General Aptitude
Q.1 – Q. 5 carry one mark each.
1. The strategies that the company to sell its products house-to-house marketing.
(A) use, includes
(B) uses, include
(C) used, includes
(D) uses, including
2. The boat arrived dawn.
(A) in
(B) at
(C) on
(D) under
3. 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.
(A) 2/3
(B) 3/4
(C) 4/3
(D) 7/3
4. Five different books (P, Q, R, S, 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_______.
(A) 2
(B) 6
(C) 12
(D) 120
5. When he did not come home, she _______him lying dead on the roadside somewhere.
(A) concluded
(B) looked
(C) notice
(D) pictured
Q.6 – Q. 10 carry two marks each.
6. Four One people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. 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
Who among them is an engineer?
(A) Seema
(B) Lohit
(C) Rahul
(D) Mathew
7. The bar graph in Panel (a) shows the proportion of male and female illiterates 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 literates from 2001 to 2011 is_______ .
(A) 30.43
(B) 33.43
(C) 34.43
(D) 35.43
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 ________
(A) was well documented and not researched but was always biased
(B) was not well documented and researched and was always biased
(C) was well documented and researched but was sometimes biased
(D) was not well documented and researched and was sometimes biased
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 tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_____ remaining in the budget.
(A) 000.00
(B) 166.67
(C) 300.00
(D) 433.33
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)
Electronics and Communication Engineering
Q.1 – Q. 25 carry ONE mark each.
1. Which one of the following functions is analytic over the entire complex plane?
(A) ln(Z)
(B) e1/z
(C) 1/1- z
(D) cos(z)
2. The families of curves represented by the solution of the equation
(A) Parabolas and Circles
(B) Circles and Hyperbolas
(C) Hyperbol as and Circles
(D) Hyperbolas and Parabolas
3. Let H(z) be t he z-transform of a real-valued discrete-time signal ℎ[𝑛]. If P(z) = H(z)H(1/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 ?
4. 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?
(A) 0.5 A
(B) 1 A
(C) 2 A
(D) 2.5 A
5. Let Y(s) be unit-step response of a casual system having a transfer function
that is, 
The forced response of the system is
(A) u(t) – 2e−tu(t) + e−3tu(t)
(B) 2u(t) – 2e−tu(t) + e−3tu(t)
(C) 2u(t)
(D) u(t)
6. For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles 𝑁𝑝 and the number of system zeros 𝑁𝑧 in the frequency range 1 Hz ≤ f ≤ 107 Hz is
(A) Np = 5, Nz = 2
(B) Np = 6, Nz = 3
(C) Np = 7, Nz = 4
(D) Np = 4, Nz = 2
7. 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 1100110, then the message 0010 is mapped to
(A) 0010011
(B) 1100001
(C) 1111000
(D) 1111111
8. 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?
9. The correct circuit representation of the structure shown in the figure is
10. The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with Φms = 0 V and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points
(A) P, Q, R
(B) Q, R, P
(C) R, P, Q
(D) Q, P, R
11. 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?
(A) HQ/ε0
(B) HQ/4ε0
(C) Hε0/4Q
(D) 4H/Qε0
12. 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.
(A) 1 – P, 2 – R, 3 – Q, 4 – S
(B) 1 – Q, 2 – R, 3 – P, 4 – S
(C) 1 – Q, 2 – S, 3 – P, 4 – R
(D) 1 – R, 2 – Q, 3 – S, 4 – P
13. 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?
(A) NML increases and NMH decreases.
(B) NML decreases and NMH increases.
(C) Both NML and NMH increase.
(D) No change in the noise margins.
14. In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?
(A) 0 and D
(B) Hi-Z and D
(c) 0 and 1
(D) 
15. In the circuit shown, A and B are the inputs and the circuit?
(A) Latch
(B) XNOR
(C) SRAM Cell
(D) XOR
16. The value of the contour integral
evaluated over the unit circle |z| = 1 is________
17. The number of distinct eigenvalues of the matrix
is equal to______.
18. If 𝑋 and 𝑌 are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] =_______.
19. The value of the integral 
is equal to ________.
20. 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 ________.
21. Consider the signal 
where t is in seconds. Its fundamental time period, in seconds, is ________.
22. The baseband signal 𝑚(𝑡) shown in the figure is phase-modulated to generate the PM signal φ(t) = cos(2πfct + k m(t)). The time 𝑡 on the x-axis in the figure is in milliseconds. If the carrier frequency is fc = 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).
