GATE 2020 Electronics and Communication Engineering Previous Year Paper

GENERAL APTITUDE 

Section -A

Q.1 Time at quarter past three angle between hour hand and minute hand is 

Ans. (7.5°) 

 

Q.2 Radius of circle is ‘a’ and PQR is the maximum possible area of rectangle. 

Find shaded area 

(a) πa² – 2a² 

(b) π 2a ² − a ² 

(c) π 3a ² − a ² 

(d) None of these 

Ans. (a) 

 

Q.3 Implicit : Explicit : : Express : __________? 

(a) Compress 

(b) Suppress

(c) Impress 

(d) Repress 

Ans. (b) 

 

Q.4 He was not only accused of theft _______ of conspiracy. 

(a) Rather than

(b) Rather 

(c) But also 

(d) But even 

Ans. (c) 

 

Q.5 The untimely loss of life is a course of serious global concern as thousands of people get killed ________ accidents every year while many others die _____ disease like cardiovascular disease cancer etc. 

(a) during, from 

(b) in, of 

(c) of, from 

(d) None of these 

Ans. (b) 

 

Q.6 The Canadian constitution requires equal importance to English and French. Last year air Canada lost a lawsuit and had to pay a six figure fine to French speaking couple after they filed a complaint about formal in-flight announcements in English lasting 15 seconds as compared to informal announcements in French lasting only for 5 seconds. The French speaking couples were upset at 

(a) The English announcements being longer than French once 

(b) The English announcements being clearer than French 

(c) Equal importance given to English and French 

(d) The in-flight announcement being made in English 

Ans. (a) 

 

Q.7 The global financial crisis in 2008 was considered to be the most serious worldwide FC. Which started with the subprime lending crisis (SPLC) in the USA in 2007? The SPLC led to a banking crisis in 2008 with the collapse of Lehman brothers in 2008. The SPL refers to the provision of loans to those borrowers. Who may have difficulties in repaying loans and its arises because of excess liquidity following the East Asian crisis. The correct precedence according to Paragraph is 

(a) Banking crisis — Subprime lending crisis — Global financial crisis — East Asian crisis

(b) Subprime lending crisis — Global financial crisis — Banking crisis — East Asian crisis

(c) Global financial crisis — East Asian crisis — Banking crisis — Subprime lending crisis

(d) East Asian crisis — Subprime lending crisis — Banking crisis — Global financial crisis 

Ans. (d) 

 

Q.8 Following quadratic equation is ax² – bx + c = 0 and it has equal root which is β and a, b, c are the real number which is true 

(a) β³ = _{2 2}bC_a 

(b) b ≠ 4ac 

(c) β = ac 

(d) β³ = ₂ab 

Ans. (a) 

Section- B

Q.1 Given a binary number 1100 and p, q, r represents its sign magnitude, 1’s complement, 2’s complement representation respectively. Then 6 digit 2’s complement form of p + q + r is 

Ans. (110101) 

Given, binary number 1100 

1’s complement of 1100 = –3 Sign magnitude of 1100 = –4 2’s complement of 1100 = –4 ∴ P + Q + R = –4 – 3 – 4 = –11 The 6 digit 2’s complement of (–11) = 110101 

 

Q.2 Output of 4 × 1 MUX F(P, Q, R) is 

Ans. 

Output, F = PQR + PQR + 

F = QR + PQ₀ 

 

Q.3 For 10 bit D/A converter, full range of voltage 0-10, then find the output value for V_input 13A (in hexadecimal) in volts is ______V. 

Ans. (3.066) 

Given, n = 10 

V_FS = 10 V Input voltage = (13A)₁₆ = (314)₁₀ Output voltage = Resolution × Decimal equivalent of input 

V_o = ₂ 10 ₁₀ × ₃₁₄ = 3.066 V

 

Q.4 Given: y ( t ) = ∫ _−∞ W ( t ) ⋅ φ ( t ) W(t) is the random variable having PSD 3W/Hz and .

Find the variance of y(t)? 

Ans. (6) 

 

Q.5 Given that m(t) = 4cos1000πt and c(t) = cos2πf_ct ; where f_c = 1 MHz. Given that s(t) = m(t) cos2πf_ct and s(t) is demodulated using a demodulator. 

Then y(t) is 

Ans. 

cos [2 π ( f _c + 40 ) t ] S(t) = m(t) cos 2πf_ct S(t) = 4 cos 1000πt cos 2π (10⁶)t Output of multiplier = [4 cos 1000πt cos 2π 10⁶t] cos 2π (f_ct + 40)t] = [2 [cos [2π (500 + 10⁶)t] + cos [2π (10⁶ 500)t] cos 2π(f_c + 40)t = 2 cos 2π (500 + 10⁶)t cos 2π ((f_ct + 40)t) + 2 cos [2π (10⁶ – 500)t) cos 2π (f_c + 40)t = cos [2π (2f_c +540t) + cos(60t) + cos [2f_c – 460)t + cos(540t)] Output of Low pass filter 

= cos [2π (460)]t = cos 920 πt 

 

Q.6 Given phase modulated and frequency modulated signals 

where, k_p is the phase deviation constant (rad/volt), k_f is the frequency deviation constant (rad/sec/volt). If the highest instantaneous frequencies of S_Pm(t) and S_Fm(t) are same, then the value of the ratio K_p/K_f is ________ sec. 

Find Kp/K_f. 

Ans. (2)

 

Q.7 A digital communication system is used to transmit a block of N-bits, if the probability of receiving 1-bit in error is α and all bits are transmitted independently. The received block is said to be erroneous if at least one bit in error. The probability of the block to be erroneous is ______. 

(a) α^N 

(b) 1 – (1 – α)^N 

(c) N(1 – α) 

(d) 1 – α^N 

Ans. (b) 

Probability of error in decoding single bit = α Then probability of no error will be 1 – α. Total N-bits transmitted, so that probability of no error in received block 

= (1 – α) (1 – α) … N times = (1 – α)^N The probability of received block is erroneous = 1 – (1 – α)^N 

 

Q.8 A binary random variable takes two values as +2 and –2 with probability P(X = 2) = α; then the value of α for which entropy will be maximum is ______. 

Ans. (1/2) 

Given that P(X = 2) = α Entropy will be maximum; provided probabilities are equal. 

i.e. P(X = 2) = P ( X = − 2) = α = 

₂ ¹ α = ¹2 

Q.9 Given that X(ω) is Fourier transform of x(t) then find

Ans. 

 

Q.10 Given that

Then which one of the following is the correct pole zero plot of above given system? 

Ans. (b) 

 

Q.11 Discrete time signals output is y(n) = max[X(k)], –∞ ≤ K ≤ n 

(a) unit impulse 

(b) unit step function 

(c) a constant function

 (d) zero 

Ans. (b) 

 

Q.12 A finite duration discrete time signals x(n) is obtained by sampling x(t) = cos[200πt] of sample instant = n/400, n = 0, 1, 2, … 7. The 8-point DFT of x(n) is defined as 

(a) X(3) and X(5) are non-zero 

(b) X(4) is non-zero 

(c) X(2) and X(6) are non-zero 

(d) All X(k) are non-zero 

Ans. (c) 

 

Q.13 The transfer function of a stable discrete time LTI system is H( Z) ₌ K(z − α) /( z + 0.5) when α and K are constants and |α| > 1. If the magnitude response is constant for all frequencies then the value of α is ____. 

Ans. (–2)

 

Q.14 For the impedance Z = jX, having X values from –∞ to ∞, which of the following is correct in the Smith chart? 

(a) A circle of radius 1, with centre at (0, 0) 

(b) A point at the centre of the Smith chart 

(c) A circle of radius 0.5 with centre at (0.5, 0) 

(d) A line passing through the centre of the Smith chart 

Ans. (a) 

For given impedance Normalized impedance is Z⁼ jX_Z 0 Z = jX ⇒ Z=0 + jX Normalized resistance = 0 ⇒ r = 0 X = –∞ to ∞ r = 0 and X from –∞ to ∞ is a unit circle (radius 1) and centre (0, 0) on a complex reflection coefficient plane: 

 

Q.15 Which one of the following is correct? 

