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# GATE 2021 Civil Engineering | Question Paper with Solution

APSEd brings you solutions of GATE 2021 Civil Engineering for both forenoon and afternoon session conducted on 6th Feb. This year GATE was conducted by IIT Bombay

In this article, I will share some memory based questions and their solution hints with you. The key highlights and subject wise weightage of paper 1 and paper 2 can be found here.

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## GATE Civil 2021 Forenoon Session

As the questions are memory-based, for most of the questions, it is not sure to say whether the question is MCQ or NAT. But, the question is correct to the best of our knowledge.

We are keeping on updating its article based on memory-based questions. Keep coming back for more. The official key will be out soon on the GATE official website.

### Question 1

Two matrices Q and R are given. Find the matrix that represents Transpose(Q) x Transpose(R).

__Hint__

This is a very simple question. There is no trick and formula involved.

You know how to find the transpose of a matrix?

You know how to multiply two matrices?

Yeah, that is all you need to know for this question.

### Question 2

What is the value of the given limit?

__Hint__

Step 1: Now the limit is in infinity - infinity form, which is undefined form. We will transfer it to zero by zero form. The 0/0 form can be brought just by subtracting the two bracketed terms simply.

Step 2: Put L'Hospital rule till the time it remains in 0/0 form.

The complete solution can be found here-

### Question 3

In a confined aquifer of width 30 m, the radius of influence is 245 m, diameter of well is 20 cm, discharge through it is 40 l/sec, the drawdown at the well is 4 m. The hydraulic conductivity of the well will be ___ m/day.

__Hint__

This is just using the formula and getting the answer.

The hydraulic conductivity, k = [Q ln(R/r)] / [2πB(H2 - H1)]

Putting, Q = 40 x 10^-3 m³/sec

R = 245 m, r = 0.20/2 = 0.10 m

B = 30 m, H2 - H1 = 4 m

So, the final answer would be, k = 35.884 m/day

### Question 4

For the given aquifer, find the number of days the flow will take to reach downstream (Take, k = 25 m/day and porosity of soil = 0.3)

__Hint__

The head loss, ΔH = 20 m

Seepage velocity, Vs = ki/n = (25 x (20/2000)) / 0.3 = 0.833 m/day

Time = distance/velocity = 2000/0.833 = 2400 days

### Question 5

Which of the following options is/are correct? (MSQ)

(A) The back bearing is calculated by fore bearing ±180 degree

(B) The boundary of the calm water pond represents a contour line

(C) The stadia interval increases as we move closer towards the staff

(D) For a WCB of 270 degrees, the reduced bearing is given as 90 NW

__Hint__

Option A: This is correct

Option B: It is correct, as all the points on its surface have the same reduced levels

Option C: The stadia interval decreases as we move closer towards the staff

Option D: This is also correct

### Question 6

The shape of the most commonly designed vertical curve is

(A) Spiral

(B) Elliptical

(C) Parabolic

(D) Circular

__Hint__

The parabolic curve is the most commonly designed vertical curve. In the case of valley curves, we design cubic parabolic and in the case of summit curves, we design square parabolic.

### Question 7

PQRS is a closed traverse. The internal angles P, Q, R and S are 92, 68, 123 and 77 degrees respectively. The fore bearing of the line PQ is given as 27 degrees. Find the fore bearing of the line RS.

__Hint__

The question is very simple. The concept is here.

FB of PQ = 27, BB of PQ = 180 + 27 = 207

FB of QR = BB of PQ - 68 = 207 - 68 = 139

BB of QR = 139 + 180 = 319

Now, FB of RS = BB of QR - 123 = 319 - 123 = 196 degrees

### Question 8

Which of the following statements is incorrect?

(A) The first reading from the station is foresight

(B) Planimeter is used to measure the area

(C) Contour lines can intersect in case of an overhanging cliff

(D) The basic principle of surveying is to work from whole to parts

__Hint__

Option A is incorrect as the first reading is always a backsight(BS).