23. 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 ______%.
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 R1 = R2 = 50 Ω. The average value of VL is ______-volts (rounded off to 1 decimal place).
25. 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.
Q.26 – Q. 55 carry TWO marks each.
26. 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]?
(A) f(x) ≤ 1/2|x + 1|
(B) f(x) ≤ 2|x + 1|
(C) f(x) ≤ 1/2|x|
(D) f(x) ≤ 2|x|
27. Consider the line integral
the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region R shown in the figure below. The region R is the area enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to
(A) 6 + π/2
(B) 8 + π
(C) 12 + π
(D) 16 +2π
28. 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 a1, a2, a3 in terms of W6 so that X[1] is obtained correctly?
(A) a1 = −1, a2 = W6, a3 = W62
(B) a1 = 1, a2 = W2, a3= W6
(C) a1 = 1, a2 = W6, a3 = W62
(D) a1 = −1, a2 = W26, a3 = W6
29. It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form
where c1 and c2 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, 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?
(A) a = 1, b = 1
(B) a = 0, b = −1
(C) a = −1, b = 1
(D) a = 0, b = 1
30. In the circuit shown, if v(t) = 2 sin(1000 t) volts, R = 1 kΩ and C = 1μF, t hen the steady-state current i(t) in miliamperes (mA), is
(A) sin(1000 t) + cos (1000 t)
(B) 2 sin(1000 t) + 2 cos(1000 t)
(C) 3 sin (1000 t) + cos (1000 t)
(D) sin(1000 t) + 3 cos(1000 t)
31. Consider a causal second-order system with the transfer function
with a unit-step R(s) = 1/s 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
(A) 5.25
(B) 4.50
(C) 3.89
(D) 2.81
32. 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 
is
33. Let the state-space representation of an LTI system be , y(t) = C x(t) + d u(t) where A, B, C are matrices, d is a scalar d is a scalar, u (t) is the input to the system, and y(t) is its output. Let B = [0 0 1]T and d = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is
34. A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density N0/2. Binary signaling, with minimizes the bit-error probability.
Let φ1(t), φ2(t) form an orthonormal signal set.
It we choose p(t) = φ1(t) and q(t) = − φ1(t), we would obtain a certain bit-error probability Pb.
If we keep p(t) = φ1(t), but take q(t) = √E φ2(t), for what value of E would we obtain the same bit-error probability Pb?
(A) 0
(B) 1
(C) 2
(D) 3
35. The quantum efficiency (η) and responsivity (R) at a wavelength λ (in µm) in a p-i-n photodetector are related by
36. 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 
between the wires at a distance r from W1 is
37. The dispersion equation of a waveguide, which relates the wave number k to the frequency ω, is
where the speed of light c = 3 × 108 m/s, and ω0 is a constant. If the group velocity is 2 × 108 m/s, then the phase velocity is
(A) 1.5 × 108 m/s
(B) 2 × 108 m/s
(C) 3 × 108 m/s
(D) 4.5 × 108 m/s
38. 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?
(A) 22 V to 34 V
(B) 24 V to 36 V
(C) 18 V to 24 V
(D) 20 V to 28 V
39. The state transition diagram for the circuit shown is
40. 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 Vout1 and Vout2, respectively, in volts, are
(A) 1.8 and 1.2
(B) 2.4 and 2.4
(C) 1.8 and 2.4
(D) 2.4 and 1.2
41. The RC circuit shown below has a variable resistance 𝑅(𝑡) given by the following expression:
where R0 = 1 Ω, and 𝐶 = 1 F. We are also given that T = 3 R0C and the source voltage is Vs = 1 V. If the current at time t = 0 is 1 A, then the current I(t), in amperes, at time t = T/2 is _____(rounded off to 2 decimal places)
42. Consider a unity feedback system, as in the figure shown, with an integral compensator k/s and open-loop transfer function
where K > 0. The positive value of 𝐾 for which there are exactly two poles of the unity feedback system on the 𝑗𝜔 axis is equal to _______ (rounded off to two decimal places)
43. Consider the homogeneous ordinary differential equation
with y(x) as a general solution. Given that
y(1) = 1 and y(2) = 14
the value of y(1.5), rounded off to two decimal places, is________.