(a) ∇ ² 0A = then ‘A’ is irrotational 

(b) ∇ ( ∇ ·A ) = ∇× ( ( ∇× A ) −∇ ² A ) 

(c) ∇ · 0A = then vector is A is solenoidal 

(d) ∇× A is also a vector quantity 

Ans. (a) 

 

Q.16 Given the magnetic field intensity of a uniform plane wave in vacuum is H ( x , y , z , t ) = ( aˆ_x + 2 aˆ_y + baˆ_z )cos( ω t + 3 x − y − z ) then find value of b _____. 

Ans. (1) 

 

Q.17 For a given two port ideal lossless transformer, the parameter S₂₁ for a reference impedance of 1 Ω is 

Ans. (0.8) 

 

Q.18 For an infinitely small dipole in free space, the electric field ‘E’ in the far field is proportional to (e^{− jkr}/r sinθ). Where K = 2π/λ  . A vertical infinite small dipole (δI << λ) is placed at a distance h(h > 0) above an infinite ideal condcutive plane as shown in figure. The minimum value of ‘h’, for which one of maximum in the far-field radiation pattern occurs at θ = 60° is _____. 

(a) 0.5 λ 

(b) λ 

(c) 0.7 λ 

(d) 0.25 λ 

Ans. (b) 

 

Q.19 For a given transistor T₁, base region has uniform doping of 10¹⁷/cm³ and transistor T₂ has base region with doping varying linearly with x. If all other parameters of the transistor are the same, then find the ratio of common emitter current gain of transistor T₁ to transistor T₂? 

(a) 0.3 times that of T₂ 

(b) 0.7 times that of T₂ 

(c) 2 times that of T₂ 

(d) 2.5 times that of T₂ 

Ans. (c) 

 

Q.20 For a solar cell, P_in = 100 mW/cm², surface area = 1 cm², V_oc = 0.7V, fill factor = 0.8, efficiency = 15%. If thickness of the cell is 200 μm, then the light generation rate will be 

Ans. 

η = ( FF) V_OCI _SC / P_in 

0.15 = 0.8 × 0.7 × I_SC /100 mW

⇒ I_SC = 15/ 0.56 mA 

G_L =  I_SC / q ×Area× thickness 

= 15 × 10⁻³ / 0.56 × 1.6 × 10⁻¹⁹ × 1 × 200 × 10⁻⁴ 

= 0.837 × 10 ¹⁹ /cm ³ /second 

 

Q.21 Given that a semiconductor has density of state function in conduction band N_C is half of density of state function in valence band N_V, then the shift in the intrinsic fermi level from the centre of forbidden gap is ____ meV. 

Ans. (9.01)

 

Q.22 In a MOS capacitor, threshold voltage is –0.16V, metal work function is 3.7V, bandgap of semiconductor is 1eV whose band diagram is shown below. C′_x = 100 pF/cm². Oxide is free from non-idealities. When the voltage across the capacitor is equal to threshold voltage, what will be the depletion charge present in the semiconductor? 

Ans. 

MOS capacitance 

φ_m = 3.7, φ_s = 4.8, φ_ms = –1.1

V_T = φ_ms – Q_ox/C_ox – Q_d/C_ox + 2 φ _Fp 

φ_Fp = E_i – E_F = 0.5 – 0.2 = 0.3 

–0.16 = -1.1-0 ₋ Q′^d/C_ox + 2 × 0.3 

Q′_d /C_ox = 0.6 + 0.16 – 1.1 = –0.34 

Q_b = –0.34 × C_ox 

      = –0.34 × 100 × 10^–9 

      = -34 nC/cm² 

 

Q.23 Consider the following MOSFET, find the equivalent Norton’s resistance 

Ans. 

v_π = –V_x 

V_x = (I_x – g_m V_x) r_ds + I_xR 

V_x(1 + g_m r_ds) = (r_ds + R)I_x 

R_N = V_x/I_x = R +r_ds / 1+g_mr_ds

 

Q.24 A sinusoidal voltage is applied to the given circuit, then the steady state output voltage V_o is _______ V. 

Ans. (650.4) 

Voltage doubles, V_o =2 V_m = 2 × 230√2 ≅ 650.4V 

 

Q.25 Consider the op-amp shown below: 

The current “I₀” is ________ mA. 

Ans. (6) 

V_o = (1 + 1) × 2 = 4 V

 2−4 /1 + I _o + 0− 4/1= 0

-2+I _o-4 =0

⇒ I_o = 6 mA 

 

Q.26 

The output V₀ is 

(a) square wave with an amplitude of 5V 

(b) sinusoidal of amplitude 10V 

(c) inverted sinusoidal of input 

(d) constant signal with either +5V and –5V 

Ans. (a) 

The given circuit is a Schmitt trigger, which produces a square wave at the output. 

 

Q.27 Find the state matrix (consider v and i as state variables). 

Ans. 

From source transformation, 

KVL in loop 1, 

2I₁ = 2 i + 0.5di/dt + v

di/dt= –2V + 4i + 4I₁                     (i) 

KCL at node, 

i = 0.25 dv/dt +V − I₂/ 1 

dv/dt = –4V + 4i + 4I₂                                     (ii) 

 

Q.28 When base current of given BJT is negligible. Given that V_t = 26 mV and V_BE = 0.7V. 

Voltage gain at low frequencies is 

Ans. (–89.423) 

 

Q.29 In the given Nyquist contour the pole zero locations are indicated as shown. If the given contour is transformed from s-plane to G(s) H(s) plane then which one of the following is true 

(a) encircles the origin in clockwise 

(b) encircles the –1 + j0 in clockwise 

(c) encircles the –1 + j0 in anticlockwise 

(d) encircles the origin in anticlockwise 

Ans. (b) 

 

Q.30 Given op-amp circuit 

R = 10 kΩ, C = 0.1 μF, then the 3dB cut-off frequency of op-amp circuit is ____ Hz. 

Ans. (159.2) 

Op-amp active filter (LPF) inverting type 3 dB cut-off frequency, 

f_c = 1/2πRC

= 1 /2 π × 10⁴ × 10⁻⁷ 

= 1000 / 2π 

= 159.2 Hz 

 

Q.31 In the following circuit, assume that I_B = 0, V_BE = 0.7V for both the transistors. If V_in = 15V (unregulated) and V₀ = 9V (regulated), then the resistance R is equal to _______ Ω. 

Ans. (800) 

 

Q.32 Consider the below figure. 

G(s) = 1/( s + 1) ( s + α )  Find the value of α. 

Ans. (4)

 

Q.33 Given: C(s) = K (s+1) / (s+3), G(s) = 1/ s(s +1) . If steady state error for ramp input is 0.1, then find the value of k or negative feedback unity gain system 

Ans. (30) 

 

Q.34 If the value of current i = 10 cos [5t− π /4 ] , the value of inductance L is 

Ans. (2.828) 

 

Q.35 For given open loop transfer function G(s)H(s)=k(s+11) / s(s+2) (s +8) . Find value of k for which system is marginally stable. 

Ans. (160) 

 

Q.36 A two port network has an impedance [Z] = find [Z_L] for maximum power transfer. Find Z_L = ? 

Ans. (48) 

 

Q.37 Find value of V_th

Ans. (3.6) 

By applying source transformation 

V_th = 3.6 V 

 

Q.38 Find the value of I_o 

Ans. (143.7)

 

Q.39 In a transmission line given Z₀ = 50, Z_L = 400, l = 3λ/ 4, find Z_in 

Ans. (6.25)

Z_in for (l = λ/4) = Z²₀ / ZL =  50²/400  = 25/4 = 6.25 Ω 

 

Q.40 For the given characteristic equation 

Q(s) = s³ + 3s² + (K + 2)s + 3K = 0 

The root locus plot will have breakaway or break-in point in the region. 

