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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.
Which of the options given below best completes the following sentence?
She will feel much better if she ________________.
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.
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
For a very large number of throws, the frequency should be same for unbiased throw. As it not same, then the die is baised.
Fill in the missing number in the series.
2 3 6 15 ___ 15 7.5 630
2nd number/ Ist number
is in increasing order as shown above
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
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?
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?
Eight consecutive odd number =656
a6, a1, a2, a ,a+2 ,a+4, a+6
a+8=656
a=81
Smallest m=75 … (1)
Average consecutive even numbers
(a2+a+a+2+a+4)/4=87
a=86
Second largest number =88
1+2=163
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?
It takes 30 minutes to empty a halffull tank by draining it at a constant rate. It is decided to
simultaneously pump water into the halffull 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?
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
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 ________.
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 __________.
For 0 t < ∞, the maximum value of the function f(t) =e^{t}  2e^{2t } occurs at
If the characteristic equation of the differential equation
has two equal roots, then the values of α are
For equal roots, Discriminant B^{2} − 4AC = 0
4α^{2 }4 =0
α = 1
Norton’s theorem states that a complex network connected to a load can be replaced with an
equivalent impedance
Norton’s theorem
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 _______.
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 cm3. Assuming complete
impurity ionization, the equilibrium electron and hole concentrations are
An increase in the base recombination of a BJT will increase
In CMOS technology, shallow Pwell or Nwell regions can be formed using
The feedback topology in the amplifier circuit (the base bias circuit is not shown for
simplicity) in the figure is
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
In the differential amplifier shown in the figure, the magnitudes of the commonmode and
differentialmode gains are A_{cm} and A_{d}, respectively. If the resistance R_{E} is increased, then
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:
For an nvariable Boolean function, the maximum number of prime implicants is
For an nvariable Boolean function, the maximum number of prime implicants
=2^{(n 1)}
The number of bytes required to represent the decimal number 1856357 in packed BCD
(Binary Coded Decimal) form is __________ .
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 4bytes to stored these BCD digits
In a halfsubtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X  Y)
are given by
An FIR system is described by the system function
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
Let x[n] = x[n]. Let X(z) be the ztransform 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).
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)
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 _______.
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
The natural frequency of an undamped secondorder system is 40 rad/s. If the system is
damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.
For the following sytem
When X_{1}( s) = 0 , the transfer function
The capacity of a bandlimited 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 onesided power spectral density of the AWGN. For a
fixed P/σ^{2 }=1000. the channel capacity (in kbps) with infinite bandwidth (W→∞) is
approximately
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 ________.
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 _________.
Which one of the following field patterns represents a TEM wave travelling in the positive x direction?
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
Q. No. 36 – 65 Carry Two Marks Each
Q.
The system of linear equations
The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14
is ________.
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
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
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
In the hparameter model of the 2port network given in the figure shown, the value of h22 (in
S) is _____ .
Imp : you should answer only the numneric value
If two, π−n ws are connected in parallel,
The yparameter are added
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?
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 ______ .
Assume electronic charge q = 1.6×10^{19} C, kT/q = 25 mV and electron mobility μ_{n} = 1000 cm^{2}/Vs. If the concentration gradient of electrons injected into a Ptype silicon sample is 1×10^{21}/cm^{4}, the magnitude of electron diffusion current density (in A/cm^{2}) is _________.
Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region
width Xn on the Nside 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
When a silicon diode having a doping concentration of N_{A} = 9 × 10^{16} cm^{3} on pside and N_{D} = 1 × 10^{16} cm^{3} on nside 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 pside and the
maximum electric field in the depletion region, respectively, are
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
For the nchannel 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
For the MOSFETs shown in the figure, the threshold voltage V_{t} = 2V and
. The value of ID (in mA) is ________.
In the circuit shown, choose the correct timing diagram of the output (y) from the given
waveforms W1, W2, W3 and W4.
This circuit has used negative edge triggered, so output of the Dflip 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.
The outputs of the two flipflops Q1, Q2 in the figure shown are initialized to 0,0. The
sequence generated at Q1 upon application of clock signal is
For the 8085 microprocessor, the interfacing circuit to input 8bit digital data (DI_{0} – DI_{7})
from an external device is shown in the figure. The instruction for correct data transfer is
This circuit diagram indicating that it is memory mapped I/O because to enable the 3to8
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 multii/p AND gate to enable I/O device.
So,
Consider a discretetime signal
If y[n] is the convolution of x[n] with itself, the value of y[4] is _________.
The inputoutput 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
The value of the integral is ______________________
Imp : you should answer only the numneric value
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 of state equation of
X(t) =L^{1}[SIA^{1}].X(0)
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_________.
→ Due to initial slope , it is a type1 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}
Consider the state space system expressed by the signal flow diagram shown in the figure.
The corresponding system is
The input to a 1bit 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 _____.
One bit quantizer will give two levels.
Both levels have probability of
1/2
Pd of input X is
Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms
where α = 4mV. Assume an AWGN channel with twosided 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
The power spectral density of a real stationary random process .X(t) is given by
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
If the electric field of a plane wave is
the polarization state of the plane wave is
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
For a rectangular waveguide of internal dimensions a × b(a > b) , the cutoff frequency for
the TE_{11} mode is the arithmetic mean of the cutoff frequencies for TE_{10} mode and TE_{20}
mode. If a = √5 cm, the value of b (in cm) is _____.
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
Integrating, we get V= e^{y} sin x
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