44. Let h[n] be a length-7 discrete-time finite impulse response filter, given by
h[0] = 4, h[1] = 3, h[2] = 2, h[3] = 1,
h[−1] = −3, h[−2] = −2, h[−3] = −1,
and h[n] is zero for |n| ≥ 4. A length-3 finite impulse response approximation g[n] of h[n] has to be obtained such that
is minimized, where H(ejω) and G(ejω) are the discrete-time Fourier transforms of h[n] and g[n], respectively. For the filter that minimizes E(h, h), the value of 10g[−1] + g[1], rounded off to 2 decimal places, is ________.
45. Let a random process 𝑌(𝑡) be described as 𝑌(𝑡) = ℎ(𝑡) ∗ 𝑋(𝑡) + 𝑍(t), where 𝑋(𝑡) is a white noise process with power spectral density 𝑆𝑋(𝑓) = 5 W/Hz. The filter ℎ(𝑡) has a magnitude response given by |𝐻(𝑓)| = 0.5 for −5 ≤ 𝑓 ≤ 5, and zero elsewhere. 𝑍(𝑡) is a stationary random process, uncorrelated with 𝑋(𝑡), with power spectral density as shown in the figure. The power in 𝑌(𝑡), in watts, is equal to_____W (rounded off to two decimal places).
46. A voice signal 𝑚(𝑡) is in the frequency range 5 kHz to 15 kHz. The signal is amplitude- modulated to generate an AM signal 𝑓(𝑡) = 𝐴(1 + 𝑚(𝑡)) cos 2𝜋𝑓𝑐𝑡, where 𝑓𝑐 = 600 kHz. The AM signal 𝑓(𝑡) is to be digitized and archived. This is done by first sampling 𝑓(𝑡) at 1.2 times the Nyquist frequency, and then quantizing each sample using a 256-level quantizer. Finally, each quantized sample is binary coded using 𝐾 bits, where 𝐾 is the minimum number of bits required for the encoding. The rate, in Megabits per second (rounded off to 2 decimal places), of the resulting stream of coded bits is _______Mbps.
47. A random variable 𝑋 takes values −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 
The minimum probability of error, rounded off to 1 decimal place, is _____.
48. 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 dioxide- Germanium 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.
49. In an ideal pn junction with an ideality factor of 1 at T=300 K, the magnitude of the reverse-bias voltage required to reach 75% of its reverse saturation current, rounded off to 2 decimal places, is _______mV.
[𝑘 = 1.38 × 10−23 JK−1, ℎ = 6.625 × 10−34 J-s, 𝑞 = 1.602 × 10−19C].
50. Consider a long-channel MOSFET with a channel length 1 µm and width 10 µm. The device parameters are acceptor concentration NA= 5 × 1016 cm-3, electron mobility µn=800 cm2/V-s, oxide capacitance/area Cox= 3.45 × 10−7 F/cm2, threshold voltage VT=0.7 V. The drain saturation current (IDsat) for a gate voltage of 5 V is ______ mA (rounded off to two decimal places). [𝜀0 = 8.854 × 10−14F/cm, 𝜀𝑆𝑖 = 11.9]
51. A rectangular waveguide of width w and height h has cut-off frequencies for TE10 and TE11 modes in the ratio 1: 2. The aspect ratio w/h, rounded off to two decimal places, is______.
52. In the circuit shown, Vs is a 10 V square wave of period, T = 4 ms with R = 500 Ω and C = 10 µF. The capacitor is initially uncharged at t=0, and the diode is assumed to be ideal. The voltage across the capacitor (Vc) at 3 ms is equal to ______volts (rounded off to one decimal place).
53. A CMOS inverter, designed to have a mid-point voltage VI equal to half of Vdd, as shown in the figure, has the following parameters:
Vdd = 3 V
μnCox = 100 μA/V2; Vtn = 0.7 V forn MOS
μpCox = 40 μA/V2; |Vtp| = 0.9 V for pMOS
The ratio of (W/L)n to (W/L)p is equal to ________(rounded off to 3 decimal places).
54. In the circuit shown, the threshold voltages of the pMOS (|Vtp|) and nMOS (𝑉tn) transistors are both equal to 1 V. All the transistors have the same output resistance rds of 6 MΩ. The other parameters are listed below:
μnCox = 60 μA/V2 ; (W/L)nMOS = 5
μpCox = 30 μA/V2 ; (W/L)pMOS = 10
μn and μp are the carrier mobilities, and 𝐶ox 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).
55. In the circuit shown, V1 = 0 and V2 = Vdd. The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of Iout is _______ mA (rounded off to 1 decimal place).
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