(a) (0, –1) 

(b) (–1, –3) 

(c) (–∞, –3) 

(d) None of these 

Ans. (a) 

Q(s) = 1 + G(s) H(s) = 0 s³ + 3s² + 2s + ks + 3k = 0 

–k = s³ + 3s² + 2s / s+3 

− dk/ds = ( s + 3)(3s²+6s+2)− (s³+3s²+2s) / (s+ 3)² = 0 

3s³ + 6s² + 2s + 9s² + 18s + 6 – s³ – 3s² – 2s = 0 

2s³ + 12s² + 18s + 6 = 0 

s = –0.46, –3.87, –1.65 

 

Q.41 d²y /dx² − 6dy/dx + 9 = 0.Find the solution of differential equation.

(a) (C₁ + C₂ x)e^3x 

(b) (C₁ + C₂ x)e^–3x

 (c) C₁ e^3x 

(d) None of these 

Ans. (a) 

 

Q.42 In sequential circuit, the maximum clock frequency at which given circuit can operate reliably? 

Ans. (76.92) 

Total propagation delay = (t_pd + t_set-up)_max = 8ns = 5 ns = 13 ns 

∴ Frequency of operations = 1000/13 MHz = 76.92 MHz 

Q.43 f(x, y, z) = e^{(1 – x cosy)} + x ze^{− 1/1+y2} partial differentiation of f(x, y, z) with respect to x 

at point (1, 0, e) will be 

Ans. (0)

 

Q.44 f(x₂ + x₂) ≥ f(x₁) + f(x₂) 

(a) ¹x 

(b) square root of x 

(c) e ^x 

(d) e ^–x 

Ans. (c) 

 

Q.45 ∫∫∫ xdxdydz

Ans. (9/4) 

 

Q.46 If x is having uniform distribution between [– 2, 10] and y = 2x – 6 then P (y <7 / x >5 ) 

Ans. (0.3) 

 

Q.47 dy / dx = ( y−1) x solution of equation satisfies. 

(a) ln y − 1 = 0.5x² + c and y = – 1 

(b) ln y − 1 = 2x² + c and y = 1 

(c) ln y − 1 = 0.5x² + c and y = 1 

(d) ln y − 1 = 2x² + c and y = –1 

Ans. (a) 

 

Q.48 Two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote labels corresponding to the outcomes of those processes for random variable X, where X = min(M, N), E(X) = _______. 

Ans. (0.25)

 

Q.49 In a digital communication system, 4 symbols are transmitted (s₁ = –3, s₂ = –1, s₃ = 1, s₄ = 2) through an AWGN channel. The variable at the input of decision device is s_i + W, where W is a Gaussian random variable with mean zero and unit variance. ML decoding is used. The conditional error probability when symbol s_i is transmitted is P_i. The value of “i” that result in maximum P_i is _____. 

Ans. (3)

Since the noise variable is Gaussian with zero mean and ML decoding is used, the decision boundary between two adjacent signal points will be their arithmetic mean. In the following graphs, the shaded area indicates the conditional probability of decoding a symbol correctly when it is transmitted. 

By comparing the above graphs, we can conclude that P₃ is larger among the four. 

 

Q.50 V₁, V₂, V₃, V₄, V₅, V₆ six vector in R⁴ which of the following statements is false? 

(a) Any 4 base for R⁴ 

(b) If V₁, V₃, V₅, V₇ span R⁴ then it forms a basis of R⁴ 

(c) These vectors are not linearly independent 

(d) It is not necessary that vector span R⁴ 

Ans. (a) 

 

Q.51 In 8085 microprocessor to access a memory of 16 kB number of address lines required is ____. 

Ans. (14) 

2ⁿ = N 

n → Number of address lines 

N → Number of Memory locations 

∴ 2ⁿ = 16 kB 

        = 2⁴ (2¹⁰)        [∵ 1 kB = 2¹⁰] 

         = 2¹⁴ 

    n = 14 

GATE 2020 Computer Science and Information Technology Previous Year Paper

GENERAL APTITUDE 

Q.1 Raman is confident of speaking English _____ six months. He has been practicing regularly ________ the last three weeks

(a) during, for

(b) for, since

(c) within, for

(d) for, in 

Ans. (c) 

• ‘Within’ is a preposition that is used to express something that occurs inside a particular period of time. 
• ‘for’ is used here because 

(i) Sentence is in ‘present perfect continuous tense’. 

(ii) For is used when we talk about a period of time. 

 

Q.2 Select the word that fits the analogy 

Cook : Cook :: Fly : 

(a) Flighter 

(b) Flew 

(c) Flyer 

(d) Flying 

Ans. (c) 

Flyer: Relation is Verb : Noun 

One who cooks is a cook and one who flies any aircraft is a flyer. 

 

Q.3 This knowledge of the subject was excellent but his class room performance was ____. 

(a) Extremely poor 

(b) Praise worthy 

(c) Desirable 

(d) Good 

Ans. (a) 

‘But’ is used for introducing an idea which contrasts with the statement that has been already said. 

 

Q.4 Mode a and e are toll booths which costs 200 and all other toll both b, c, d, f costs only 100. Minimum cost for each from 1 to 2. (Path was given) 

Ans. (*) 

 

Q.5 Goods services tax (GST) is an indirect tax introduced in India in 2014 that is imposed on the supply of goods and services used and it subsumes all indirect taxes except few. It is a district based tax imposed on goods and services used; it is not imposed at the point of origin from where goods come. GST also has a few components specific to state government, central government and UTs? Which one of the following can be inferred from the given passage? 

(a) GST includes all indirect taxes 

(b) GST is imposed on the product of goods and services 

(c) GST imposed at point of usage of goods and services 

(d) GST does not has a component specific for UT 

Ans. (c) 

 

Q.6 If P = 3, R = 27, T = 243, then Q + S = 

(a) 80 

(b) 110 

(c) 90 

(d) 40 

Ans. (c) 

 

Q.7 The total revenue of a company during 2014-2018 is shown in a bar graph. The total expenditure of the company in each year is 500 million rupees. The aggregate profit/ loss percentage on the total expenditure of the company during 2014-2018 is ______. 

Ans. (20% profit) 

Total expenditure = 2500 million 

Total revenue = 3000 million 

So, profit % = 500/2500 × 100 = 20% 

 

Q.8 The figure below shows an angular ring with outer inner radii b and a. The angular space has been pointed in the form of a blue colour circle touching the outer and inner peripheral gular space. If a maximum n number of circles can be pointed then the unpainted area available in angular space is ________. 

(a) π[(b² – a²) -n (b – a)²]

(b) π[(b² – a²) -n (a/2)²]

(c) π[(a² – b²) -n (b/2)²]

(d) π[(b² – a²) -n (b-a/2)²]

Ans. (d) 

The area of unpainted region will be 

π[(b² – a²) -n (b – a/2)²]

 

Q.9 The straight lines are drawn perpendicular to each other in the XY plane. The angle α and β are acute angles made by line as with x-axis then α + β = ? 

(a) 180° 

(b) 90° 

(c) 60° 

(d) 120° 

Ans. (b) 

 

Q.10 In a decoder with in input lines and n output lines, then 1 KB RAM is given and now find (m + n). 

Ans. (1034) 

We need 2¹⁰ outputs to map 1 kB RAM. 

For this we need 10 × 2¹⁰ decoder. 

Here m = 10 and n = 2¹⁰ 

m + n = 1034 

 

Q.11 Given main memory with single level paging main memory access time 100 ns TLB access time 20 ns. TLB hit ratio 95% page fault rate 10% and when there is page fault in 20% cases it uses write back and retrieve page from secondary memory with 5000 ns access time calculate average access time? With upto 1 decimal place. 

