βI cannot support this proposal. My ________ will not permit it.β
a.
conscious
b.
consensus
c.
conscience
Correct Answer
d.
consent
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Q2mcq
Courts: _______:: Parliament: Legislature (By word meaning)
a.
Judiciary
Correct Answer
b.
Executive
c.
Governmental
d.
Legal
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Q3mcq
What is the smallest number with distinct digits whose digits add up to 45?
a.
123555789
b.
123457869
c.
123456789
Correct Answer
d.
99999
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Q4mcq
In a class of 100 students, (i) there are 30 students who neither like romantic movies nor comedy movies, (ii) the number of students who like romantic movies is twice the number of (iii) the number of students who like both romantic movies and comedy movies
students who like comedy movies, and
is 20. How many students in the class like romantic movies?
a.
40
b.
20
c.
60
Correct Answer
d.
30
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Q5mcq
How many rectangles are present in the given figure?
.
a.
8
b.
9
c.
10
Correct Answer
d.
12
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Q6mcq
Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious. Based only on the information provided above, which one of the following options can be logically inferred with certainty?
a.
All creatures with claws are animals.
b.
Some creatures with claws are non-ferocious.
c.
Some non-ferocious creatures have claws.
d.
Some ferocious creatures are creatures with claws.
Correct Answer
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Q7mcq
Which one of the following options represents the given graph?
a.
f x = x 2 2 ()
Correct Answer
b.
f x = x. 2 () - x
c.
f x = x 2 x
d.
f x = x. 2 x
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Q8mcq
Which one of the following options can be inferred from the given passage alone?
When I was a kid, I was partial to stories about other worlds and
interplanetary travel. I used to imagine that I could just gaze off into space
and be whisked to another planet.
[Excerpt from The Truth about Stories by T. King]
a.
It is a childβs description of what he or she likes.
b.
It is an adultβs memory of what he or she liked as a child.
Correct Answer
c.
The child in the passage read stories about interplanetary travel only in parts.
d.
It teaches us that stories are good for children.
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Q9mcq
Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to: (i) Collect saliva samples from all 1000 individuals and randomly group
them into sets of 5. (ii) Mix the samples within each set and test the mixed sample for covid. (iii) If the test done in (ii) gives a negative result, then declare all the 5
individuals to be covid negative. (iv) If the test done in (ii) gives a positive result, then all the 5 individuals
are separately tested for covid. Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.
a.
700
Correct Answer
b.
600
c.
800
d.
1000
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Q10mcq
A 100 cm $\times$ 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm $\times$ 1 cm. The total number of creases visible when the sheet is unfolded is _______.
a.
32
b.
5
c.
31
Correct Answer
d.
63
No explanation saved for this question yet.
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1 2 Let $v 1$ = [ 2 ] and $v 2$ = [ 1 ] be two vectors. The value of the coefficient $Ξ±$ in the 0 3 expression $v 1$ = $Ξ±v 2$ + $e,$ which minimizes the length of the error vector $e,$ is
a.
7 2
b.
-2 7
c.
2 7
d.
-7 2
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The value of the contour integral, $\oint$ () $dz$, where the contour C is $z+2$
$C z$ 2 $+2z+2$ $j2Ο$ $jΟ$ $j5Ο$ $j9Ο$
3 ${z: |z$ + 1 - $j|$ = 1}, taken in the counter clockwise direction, is
2
a.
$-Ο(1$ + $j)$
b.
$Ο(1$ + $j)$
c.
$Ο(1$ - $j)$
d.
$-Ο(1$ - $j)$
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Let the sets of eigenvalues and eigenvectors of a matrix $B$ be ${Ξ» k$ | 1 $\le k \le n}$ and ${v k$ | 1 $\le k \le n},$ respectively. For any invertible matrix $P,$ the sets of eigenvalues and eigenvectors of the matrix $A,$ where $B$ = $P$ -1 $AP,$ respectively, are
a.
${Ξ» k$ det $(A)$ | 1 $\le k \le n}$ and ${Pv k$ | 1 $\le k \le n}$
b.
${Ξ» k$ | 1 $\le k \le n}$ and ${v k$ | 1 $\le k \le n}$
c.
${Ξ» k$ | 1 $\le k \le n}$ and ${Pv k$ | 1 $\le k \le n}$
d.
