solution:

*Answer can only contain numeric values

QUESTION: 12

Let X be a random variable which is uniformly chosen from the set of positive odd numbers

less than 100. The expectation E[X]is __________.

Solution:

QUESTION: 13

For 0 t < ∞, the maximum value of the function f(t) =e^{-t} - 2e^{-2t } occurs at

Solution:

QUESTION: 14

The value of

Solution:

QUESTION: 15

If the characteristic equation of the differential equation

has two equal roots, then the values of α are

Solution:

For equal roots, Discriminant B^{2} − 4AC = 0

4α^{2 }-4 =0

α = 1

QUESTION: 16

Norton’s theorem states that a complex network connected to a load can be replaced with an

equivalent impedance

Solution:

Norton’s theorem

*Answer can only contain numeric values

QUESTION: 17

In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then

the magnitude of the current (in mA) through the 4k? resistor at t = 0+ is _______.

Solution:

QUESTION: 18

A silicon bar is doped with donor impurities N_{D} = 2.25 x 10^{15} atoms / cm^{3}. Given the intrinsic

carrier concentration of silicon at T = 300 K is n_{i} = 1.5 x 1010 cm-3. Assuming complete

impurity ionization, the equilibrium electron and hole concentrations are

Solution:

QUESTION: 19

An increase in the base recombination of a BJT will increase

Solution:

QUESTION: 20

In CMOS technology, shallow P-well or N-well regions can be formed using

Solution:

QUESTION: 21

The feedback topology in the amplifier circuit (the base bias circuit is not shown for

simplicity) in the figure is

Solution:

By opening the output feed back signed becomes zero. Hence it is current sampling.

As the feedback signal v_{f} is subtracted from the signal same v_{s} it is series mixing

QUESTION: 22

In the differential amplifier shown in the figure, the magnitudes of the common-mode and

differential-mode gains are A_{cm} and A_{d}, respectively. If the resistance R_{E} is increased, then

Solution:

*Answer can only contain numeric values

QUESTION: 23

A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The openloop

gain A_{v0}, input resistance R_{in}, and output resistance RO for A1 and A2 are as follows:

Solution:

QUESTION: 24

For an n-variable Boolean function, the maximum number of prime implicants is

Solution:

For an n-variable Boolean function, the maximum number of prime implicants

=2^{(n -1)}

*Answer can only contain numeric values

QUESTION: 25

The number of bytes required to represent the decimal number 1856357 in packed BCD

(Binary Coded Decimal) form is __________ .

Solution:

In packed BCD (Binary Coded Decimal) typically encoded two decimal digits within a single

byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9.

So, 1856357 is required 4-bytes to stored these BCD digits

QUESTION: 26

In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y)

are given by

Solution:

QUESTION: 27

An FIR system is described by the system function

Solution:

Minimum phase system has all zeros inside unit circle maximum phase system has all zeros outside unit circle mixed phase system has some zero outside unit circle and some zeros inside unit circle.

One zero is inside and one zero outside unit circle hence mixed phase system

QUESTION: 28

Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j 0.25 is a zero o X(z), which

one of the following must also be a zero of X(z).

Solution:

Given x[n] = x[−n]

x(z ) =x(z)^{-1} Time reversal property in z -transform

if one zero is 0.5 +j0.25

then other zero will be 1/(0.5+j0.25)

*Answer can only contain numeric values

QUESTION: 29

Consider the periodic square wave in the figure shown.

The ratio of the power in the 7^{th} harmonic to the power in the 5^{th} harmonic for this waveform

is closest in value to _______.

Solution:

For a periodic sequence wave, nth harmonic component is α(1/n)

power in n^{th} harmonic component is α(1/n^{2})

Ratio of the power in 7^{th} harmonic to power in 5^{th} harmonic for given waveform is

*Answer can only contain numeric values

QUESTION: 30

The natural frequency of an undamped second-order system is 40 rad/s. If the system is

damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.

Solution:

QUESTION: 31

For the following sytem

When X_{1}( s) = 0 , the transfer function

Solution:

QUESTION: 32

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by bits per second (bps), where W is the channel bandwidth, P is the

average power received and σ^{2 }is the one-sided power spectral density of the AWGN. For a

fixed P/σ^{2 }=1000. the channel capacity (in kbps) with infinite bandwidth (W→∞) is

approximately

Solution:

*Answer can only contain numeric values

QUESTION: 33

Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the

modulation index (μ) when the maximum and minimum values of the envelope,

respectively, are 3 V and 1 V, is ________.