Ans. (*) 

 

Q.12 Consider the following statements: 

I. Daisy chain uses priorities for selecting devices. 

II. When there is vectored interrupt and polling is used for getting an address. 

III. Polling processor uses periodically checks status bit to check if interrupt needs to process. 

IV. DMA access processor and DMA controller can simultaneously access at the same  time. 

(a) I and II only 

(b) I and III only 

(c) I, II and IV only 

(d) I, and IV only 

Ans. (b) 

 

Q.13 A non-pipeline processor having 2.5 GHz clock frequency. Where each instruction takes 5 cycles and when this processor utilizes a same 5 stage pipeline having 2 GHz clock frequency and 30% are memory instruction 60% are ALU instruction and remaining are branch instruction. Given that 5% memory instruction takes 50 stall cycles and 50% branch instruction takes 2 cycles then what will be the speed up when the pipeline processor is used over the non-pipeline processor ________. 

Ans. (2.16) 

 

Q.14 A 16-bit instruction having two type of instruction i.e. R-type and I-type where 16-bit instruction supports 64 registers set. Now I-type of instruction has 1 register field and 4-bit immediate field. R-type instruction supports 2 register address fields and given that there are 8 different I-type instructions then how many different R-types of instruction are possible _______. 

Ans. (14) 

Given, 16 bit instruction and 64 registers 

I type: 

R type: 

1. Primitive instruction 

R-type: 

2. Number of operations possible = 2⁴ = 16 3. Number of tree opcodes = (16 – x) 

Assume x is the number of R-type instructions existed. 4. Number of I-type instruction possible = (16 – x) × 2² 8=64 – 4x 4x = 64 – 8 = 56 

x = 56/4

^{⇒ 14} 

 

Q.15 The number of permutations of the characters LILAC if no characters appears in its the original position if two Ls are indistinguishable is _______. 

Ans. (12) 

Number of derangements. 

Since both L’s are indistinguishable. 

First L’s can be arranged remaining 3 positions in ³C₂ ways. 

[i.e., _ L _ L _ or _ L _ L _ or _ L _ _ L _] 

For each of these cases remaining 3 letters can be deranged in 2 × 2! ways = 4 ways 

[i.e., L L C can lake only 1 or 3 positions → 2 ways. For each of these IA can be arranged in remaining 2 positions in 2 ways]. 

Number of derangements = ³C₂ × 2 × 2! = 12 

 

Q.16 A = {1, 2, 3}. What is the probability of getting reflexive relation on A. By choosing any relation randomly. 

Ans. (0.125) 

 

Q.17 A graph G K_{3, 4} is given. Suppose, a vertex ‘S’ is added which is adjacent to every vertex in K_{3, 4} then the minimum number of edge-color required ________. 

Ans. (7)

Minimum number of edge-colors required = 3 + 4 = 7. 

 

Q.18 Rank(M) is rank of matrix M and det(M) is determinant of matrix M then 

1.Rank(AB) = Rank(A) ⋅ Rank(B)

2.det(AB) = det(A) ⋅ det(B)

3.Rank(A + B) ≤ Rank(A) + Rank(B)

4.det(A + B) ≤ det(A) + det(B)

Which of the above statements is correct?

(a) 2 and 3

(b) 3 and 4

(c) 1 and 2

(d) 1 and 4 

Ans. (a) 

Statement 2 and 3 are correct statements directly based on properties of matrices. 

 

Q.19 A group with 35 elements has subgroups. The maximum size of the proper subgroup is ________. 

Ans. (7) 

Size of group = Ο(G) = 35 

Let H be subgroup of G 

∴ Ο(H)⏐Ο(G) 

Possible orders of H are 1, 5, 7, 35 

Size of largest possible proper subgroup = 7. 

 

Q.20 Which of the following is not valid? 

(a) ∃x (p(x) → w) ≡ ∀x p(x) → w 

(b) ∀x (p(x) → w) ≡ ∀x p(x) → w 

(c) ∃x (p(x) ∧ w) ≡ ∃x p(x) ∧ w 

(d) ∀x (p(x) ∨ w) ≡ ∀x p(x) ∨ w 

Ans. (b) 

∀x (p(x) → w) ≡ ∀x p(x) → w is wrong 

Since ∀x [p(x) → w] 

≡ ∀x [¬p(x) ∨ w] 

≡ ∀x (¬p(x) ∨ w

≡ ¬(∃x p(x)) ∨ w

≡ ∃x p(x) → w 

 

Q.21 Given vertex set (v₁, v₂, v₃, ….. v₁₀₀), the edge weight is ⏐v_i – v_j ⏐ where i ≤ i ≤ j ≤ 100 then the weight of the minimum spanning tree is ________. 

Ans. (99) 

 

Q.22 T(n) = T(n^1/a) + 1, T(b) = 1 find T(n) 

(a) θ(log_b log_an)

(b) θ(log_a log_bn) 

(c) θ(log_abn) 

(d) θ(log₂n) 

Ans. (a) 

 

Q.23 What is the worst case time complexity of inserting n elements in empty linked list in the sorted order? 

(a) n 

(b) n logn 

(c) n² 

(d) n² logn 

Ans. (b) 

Insert element at the beginning of linked list, take Ο(1) 

 

Q.24 In the AVL tree n element are there what is the time complexity of inserting other n² elements? 

(a) n² 

(b) Ο(n² logn) 

(c) Ο(n) 

(d) Ο(n logn) 

Ans. (b) 

AVL with n element: [height balanced [–1, 0, +1] BST] 

logn level due to balanced BST. 

(i) Every insertion of element: 

logn: Find place to insert. 

logn: If property is not satisfied do rotation. 

∴ n² element insertion: 

For 1 element ≡ 2 logn 

So, for n² element ≡ Ο(n² logn) 

 

Q.25 There are n elements in the balanced binary search tree. What is the time complexity to report the k elements in the range [a, b]? 

(a) Ο(logn + k) 

(b) Ο(k logn) 

(c) Ο(k) 

(d) Ο(kn) 

Ans. (a) 

Let a = 16, b = 42 

16: Find the ‘16’ element in the BST = Ο(logn) 

42: Find the ‘42’ element in the BST = Ο(logn) 

[16, 42]: Inorder sorted element between 

16 to 42 {16, 18, 19, 20, 25, 30, 35, 40, 42} ⇒ requires Ο(k) time for k element 

So total time: Ο(2 logn + k) ≡ Ο(logn + k) 

 

Q.26 Binary min-heap has 1023 elements. Find the number of comparisons required to find the maximum element? 

Ans. (511) 

Number of element = [1023/2] = 512

No bubble sort requires 511 comparisons. 

 

Q.27 Let A, B, C be the inputs which give output Z as shown in below figure. The minterms required to represent the output function Z(A, B, C) is ________. 

(a) ∑m(1, 3, 5, 6, 7) 

(b) ∑m(1, 4, 5, 6, 7) 

(c) ∑m(1, 2, 3, 6, 7) 

(d) ∑m(4, 5, 6, 7) 

Ans. (b)

∴ Z(A, B, C) = A + BC 

K-map of the output Z is 

∴ Z(A, B, C) = ∑m(1, 4, 5, 6, 7) 

 

Q.28 You are given accumulator and memory of 32 registers in between then there is a multiplexer the number of select lines in multiplexer. 

Ans. (5)

Number of registers = n = 32 Required multiplexer size is n : 1 i.e. 32 : 1 No of select lines required to the multiplexer = m ∴ m = log₂ n 

m = log₂ 32 m=5 

 

Q.29 

SELECT S.sno, S.sname

FROM Supplier S, catalog C

WHERE S.sno = C.sno AND

cost > (SELECT AVG (cost)

FROM Catalog

WHERE pno = ‘P₄’ GroupBy pno);

Number of rows returned by above query ________.

Ans. (4) 

SELECT S.sno, S.sname

FROM Supplier S, catalog C

WHERE S.sno = C.sno AND

cost > (SELECT AVG (cost)

FROM Catalog

WHERE pno = ‘P₄’ GroupBy pno);

Q.30 Given relation is in 3NF but not in BCNF 

(a) because for non-trivial FD x → A, with x is not super key and A is prime attribute. 

(b) because for non-trivial FD x → A, with x is not super key and A is not prime attribute, x is not a proper subset of key. 