${Ξ» k$ | 1 $\le k \le n}$ and ${P$ -1 $v k$ | 1 $\le k \le n}$
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For a MOS capacitor, V fb and V t are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width (W dep) for varying gate voltage (V g) is best represented by
a.
w dep v fb v t accumulation depletion
b.
w dep v fb v t accumulation depletion
c.
w dep v fb v t accumulation depletion
d.
w dep v fb v t v g accumulation depletion inversion
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Consider a narrow band signal, propagating in a lossless dielectric medium $(Ξ΅ r$ = 4, $ΞΌ r$ = 1), with phase velocity $v p$ and group velocity $v g$. Which of the following statement is true? $(c$ is the velocity of light in vacuum.)
a.
$v p$ > $c, v g$ > $c$
b.
$v p$ < $c, v g$ > $c$
c.
$v p$ > $c, v g$ < $c$
d.
$v p$ < $c, v g$ < $c$
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The synchronous sequential circuit shown below works at a clock frequency of 1 GHz. The throughput, in Mbits/s, and the latency, in ns, respectively, are
Input
Q 0 D 0 Q 1 D 1
D D
Flip Flop Flip Flop
CLK = 1 GHz
a.
1000, 3
b.
333.33, 1
c.
2000, 3
d.
333.33, 3
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The open loop transfer function of a unity negative feedback system is
$k G(s)$ =, where $k, T$ and $T$ are positive constants. The phase cross-
$s(1+sT)(1+sT$) 1 2 1 2 over frequency, in rad/s, is
a.
1 $\sqrt{T}$ 1 $T$ 2
b.
1 $T$ 1 $T$ 2
c.
1 $T$ 1 $\sqrt{T}$ 2
d.
1 $T$ 2 $\sqrt{T}$ 1
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Let $m(t)$ be a strictly band-limited signal with bandwidth $B$ and energy $E.$ Assuming $Ο$ 0 = $10B,$ the energy in the signal $m(t)$ cos $Ο$ 0 $t$ is
a.
$E$ 4
b.
$E$ 2
c.
$E$
d.
$2E$
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The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 dB. The resolution of the ADC is ________ bits (rounded off to the nearest integer).
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For the circuit shown below, the propagation delay of each NAND gate is 1 ns. The critical path delay, in ns, is __________ (rounded off to the nearest integer).
A Q
Q
B
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In the circuit shown below, switch S was closed for a long time. If the switch is opened at $t$ = 0, the maximum magnitude of the voltage V R, in volts, is _________ (rounded off to the nearest integer).
2 β¦
S 1 β¦ V
R
1 H
V s = 2 V
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A random variable X, distributed normally as $N(0,1),$ undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of $Y$ is (In the options given below, $a, b, c$ are non-zero constants and $g(y)$ is piece-wise continuous function)
y = h(x)
1
-2 1 -1
-1
a.
$aΞ΄(y$ - 1) + $bΞ΄(y$ + 1) + $g(y)$
b.
$aΞ΄(y$ + 1) + $bΞ΄(y)$ + $cΞ΄(y$ - 1) + $g(y)$
c.
$aΞ΄(y$ + 2) + $bΞ΄(y)$ + $cΞ΄(y$ - 2) + $g(y)$
d.
$aΞ΄(y$ + 2) + $bΞ΄(y$ - 2) + $g(y)$
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The value of the line integral $\int (z$ 2 $dx$ + $3y$ 2 $dy$ + $2xz dz)$ along the straight line
$P$ joining the points $P$ (1,1,2) and $Q$ (2,3,1) is
a.
20
b.
24
c.
29
d.
-5
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In the circuit shown below, D 1 and D 2 are silicon diodes with cut-in voltage of 0.7 V. V IN and V OUT are input and output voltages in volts. The transfer characteristic is
D 1
V IN V OUT
1 kβ¦
D 2
a.
V OUT
1 1 0.3 1
b.
V OUT
1 - 0.7 V
IN 0.7 1
c.
V OUT
1 1 1 -1.7
d.
V OUT
1 0.3 1.7 V IN 1
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A closed loop system is shown in the figure where k > 0 and Ξ± > 0. The steady state error due to a ramp input (R(s) = Ξ±/s 2) is given by R(s) = Ξ± /s
a.