Solution:

*Answer can only contain numeric values

QUESTION: 34

To maximize power transfer, a lossless transmission line is to be matched to a resistive load

impedance via a λ / 4 transformer as shown.

The characteristic impedance (in?) of the λ / 4 transformer is _________.

Solution:

QUESTION: 35

Which one of the following field patterns represents a TEM wave travelling in the positive x direction?

Solution:

For TEM wave

Electric field (E), Magnetic field (H) and

Direction of propagation (P) are orthogonal to each other.

Here P = + a_{x}

By verification

E =-2a_{y} , H =-3a_{z}

E x H=- a_{y }x -a_{z } = +a_{x}→ P

QUESTION: 36

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

**Q.**

The system of linear equations

Solution:

*Answer can only contain numeric values

QUESTION: 37

The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14

is ________.

Solution:

Using maxima and minima of a function of two variables, we have f is maximum at

x = 0, y = 7 and therefore, maximum value of the determinant is 49

*Answer can only contain numeric values

QUESTION: 38

Solution:

*Answer can only contain numeric values

QUESTION: 39

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,

respectively, the operating angular frequency (in rad/s) is ________.

**Imp : you should answer only the numneric value**

Solution:

The operating frequency (w_{x}), at which current leads the supply.

i.e., w_{x} < w_{r}

again magnitude of current is half the value at resonance

*Answer can only contain numeric values

QUESTION: 40

In the h-parameter model of the 2-port network given in the figure shown, the value of h22 (in

S) is _____ .

**Imp : you should answer only the numneric value**

Solution:

If two, π−n ws are connected in parallel,

The y-parameter are added

QUESTION: 41

In the figure shown, the capacitor is initially uncharged. Which one of the following

expressions describes the current I(t) (in mA) for t > 0?

Solution:

*Answer can only contain numeric values

QUESTION: 42

In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ______ .

Solution:

*Answer can only contain numeric values

QUESTION: 43

Assume electronic charge q = 1.6×10^{-19} C, kT/q = 25 mV and electron mobility μ_{n} = 1000 cm^{2}/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1×10^{21}/cm^{4}, the magnitude of electron diffusion current density (in A/cm^{2}) is _________.

Solution:

*Answer can only contain numeric values

QUESTION: 44

Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region

width Xn on the N-side of the junction is 0.2 μm and the permittivity of silicon ( ε_{si} ) is

1.044×10^{-12} F/cm. At the junction, the approximate value of the peak electric field (in kV/cm)

is _________.

**Imp : you should answer only the numneric value**

Solution:

QUESTION: 45

When a silicon diode having a doping concentration of N_{A} = 9 × 10^{16} cm^{-3} on p-side and N_{D} = 1 × 10^{16} cm^{-3} on n-side is reverse biased, the total depletion width is found to be 3μm . Given that the permittivity of silicon is 1.04 × 10^{–12} F/cm, the depletion width on the p-side and the

maximum electric field in the depletion region, respectively, are

Solution:

QUESTION: 46

The diode in the circuit shown has V_{on} = 0.7 Volts but is ideal otherwise.

If V_{i} = 5sin (ωt) Volts, the minimum and maximum values of V_{O} (in Volts) are, respectively

Solution:

QUESTION: 47

For the n-channel MOS transistor shown in the figure, the threshold voltage V_{Th} is 0.8 V.

Neglect channel length modulation effects. When the drain voltage V_{D} = 1.6 V, the drain

current I_{D} was found to be 0.5 mA. If V_{D} is adjusted to be 2 V by changing the values of R

and V_{DD}, the new value of ID (in mA) is

Solution:

*Answer can only contain numeric values

QUESTION: 48

For the MOSFETs shown in the figure, the threshold voltage |V_{t}| = 2V and

. The value of ID (in mA) is ________.

Solution:

QUESTION: 49

In the circuit shown, choose the correct timing diagram of the output (y) from the given

waveforms W1, W2, W3 and W4.