(c) because for non-trivial FD x → A with x is not super key and A is not prime attribute, x is a proper subset of the key. 

(d) None of these 

Ans. (a) 

 

Q.31 For a database we are using B⁺ tree indexing with 1 million records in the database, each record fits in one block. Block size is 8 KB and search key size is 12 bytes, block pointer size is 8 bytes. Minimum number of block access required for database record is ________. 

Ans. (4) 

Total = 3 + 1 = 4 block access 

 

Q.32 Which of the following many-to-one rules of weak-entity set in an ER diagram? 

(a) Oval shape with double/bold borders 

(b) Diamond shape with double/bold borders 

(c) Rectangular shape with double bold/borders 

(d) Oval shape with identifier underlined 

Ans. (b) 

Diamond shape with double/bold borders 

 

Q.33 TCP connection maximum segment size = 2 KB is starting at t = 0 and threshold is 32 KB and calculates sender window size at (t + 60 ms) where (RTT = 6 ms) given 50 KB as maximum segment. 

Ans. (44) 

 

Q.34 A web page has some text and 4 small size images, used non-persistent HTTP connection, then the number of HTTP connections required ________. 

Ans. (5) 

In non persistent HTTP for every object there is a TCP connection required. Hence 1 TCP connection for text and 4 TCP connections for images required. 

 

Q.35

L₁ = {wxyx⏐w, x, y ∈ (0 + 1)⁺} 

L₂ = {xy⏐x, y, ∈ (a + b)*, ⏐x⏐=⏐y⏐, x ≠ y}

(a) L₁ is not regular but L₂ is CFL

(b) L₁ is CFL and L₂ is not CFL

(c) L₁ and L₂ are not CFL

(d) L₁ is regular and L₂ is CFL 

Ans. (d) 

L₁ is regular and L₂ is CFL. 

In L₁ putting x as 0 and 1 we get a subset 

w0y0 + w1y1 = (0 + 1)⁺ 0 (0 + 1)⁺ 0 + (0 + 1)⁺ 1(0 + 1)⁺ 1 

Now by putting x as 00, 01, 10, 11 we can show that above minimal regular expression covers all such things and hence above expression is not a subset but is equal to given language. Since we wrote regular expressions for L₁, it is regular. 

 

Q.36 S → aSB⏐d B → b “aaadbbb” using bottom up parser, how many steps required? 

Ans. (7) 

S → aSB

→ aaSBB [S → aSB]

→ aaaSBBB [S → aSB]

→ aaadBBB [S → d]

→ aaadbBB [B → b]

→ aaadbbB [B → b]

→ aaadbbb [B → b]

Total 7 steps required

 

Q.37 Which of the following regular expressions will contain a set of all binary strings containing an odd number of 1’s?

(a) 1 0* (0* 1 0* 1 0*)* 

(b) 0* (0* 1 0* 1 0*)* 1 0* 

(c) (0* 1 0* 1 0*)* 0* 1 

(d) ((0 + 1)* 1 + (0 + 1)*) 1 0* 

Ans. (b) 

Try to find a counterexample to show the expression incomplete. 

(a) is incorrect because it forces the string to start with “1” and hence cannot generate 

a string like “01”, which has an odd number of ones. 

(c) is incorrect because it forces it to end with “1” and hence cannot generate “10”. 

(d) is same as (0 + 1)*10* which will generate some wrong strings like “110” which 

has an even number of 1’s. It is a superset and hence not correct. 

(b) is same as (0* 1 0* 1 0*)* 1 0* which is correct. 

 

Q.38 Given L = {aⁿ⏐n ≥ 0} ∪ {aⁿbⁿ⏐n ≥ 0}. Tell us where L is 

(a) DCFL 

(b) Non-DCFL 

(c) Context-free language 

(d) CFL but not DCFL 

Ans. (a) 

{aⁿbⁿ⏐n ≥ 0} is a well known DCFL. 

{aⁿ⏐n ≥ 0} is a well known regular language.

So, L = DCFL ∪ Regular = DCFL by closure properly 

DCFL is the strongest correct answer. 

 

Q.39 Given four languages, which of the following are undecidable?

Where <M> denotes encoding of a Turing Machine M 

L₁ = {<M>⏐L(M) = φ} 

L₂ = {<M>⏐L(M) is non recursive} 

L₃ = {< M, w, q >⏐M will visit the state q when M execute on w and take exactly 100 steps]

L₄ = {<M>⏐L(M) accept strings where strings length is at least 20}

Which one of the following are/in undecidable? 

(a) L₁ and L₂ 

(b) L₂ and L₃ 

(c) L₁ and L₄ 

(d) L₁, L₂ and L₃ 

Ans. (d) 

(i) L(M) = φ is emptiness problem of TM, which is undecidable, by Rice’s theorem since 

it is a non-trivial problem. 

(ii) L(M) = non-recursive is also a non-trivial question, since some TM can accept non- recursive language and some may not, so by Rice’s theorem it is undecidable. 

(iii) Rice’s theorem applied and hence L₃ is undecidable. 

(iv) With UTM we can check if M accepts a string by 100 steps. So L₄ decidable L₁, L₂ and L₃ are undecidable. 

 

Q.40 Which of the following is true? 

I. If L₁ ∪ L₂ is regular, then both L₁ and L₂ must be regular. 

II. The class of regular language is closed under infinite union. 

(a) I only 

(b) Both I and II 

(c) II only 

(d) Neither I nor II 

Ans. (d) 

I is false, since {a_nb_n} ∪ {a_nb_n} = ∑* which is regular, but {anbn} not regular. 

II is false, since many infinite languages can be broken into individual strings which will be an infinite union of finite languages. So if regular is closed under infinite union, then all infinite language will become regular, which is untrue. So II is also false. 

 

Q.41 The number of states in a minimal DFA accepting all strings on {a, b}* with number of a’s multiple of 2 but not multiple of 3 is ________. 

Ans. (6) 

L = {w ∈ {a, b}*⏐n_a(w) = multiple of 2 but not 3} 

Let, L₁ = {w ∈ {a, b}*⏐n_a(w) = multiple of 2} 

L₂ = {w ∈ {a, b}*⏐n_a(w) = multiple of 3} 

Given language is L₁ – L₂ = L₁ ∩ L₂c 

We can make a DFA for L₁ with 2 states. 

We can make a DFA for L₂c with 3 states. 

Then use product automata construction to get a DFA for L₁ – L₂ = L₁ ∩ L₂c with 6 states. Since neither of the L₁ or L₂c has a trap state, the resulting product automata also has no trap state. 

So, min DFA has 6 states. 

Alternate solution: 

We can directly design DFA for multiple of 2 but not 3 with 6 states as shown below with 6 states by accepting 2a’s, 4a’s but not 6a’s in trap. 

 

Q.42 Preorder of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19. Then what would be its post order. 

(a) 11, 12, 10, 16, 19, 18, 20, 15 

(b) 12, 10, 16, 19, 18, 20, 15, 11 

(c) 15, 16, 12, 19, 11, 18, 20, 15

(d) 15, 20, 10, 16, 19, 18, 11, 12 

Ans. (a) 

Post order: 11, 12, 10, 16, 19, 18, 20, 15 

 

Q.43 Consider the codes given below: 

fun 1 (int n)

{

static int i = 0;

if(n > 0)

{

i++;

fun1(n – 1);

}

return (i);

}

fun2 (int n)

{

static int i = 0;

if(n > 0)

{

i = i + fun1(n);

fun2(n – 1);

}

return i;

}

What the program will return when fun2(5) is called ________

Ans. (55) 

 

Q.44 Consider the C program: 

Arr [4] [5] = {{1, 2, 3, 4, 5} 

                    {6, 7, 8, 9, 10} 

                    {11, 12, 13, 14, 15} 

                     {16, 17, 18, 19, 20}} 

printf(“%d”, *(*(a + **a) + 3)) 

The output of the above C program is ________. 