2Ξ± k
b.
Ξ± k
c.
Ξ± 2k
d.
Ξ± 4k
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In the following block diagram, R(s) and D(s) are two inputs. The output Y(s) is expressed as Y(s) = G 1 (s)R(s) + G 2 (s)D(s). G 1 (s) and G 2 (s) are given by
D(s)
Y(s)
G(s)
R(s)
H(s)
a.
b.
c.
d.
G 1 (s) = and G 2 (s) =
G(s) G(s)
1 + G(s) + G(s)H(s) 1 + G(s) + H(s)
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The state equation of a second order system is $x$ Μ $(t)$ = $Ax(t), x(0)$ is the initial condition. Suppose Ξ» 1 and Ξ» 2 are two distinct eigenvalues of A and $v$ 1 and $v$ 2 are the corresponding eigenvectors. For constants $Ξ±$ 1 and $Ξ±$ 2, the solution, $x(t),$ of the state equation is
a.
2 β $Ξ± i e$ Ξ» $i$ t $v i$ $i=1$
b.
2 β $Ξ± i e$ 2Ξ» $i$ t $v i$ $i=1$
c.
2 β $Ξ± i e$ 3Ξ» $i$ t $v i$ $i=1$
d.
2 β $Ξ± i e$ 4Ξ» $i$ t $v i$ $i=1$
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The switch S 1 was closed and S 2 was open for a long time. At $t$ = 0, switch S 1 is opened and S 2 is closed, simultaneously. The value of i c (0 +), in amperes, is
S 1 i 100 β¦ S
1 A 0.01 F 25 β¦
c 2
1 H
a.
1
b.
-1
c.
0.2
d.
0.8
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Let a frequency modulated (FM) signal
$t x(t)$ = $A cos(Ο t$ + $k \int m(Ξ»)dΞ»)$, where $m(t)$ is a message signal of bandwidth
$c f -\infty$ W. It is passed through a non-linear system with output $y(t)$ = $2x(t)$ + $5(x(t))$ 2. Let $B T$ denote the FM bandwidth. The minimum value of $Ο c$ required to recover $x(t)$ from $y(t)$ is
a.
$B T$ + $W$
b.
3 $B T$ 2
c.
$2B T$ + $W$
d.
5 $B T$ 2
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Consider a discrete-time periodic signal with period $N$ = 5. Let the discrete-time
$jk2Οn 4k=0$ Fourier series (DTFS) representation be $x[n]$ = β $a k e$ 5, where $a$ 0 = 1, $a$ 1 =
$4Οn 3j, a$ = $2j, a$ = $-2j$ and $a$ = $-3j.$ The value of the sum β $4n=0 x[n]$ sin is 2 3 4 5
a.
-10
b.
10
c.
-2
d.
2
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Let $x(t)$ = 10 $cos(10.5Wt)$ be passed through an LTI system having impulse
sin $Wt$ 2 response $h(t)$ = $Ο$ () cos $10Wt$. The output of the system is
$Οt$
a.
$15W$ () $cos(10.5Wt)$ 4
b.
$15W$ () $cos(10.5Wt)$ 2
c.
$15W$ () $cos(10.5Wt)$ 8
d.
$(15W) cos(10.5Wt)$
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Let x 1 (t) and x 2 (t) be two band-limited signals having bandwidth $B$ = $4Ο \times$ 10 3 rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is
$cos(4Ο\times10$ 3 t)
x 1 (t)
$cos(12Ο\times10$ 3 t)
x 2 (t)
a.
$20Ο \times$ 10 3
b.
$40Ο \times$ 10 3
c.
$8Ο \times$ 10 3
d.
$32Ο \times$ 10 3
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The S-parameters of a two port network is given as
$S$ 11 $S$ 12
$[S]$ = [ ]
$S$ 21 $S$ 22 with reference to $Z$ 0. Two lossless transmission line sections of electrical lengths $ΞΈ$ 1 = $Ξ²l$ 1 and $ΞΈ$ 2 = $Ξ²l$ 2 are added to the input and output ports for measurement purposes, respectively. The S-parameters $[Sβ²]$ of the resultant two port network is
a.