Solution:

This circuit has used negative edge triggered, so output of the D-flip flop will changed only

when CLK signal is going from HIGH to LOW (1 to 0)

This is a synchronous circuit, so both the flip flops will trigger at the same time and will

respond on falling edge of the Clock. So, the correct output (Y) waveform is associated to w3 waveform.

QUESTION: 50

The outputs of the two flip-flops Q1, Q2 in the figure shown are initialized to 0,0. The

sequence generated at Q1 upon application of clock signal is

Solution:

QUESTION: 51

For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI_{0} – DI_{7})

from an external device is shown in the figure. The instruction for correct data transfer is

Solution:

This circuit diagram indicating that it is memory mapped I/O because to enable the 3-to-8

decoder is required active low signal through is required active low through it means I/o device read the status of device LDA instruction is

appropriate with device address.

Again to enable the decoder o/p of AND gate must be 1 and Ds_{2} signal required is 1 which is the o/p of multi-i/p AND gate to enable I/O device.

So,

*Answer can only contain numeric values

QUESTION: 52

Consider a discrete-time signal

If y[n] is the convolution of x[n] with itself, the value of y[4] is _________.

Solution:

QUESTION: 53

The input-output relationship of a causal stable LTI system is given as

y[n] = αy[n −1] + βx[n]

If the impulse response h[n] of this system satisfies the condition relationship between α and β is

Solution:

*Answer can only contain numeric values

QUESTION: 54

The value of the integral is ______________________

**Imp : you should answer only the numneric value**

Solution:

QUESTION: 55

An unforced liner time invariant (LTI) system is represented by

If the initial conditions are x_{1}(0) = 1 and x_{2}(0) = -1, the solution of the state equation is

Solution:

Solution of state equation of

X(t) =L^{-1}[SI-A^{-1}].X(0)

*Answer can only contain numeric values

QUESTION: 56

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure

If the system is connected in a unity negative feedback configuration, the steady state error of

the closed loop system, to a unit ramp input, is_________.

Solution:

→ Due to initial slope , it is a type-1 system, and it has non zero velocity error coefficient

( K_{v})

→ The magnitude plot is giving 0dB at 2 r / sec.

Which gives k_{v}

QUESTION: 57

Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

Solution:

*Answer can only contain numeric values

QUESTION: 58

The input to a 1-bit quantizer is a random variable X with pdf f_{x (}x) = 2e^{−2x} for x0 and

f_{x}(x) = 0 for x < 0 , for x < 0 For outputs to be of equal probability, the quantizer threshold

should be _____.

Solution:

*One bit quantizer will give two levels.
Both levels have probability of
1/2
Pd of input X is*

QUESTION: 59

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms

where α = 4mV. Assume an AWGN channel with two-sided noise power spectral density N_{0}/2=0.5 x 10^{-12 }W/Hz. Using an optimal receiver and the relation du the bit error probability for a data

rate of 500 kbps is

Solution:

*Answer can only contain numeric values

QUESTION: 60

The power spectral density of a real stationary random process .X(t) is given by

Solution:

*Answer can only contain numeric values

QUESTION: 61

In the figure, M(f) is the Fourier transform of the message signal .m(t) where A = 100 Hz and

B = 40 Hz. Given v(t) = cos (2πf_{c}t) and w(t ) = cos( 2π (f_{c} + A) t) , where f_{c} > A The cutoff

frequencies of both the filters are F_{c}

The bandwidth of the signal at the output of the modulator (in Hz) is _____.

**Imp : you should answer only the numneric value**

Solution:

QUESTION: 62

If the electric field of a plane wave is

the polarization state of the plane wave is

Solution:

*Answer can only contain numeric values

QUESTION: 63

In the transmission line shown, the impedance Zin (in ohms) between node A and the ground

is _________.

**Imp : you should answer only the numneric value**

Solution:

*Answer can only contain numeric values

QUESTION: 64

For a rectangular waveguide of internal dimensions a × b(a > b) , the cut-off frequency for

the TE_{11} mode is the arithmetic mean of the cut-off frequencies for TE_{10} mode and TE_{20}

mode. If a = √5 cm, the value of b (in cm) is _____.

Solution:

QUESTION: 65

**The real part of an analytic function f(z) where z =.x + jy is given by e ^{-y} cos(x). The
imaginary part of f(z) is**

Solution:

Integrating, we get V= e^{-y} sin x

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