Ans. (19) 

 

Q.45 Consider to semaphore a and b whose initial values are 1 and 0 respectively. Count is the shared variable which is not used in code section P: 

Code section P 

wait (a); 

if (count == n); signal(b); 

signal(a); wait(b); signal(b); 

Code section Q 

What does this code achieve? 

(a) At any time there will be 2 processes in Q. 

(b) All processes will run P and then enter into Q. 

(c) (n – 1) process will run P and then Q. 

(d) All processes run P in a mutually exclusive manner. 

Ans. (a) 

 

Q.46 Assume all the processes arrive at time 0. Find the absolute difference between average Turnaround Time (TAT) in SJF and Round Robin if time quantum 4 ns 

Ans. (5.25) 

Turn Around Time (TAT) = (21 – 0) + (13 – 0) + (2 – 0) + (6 – 0) 

Average TAT = ⁴²/₄ = 10.5 

Turn Around Time (TAT) = (18 – 0) + (21 – 0) + (10 – 0) + (14 – 0) 

= 18 + 21 + 10 + 14 

Average TAT = ⁶³/₄ = 15.75 

Hence, ⏐SJF (TAT) – RR(TAT)⏐ 

= ⏐10.5 – 15.75⏐ = 5.25 

 

Q.47 Consider the following state changes for a preemptive scheduling OS: 

I. Ready to running 

II. Running to ready 

III. Blocked to running 

IV. Blocked to ready Which of the above statement 

(a) I and II only 

(b) I only 

(c) I and III only 

(d) I, II and IV only 

Ans. (d) 

 

Q.48 A new process needs to be allocated memory. The size of the process cannot be exactly fit in available holes. If memory is allocated to any of the available holes, then a new smaller hole will be created. Which of the following options is correct in this context? 

(a) The size of hole created using best fit is never greater than size created by first fit 

(b) The size of hole created using best fit is never greater than size created by next fit 

(c) The size of hole created using next fit is never greater than size created by first fit 

(d) The size of hole created using worst fit is never greater than size created by first fit 

Ans. (a) 

 

Q.49 Which of the following statements are TRUE? 

1. Symbol table is accessed only during lexical analysis and syntax analysis. 
2. Compilers for programming L that support recursion necessarily need heap storage for memory allocation in the runtime environment. 
3. Errors violating the condition any variable must be declared before its use are detected during syntax analysis. 

(a) None of 1, 2, 3 

(b) 1 and 3 

(c) 2 only 

(d) 1 only 

Ans. (a) 

 

Q.50 Consider A → PQ, A → XY are production of a grammar P, Q, X, Y, A are non-terminals, s is synthesized attribute, i is inherited attribute 

Rule 1: P . i = A. i + 2, Q . i = P . i + A . i, A . s = P . s + Q . s 

Rule 2: X . i = A. i + Y . s and Y . i = X . s + A . i 

Which of the following is TRUE? 

(a) Only Rule 1 is L attributed 

(b) Rule 1 and Rule 2 are L attributed 

(c) Neither Rule 1 Nor Rule 2 

(d) Only Rule 2 is L attributed 

Ans. (a) 

GATE 2020 Civil Engineering Previous Year Paper

Civil Engineering 

General Aptitude 

Q.1 Sum of two positive numbers is 100. After subtracting 5 from each number product of  the resulting number is 0. One of the original number is 

(a) 95 

(b) 92 

(c) 85 

(d) 90 

Ans. (a) 

Let the two positive numbers be x and y. 

∴ x + y = 100 …(i) 

(x – 5) (y – 5) = 0 …(ii) 

⇒ x = 5 or y = 5 

If x = 5 then y = 95 

If y = 5 then x = 95 

∴ One of the numbers is 95 since 5 is not in any of the options. 

 

Q.2 If 0, 1, 2, …… 8, 9 are coded as O, P, Q, ….. W, X then 45 is coded as 

(a) TS 

(b) SS 

(c) ST 

(d) SU 

Ans. (c) 

∴ 45 is coded as ‘ST’.

 

Q.3 Unit place in 26591749¹¹⁰⁰¹⁶ is 

(a) 6 

(b) 1 

(c) 3 

(d) 9 

Ans. (b) 

≃ 26591749^(110016) 

≃ Unit place of 9° = 1 

∴ Cycle of equation is (9, 1) (9, 1), (9, 1) 

So the answer will be 1.

 

Q.4 Insert seven numbers between 2 and 34 such is an AP. The sum of those seven inserted seven number is 

(a) 124 

(b) 130 

(c) 120 

(d) 126 

Ans. (d) 

2, a, (a + d), (a + 2d), …… (a + 6d), 34 

∴ Total number of terms of AP(n) = 9 

Let sum of seven inserted numbers = S 

∴ S = 7/2[a + (a + 6d )] = 7[a + 3d ]

T_n = 34

Also, a – 2 = (a + d – a)

⇒ a – d = 2

Similarly a – 2 = 34 – (a + 6d)

⇒ a – 2 = 34 – a – 6d

⇒ 2a = 36 – 6d = 36 – 6(a – 2)

⇒ 2a = 36 – 6a + 12

⇒ 8a = 48

⇒ a = 6

∴ d = a – 2 = 6 – 2 = 4

∴ S = 7(a + 3d) = 7(6 + 3 × 4) = 126

General English 

Q.5 It is a common criticism that most of the academicians live in their ________, so they are not aware of the real life challenge. 

(a) Ivory tower 

(b) homes 

(c) Glass palaces 

(d) Big flats 

Ans. (a) 

 

Q.6 His hunger for reading is insatiable. He reads indiscriminately. He is most certainly a/an _________ reader. 

(a) all round 

(b) voracious 

(c) wise 

(d) precarious 

Ans. (b) 

 

Q.7 If Fuse : Fusion :: Use : ___________. 

(a) Usage 

(b) Usion 

(c) Uses 

(d) User 

Ans. (a) 

Solid Mechanics 

Q.1 In a 2-D stress analysis, the state of stress at point P is .The necessary and sufficient condition for existence of the state of pure shear at point P 

(a) (σ_xx – σ_yy)² + 4τ²xy ^{= 0} 

(b) τ_xy 

(c) σ_xx + σ_yy = 0 

(d) σ_xxσ_yy – τ²xy ^{= 0} 

Ans. (c) 

In pure shear condition 

σ_x = 0, σ_y = 0, τ_xy = τ 

For this condition (c) is correct 

σ_xx + σ_yy = 0 

 

Q.2 A cantilever beam PQ of uniform flexural rigidity is subjected to concentrated moment M at R 

Deflection at free end Q. 

(a) 3ML²/8EI 

(b) ML²/6EI 

(c) 3ML²/4EI 

(d) ML²/6EI

Ans. (b) 

(d) M 

δc = δ1 = CC₁ + C1C₂

= BB₁ + C1C₂

= ML222EI+ML2EIL2

δc = 3ML28EI

 

Q.3 The initial condition is shown in figure. Axial stiffness of each of the bars is 10 kN/mm. A load W is applied such that the system remains horizontal and total deflection is 5 mm. The load W will be ________. 

Ans. (130 kN) 

Structural Analysis 

Q.4 How many zero force members are there in the above truss 

 

(a) 6 

(b) 7 

(c) 8 

(d) 9 

Ans. (c) 

As Δ_AB = 0, hence F_AB = 0 

Total number of zero force member = 8 

 

Q.5 A planer elastic structure is subjected to UDL as shown in figure. Where maximum BM any in the structure will be ________. 

Ans. (0) 

M_x = 0 of all points 

 

Q.6 Distributed load (continuous or in patches) of 50 kN/m may occupy any position on the grid the maximum –ve BM at R will be 

(a) 56.25 kN-m 

(b) 150 kN-m 

(c) 93.75 kN-m 

(d) 22.5 kN-m 

Ans. (a) 

ILD for MS 

∴ M_max at support = − [½ × 1.5 × 1.5 × 50]

= –56.25 kNm or 56.25 kNm (hogging) 

ILD for BM at the centre of span ‘QS’ 

M_C = − [½ × 1.5 × 0.75 × 50] × 2

= –56.25 kNm or 56.25 kNm (hogging) 

So, it can be concluded that for maximum hogging moment, overhang span (PQ & ST) can be loaded. And because of symmetry, the magnitude of maximum hogging moment remains the same throughout span QS. 