$S e -j2ΞΈ$ 1 11 $S$ 12 $e -j(ΞΈ$ 1 $+ΞΈ$ 2) [ ] $-j(ΞΈ +ΞΈ$) 1 2 $S e S e -j2ΞΈ$ 2 21 22
b.
$S e j2ΞΈ$ 1 11 $S$ 12 $e -j(ΞΈ$ 1 $+ΞΈ$ 2) [ ] $-j(ΞΈ +ΞΈ$) 1 2 $S e S e j2ΞΈ$ 2 21 22
The electric field of a plane electromagnetic wave is $E$ = $a x C 1x cos(Οt$ - $Ξ²z)$ + $a y C 1y cos(Οt$ - $Ξ²z$ + $ΞΈ)$ V/m. Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?
a.
$C 1x$ = 1, $C 1y$ = 1, $ΞΈ$ = $Ο/4$
b.
$C 1x$ = 2, $C 1y$ = 1, $ΞΈ$ = $Ο/2$
c.
$C 1x$ = 1, $C 1y$ = 2, $ΞΈ$ = $3Ο/2$
d.
$C 1x$ = 2, $C 1y$ = 1, $ΞΈ$ = $3Ο/4$
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The value of the integral β¬ xy dx dy over the region R, given in the figure, is
R _______ (rounded off to the nearest integer).
y
2
y = -x+2 y = x+2
R 1
y = x y = -x
x O
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In an extrinsic semiconductor, the hole concentration is given to be $1.5n i$ where $n i$ is the intrinsic carrier concentration of 1 $\times$ 10 10 $cm$ -3. The ratio of electron to hole mobility for equal hole and electron drift current is given as __________ (rounded off to two decimal places).
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The asymptotic magnitude Bode plot of a minimum phase system is shown in the
$k(s+z) a$ figure. The transfer function of the system is $(s)$ =, where $k, z, p, a, b$ and
$b c s (s+p)$ $c$ are positive constants. The value of $(a$ + $b$ + $c)$ is __________(rounded off to the nearest integer).
-20 dB/decade
|G(jΟ)| in dB
-40 dB/decade
Ο 1 Ο 2 log Ο
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Let x 1 (t) = u(t + 1.5) - u(t - 1.5) and x 2 (t) is shown in the figure below. For
$\infty$ y(t) = x (t) β x (t), the $\int$ y(t)dt is ______________________(rounded off to
1 2 $-\infty$ the nearest integer).
x 2 (t)
2
1 1
-3 -2 -1 0 1 2 t
1
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Let $X(t)$ be a white Gaussian noise with power spectral density W/Hz. If $X(t)$ is
2 input to an LTI system with impulse response $e -t u(t).$ The average power of the system output is ___________ W (rounded off to two decimal places).
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A transparent dielectric coating is applied to glass $(Ξ΅ r$ = 4, $ΞΌ r$ = 1) to eliminate the reflection of red light $(Ξ»$ 0 = 0.75 ΞΌm). The minimum thickness of the dielectric coating, in ΞΌm, that can be used is _________ (rounded off to two decimal places).
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In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at T = 300 K is 1 $\times$ 10 19 cm -3. The thermal equilibrium hole concentration in silicon at 400 K is ____________ $\times$ 10 13 cm -3 (rounded off to two decimal places). Given kT at 300 K is 0.026 eV.
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A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 ΞΌs. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is _______ ΞΌs (rounded off to two decimal places).
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In a given sequential circuit, initial states are Q 1 = 1 and Q 2 = 0. For a clock frequency of 1 MHz, the frequency of signal Q 2 in kHz, is ___________ (rounded off to the nearest integer).
D 1
Q 1
D 2
Q 2
Flip
Flip
Q 1
Q 2
CLK = 1 MHz
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In the circuit below, the voltage V L is ____________ V (rounded off to two decimal places).
V DD
W/L = 1 W/L = 10 W/L = 7
V L
1 mA W/L = 10 W/L = 5 1
kβ¦
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The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of βyes/noβ questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _______ (rounded off to two decimal places).
Symbols
a
b
c
d
e
f
g
h
Frequency
1
1
1
1
1
1
1
1
of
2
4
8
16
32
64
128
128
occurrence .
END OF QUESTION PAPER
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