Irrigation Engineering 

Q.7 For a certain region:

Pan evaporation = 100 mm

Effective rainfall = 20 mm

Crop coefficient = 0.4

Irrigation efficiency = 0.5

What will be the amount of water required for irrigation?

Ans. (40 mm) 

Water required by crop = 100 × 0.4 mm = 40 mm

Effective rainfall = 20 mm

Additional water required = 20 mm

Amount of water required after accounting irrigation efficiency = 20/0.5 = 40mm

Geotechnical Engineering 

Q.8 Water flows in upward direction in a tank through 2.5 m thick sand layer. The e and G of sand are 0.58 and 2.7. Sand is fully saturated. γ_w is 10 kN/m³. Effective stress at point A, located 1 m above the base of the tank is _____ kN/m². 

Ans. (8.94 kN/m ²) 

 

Q.9 SPT was conducted at a survey 1.5 m internal upto 30 m depth. At 3 m depth, the observed no. of hammer blows for 3 successive 150 mm penetration were 8, 6 and 9. SPT, N value at 3 m depth is 

(a) 15 

(b) 23 

(c) 17 

(d) 14 

Ans. (a) 

No. of blows for each 150 mm penetration 8, 6 and 9.

We will not consider the first 150 mm number of blows.

Hence, for the last 300 mm, the number of blows is 15.

Hence, observed SPT number = 15.

 

Q.10 Velocity of flow is proportional to the first power of hydraulic gradient in Darcy’s law, the law is applicable to 

(a) turbulent flow in porous media

(b) transitional flow in porous media

(c) laminar flow in porous media

(d) laminar as well as turbulent flow in porous media

Ans. (c) 

Darcy’s law is valid for laminar flow conditions. 

 

Q.11 A drained triaxial test is conducted on a sand sample. If σ_d = 150 kPa and consolidation stress is 50 kPa the calculated the value of angle of internal friction (φ)? 

Ans. (36.87°) 

 

Q.12 A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. γ_sat and effective angle of internal friction of sand are 18 kN/m³ and 38°. Assume γ_w = 10 kN/m³. Seepage is parallel to the slope. Factor of safety against shear failure is ______. 

Ans. (0.601) 

 

Q.13 A vertical retaining wall of 5 m height has to support soil of γ = 18 kN/m³, effective cohesion 12 kN/m² and effective friction angle 30°. As per Rankine, assuming that tension crack has occurred the lateral active thrust on wall per meter length is _____. 

Ans. (21.714 kN/m) 

After tension crack

Pa =½ × 16.144(5 – 2.309)

= 21.714 kN/m

 

Q.14 The water table is at a depth of 3 m below ground level, γ_w = 9.81 kN/m³. Surcharge is applied instantaneously Immediately after pre-loading, the effective stress (kN/m²) at point P and Q will be 

 

(a) 54 and 95 

(b) 36 and 90 

(c) 36 and 126 

(d) 124 and 204 

Ans. (a) 

( σ )_P =q + 3γ = 3 × 18 = 54 Surcharge is applied suddenly. 

∴ Excess pore water pressure developed. 

( σ )_Q = ( q + 3 γ _b + 4 γ _sat ) − (4 γ _w + 70) 

= 70 + 3 × 18 + 4 × 20 – (4 × 9.81 + 70) 

= 94.76 kN/m² 

 

Q.15 A fill of 2 m thick sand with unit weight of 20 kN/m³ is placed above the clay layer to accelerate the rate of consolidation of clay, c_v = 9 × 10^–2 m²/year. m_v = 2.2 × 10^–4 m²/kN. The settlement of clay layer 10 year after the construction is ____________. 

Ans. (18.832) 

Fluid Mechanics 

 

Q.16 Uniform flow with velocity u makes angle Q with axis. The velocity potential φ is 

(a) ±u(x sinθ – y cosθ) 

(b) ±u(y sinθ + x cosθ) 

(c) ±u(x sinθ + y cosθ) 

(d) ±u(y sinθ – x cosθ) 

Ans. (c) 

Velocity in x-depth, u_x = usinθ 

Velocity in y-depth, u_y = ucosθ 

₋ ∂φ/∂x = u_x 

Integrating it φ = –u_xx + f(x) + c 

= –(usinθ)x + f(y) + c …(i) 

− ∂φ/∂y= u _y

Integrating it φ = –u_y y + f(x) + c 

= –(ucosθ)y + f(x) + c …(ii) 

By equation (i) and (ii), 

φ = − u ( x sin θ + y cos θ ) 

If we take ∂φ/∂x = u_x and ∂φ/∂y = u_y

Then φ = u( x sin θ + y cos θ ) 

So, φ = ± u (xsinθ + ycosθ) 

 

Q.17 A floating body in a liquid is in a stable condition if 

(a) metacentre lies above centre of gravity

(b) metacentre lies below centre of gravity

(c) centre of buoyancy lies below the centre of gravity

(d) centre of buoyancy lies above the centre of gravity

Ans. (a) 

For stability of floating body M lies above G 

GM > 0 

 

Q.18 A circular water tank of 2 m dia has circular orifice of dia 1 m at bottom. Water is entering the tank at 20 l/s and escaping through orifice. Take C_D for orifice = 0.8. Neglect any friction losses. g = 9.81 m/s². Height of the water level in the tank at a steady rate is _____. 

Ans. (0.5164 m) 

Open Channel Flow 

Q.19 For an open channel flow discharge is 12 m³/s and width is 6 m. Hydraulic jump is formed. Depth at upstream was 30 cm. Take g = 9.81 m/s² and ρ_w = 100 kg/m³. Calculate the energy loss in jump? 

(a) 114.2 MW 

(b) 114.2 kW 

(c) 141.2 J/s 

(d) 141.2 HP 

Ans. (a) 

Q.20 For a rectangular open channel flow, the width of section is 4 m. The discharge is 6 m³/s. The Manning’s roughness coefficient is 0.02. The critical velocity for the channel will be ____________. 

Ans. (2.45 m/s) 

Critical depth (Y_C) = q2g1/3

=1.529.811/3=0.612 cm

Critical velocity (V_C) = gYc = 9.81 × 0.612 = 2.45 m/s 

Engineering Hydrology 

Q.21 The probability that a 50 year flood may not occur at all during the 25 year life of a project is _________. 

Ans. (0.603) 

P = 1/T = 1/50 = 0.02

q = 1 – P = 0.98 

∴ Probability of non-occurrence of an event is given by, 

Assurance = qⁿ 

= (0.98)²⁵ 

= 0.603 

Environmental Engineering 

Q.22 In a homogenous unconfined aquifer of area 3 km², water table elevation is 102 m. After natural recharge of volume 0.9 million cubic meter (Mm³) the water table rose to 103.2 m. After this recharge, pumping took place and W_T dropped down to 101.20 m. The volume of groundwater pumped after the natural recharge is __________ Mm³. 

Ans. (1.5 Mm³) 

V_R = 0.9 Mm³ 

V = 3 × (103.2 – 102) 

= 3 × 1.2 = 3.6 Mm³ 

y_s or y_R = VR_V = ^0.9/_3.6 

Now, 1/S ⁼ V_D/V 

V_D = ^0.9/_3.6  [ 3 × ( 103.2 − 101.2 ) ]

V_D = 1.5 Mm³ 

 

Q.23 35.67 mg HCl is added to distilled water and the total solution is made 1 l. The atomic weight of H and Cl is 1 and 35.5. Neglecting the dissociation of H₂O, the pH of solution is 

(a) 3.5 

(b) 2.5 

(c) 2.01 

(d) 3.01 

Ans. (d) 

HCl →H⁺ + Cl^– 

1 mole of HCL gives 1 mole H⁺ ions 

36.5 gm of HCl gives 1 gm of H⁺ ions 

35.67 mg = 1/36.5 × 35.67 = 0.977 mg of H ⁺

 = 0.977 × 10^{− 3}/1 = 9.77 × 10 ^{− 4} moles of H⁺ 

pH = –log₁₀[H⁺] = –log₁₀[9.77 × 10^–4] 

= –log₁₀9.77 + 4log₁₀10 

= 4 – 0.989 = 3.01 

 

Q.24 As chlorine reacts rapidly with water to form Cl^–, HOCl and H⁺. The most active disinfectant in the chlorination process is 

Cl_2(g) + H₂O ⇌ HOC l + Cl⁻ + H⁺ 

(a) HOCl 

(b) H⁺ 

(c) H₂O 

(d) Cl^– 

Ans. (a) 

 

Q.25 A gaseous chemical has a concentration of 41.6 μmole/m³ in air at 1 atm pressure and temp 293 k gas constant R is 82.05 × 10^–6 m³/atm/molK. Assume ideal gas law is valid, the concentration of gaseous chemical will be __________ ppm. 

Ans. (1) 

 

Q.26 For a river the discharge is 1000 MLD. BODs for the river are 5 mg/l and dissolved oxygen is 8 mg/l before receiving wastewater discharge at a location. For existing environment conditions dissolved oxygen is 10 mg/l. Waste water discharge of 100 MLD drains into the river. BOD ultimate of waste water is 200 mg/l and dissolved oxygen is 2 mg/l falls at a location. Assume complete mixing. Immediate do deficit is ______ mg/l. 

Ans. (2.545) 

 

Q.27 Surface overloading rate of primary settling tank (discrete) is 200 l/m² per day. ν = 1.01 × 10^–2 cm²/s. G = 2.64, the minimum dia of particle that will be removed with 80% of efficiency will be _______ μm. 

Ans. (14.53) 

 

Q.28 Stream with a flow rate of 5 m³/sec, BOD_U = 30 mg/L. Waste water discharge 0.2 m³/s, BOD₅ = 500 mg/l joins the stream at a location and mix up instantaneously. Area of stream 40 m² which remains constant. BOD exertion rate constant is 0.3/day (log_e). BOD remaining 3 km downstream from the mixing location is _________. 

Ans. (49.57) 

 

Q.29 A water supply scheme transport 10 MLD water through a 450 mm diameter pipe for a distance 2.5 km. A chlorine dose of 3.5 mg/L is applied at the starting point. It is decided to increase the flow from 10 MLD to 13 MLD in the pipeline. Assume exponent for concentration n = 0.36 with this increased flow in order to attain the same level of disinfection. The chlorine is applied at the starting point. 

(a) 3.95 

(b) 4.4 

(c) 5.55 

(d) 4.75 

Ans. (d) 

Construction Materials 

Q.30 The los angeles test for stone aggregate is used to examine 

(a) crushing strength 

(b) abrasion 

(c) toughness 

(d) none of these 

Ans. (b) 

Los Angeles test of stone is used for Abrasion resistance. 

 

Q.31 During the process of hydration of cement, due to increase in C₂S content in cement ,clinker, the heat of hydration 

(a) does not change 

(b) initially decrease the increase 

(c) decrease 

(d) increase 

Ans. (c) 

Geomatics Engineering 

Q.32 An open traverse PQRST is surveyed using theodolite 

If the independent coordinated (Northing and Easting) of station P are (400, 200 m) the independent coordinates of station T are 

(a) 194.7, 370.1 

(b) 405.3, 229.9 

(c) 205.3, 429.9 

(d) 394.7, 170.1 

Ans. (d) 

ΔL = –5.3

ΔD = –29.9

T, Northing{400 + (–5.3) = 394.7

T, Easting{200 + (–29.9) = 170.1

T [394.7 m, 170.1 m]

 

Q.33 The length of line segment SP is __________. 

Ans. (44.784 m) 

ΔL = 40cos80° + 50cos10° + 30cos210° 

= 30.20 

ΔD = 40sin80° + 50sin10° + 30sin210° 

= 33.07 

Length, SP = √ΔL² + ΔD² 

= 44.784 m 

Highway Engineering 

Q.34 Gradient of a road is 4.5%, radius is 100 m the compensated as per IRC will be _____. 

Ans. (4%) 

Gradient = 4.5%, R = 100 m 

Grade compensation = (30 + R/R) ⊁ (75/R)% = 30 + 100/100 ⊁ 75/100 = 1.3% ⊁ 0.75} G.C = 0.75 

 Compensated Gradient = Gradient G.C = 4.5% – 0.75 = 3.75 ⊀ 4% 

Hence C.G = 4% 

 

Q.35 As per IRC, the minimum width of median in urban areas is ____________. 

Ans. (1.2 m) 

Desirable width of median in urban roads = 5m 

And As per IRC : 86-1983 min. width = 1.2m 

 

Q.36 For the contraction joint, which is correct position of dowel bar 

Ans. (b) 

RCC Structures and Prestressed Concrete 

Q.37 Calculate the design bending moment of a singly reinforced section 

If width = 300 mm

Effective depth = 450 mm

Area of steel in tension = 942 mm²

Grade of concrete is M25 and Fe500 Steel

Ans. (158.28 kN-m) 

Q.38 A simply supported prismatic concrete beam of rectangular cross-section of span 8 m is prestressed with effective prestress force of 600 kN. Eccentricity is zero at support and varies linearly to value ‘e’ at mid span. Required value of e ________. 

Ans. (40 mm) 

P = 600 kN

Simply supported span = L = 8 m

To support a point load applied at mid span (W)

= 12 kN

Balancing load = Point load

2P sin θ = W

2P (E/L/2) = 2

2Pe × 2/L = W

4Pe/L = W

e = WL/4P = 12000N × 8000mm/ 4 × 600 × 1000N

= 40mm

 

Q.39 The variation of bond stress varies as 

Ans. (c) 

Design of Steel Structures 

Q.40 For a given beam shown below the permissible stress in the weld is 20 N/mm², 

I_xx = 7.73 × 10⁶ mm⁴. The allowable shear force in kN will be __________. 

Ans. (323.527 kN) 

Engineering Mathematics 

Q.41 The area of an ellipse represented by an equation is 

(a) πab/4

(b) 4πab/3

(c) πab 

(d) πab/2

Ans. (c) 

Q.42 The value of

(a)  1/2

(b) 1/4

(c) 0 

(d) 1 

Ans. (b) 

 

Q.43 for the ordinary differential equation d²x/dt² -5dx/dt+6x=0,intial condition x(0) =0 and dx/dt (0) =10 ,the solution of the given equation

(a) -10e^2t+10e^3t

(b)10e^2t+10e^3t

(c) 5e^2t+6e^3t

(d) -5e^2t+6e^3t

Ans.(a)

 

Q.44 value of X₃ will be

Ans.(3)

 

Q.45 If C represents, a line segment between (0, 0, 0) and (1, 1, 1) in Cartesian coordinate system, the value of line integral ∫_C[ ( y + z ) dx + ( x + z )dy + ( x + y )dz] is 

Ans. (3)

 

Q.46 If the true value of ln2 is 0.69. If value of ln2 is also calculated by linear regression between ln1 and ln6 then calculate the percentage error in the value of ln2. 

Ans. (48.11%) 

 

Q.47 θ = f(t, z) and D = f(θ), k = f(θ) then _{D ( θ ) ∂} ∂ _z2 θ 2 ₊ ∂ k _∂ ( _z θ ) ₋ ∂θ _{∂ t = 0} is _______. 

(a) Second order linear equation 

(b) Second order nonlinear equation 

(c) Second degree linear equation 

(d) Second degree non-linear equation 

Ans. (d) 

∵ 1^st term of given D. Equation contains a product of dependent variable with its derivative, so it is non-linear and also we have 2nd order derivative so it’s order is two i.e., 2^nd order is non linear.