Option B is correct. A planimeter is used to measure the area of an irregular body.

Option C: Contour lines can intersect in case of an overhanging cliff. This is a property of contour line.

Option D: The basic principle of surveying is to work from part to whole, not whole to part.

### Question 9

The triple integration of (8xyz dx dy dz) within (2, 3) x (1, 2) x (0, 1).

__Hint__

The question was from volumetric integration. Just take the limit for x from 2 to 3. Limit of y is from 1 to 2 and the limit of z is from 0 to 1.

### Question 10

__Hint__

This is a repeat here. It has been asked many times in GATE.

It is a homogeneous differential equation. If you know how to find the IF, the problem got way for you.

### Question 11

The linear traffic model is given by an equation, V = 70 -0.7k. Determine the time headway at maximum traffic volume.

__Hint__

The speed density relation is,

v = Vsf(1-k/kj)

Vsf: free flow speed, k: density, kj: jam density

So, the given relationship can be written as,

V = 70(1-k/(70/0.7))

So, Vsf = 70 and kj = 100

Q = Vsf x Kj = 4 = 1750

Time headway = 3600/Q = 3600/1750 = 2.1 s

### Question 12

A signalised intersection operates in two phases. Loss time = 3 seconds per phase. The maximum ratio of approach flow to saturation flow for the two phases are 0.37 and 0.40 respectively.

__Hint__

Q/S are given. We are asked to find the optimum cycle length using the Webster method.

C0 = (1.5L+5)/(1-Y)

C0 = ((1.5 x 6) + 5) / (1-0.37-0.40) = 60.869

### Question 13

The spot speeds of a vehicle observed on a point on a highway are 40, 55, 60, 65 and 80 kmph. Space mean speed in kmph is __.

__Hint__

5/V = 1/40 + 1/55 + 1/60 + 1/65 + 1/80

So, V = SMS = 56.999 kmph

### Question 14

If water is flowing at the same depth is the most hydraulically efficient triangular and rectangular triangle section. The ratio of the hydraulic radius of the triangular section to that of the rectangular channel section is ___.

__Hint__

We will find the ratio of Area/perimeter of triangle section to that of Area/perimeter of rectangular section.

The required ratio = (Y/2√ 2) / (Y/2) = 1/√ 2

### Question 15

For a soil

C = 15 kPa

The angle of internal friction = 20 degrees

Bulk unit weight = 17.5 kN/m^3

Find the maximum depth of excavation.

__Hint__

We have to find the critical depth of excavation here.

Ka = (1 - sin φ)/(1 + sin φ) = 0.4963

Hc = 4C / γ√Ka = 4.89 m

### Question 16

In partially saturated soil,

γ = 18.5 kN/m^3

The water content, w = 25%

The specific gravity of soil = 2.65

γw=9.81 kN/m^3

What is the value of γsat?

__Hint__

γ=(G+wG)/(1+e) x γw

18.5 = (2.65+0.25 x 2.65) / (1+e) x 9.81

So, e = 0.7565

So, γsat = (G + e) / (1 + e) x γw = 19.03 kN/m^3

### Question 17

Four-person P, Q, R and S are to be seated in a row, all are facing the same direction, but not necessarily in the same order. P and R can not seat adjacent to each other. S should be seated to the right of Q. The total number of distinct seating arrangement possible is

(A) 2

(B) 4

(C) 6

(D) 8

__Hint__

The two conditions given are,

P and R can not seat adjacent to each other.

S should be seated to the right of Q (Note:

**to the right**and**to the immediate right**are two different things)

The possible arrangements are- QPSR, QRSP, PQSR, RQSP, PQRS and RQPS. So the possible number of cases is 6.

### Question 18

Gypsum is added

(A) To prevent the quick setting

(B) To increase hardening

(C) To improve workability

(D) To decrease the heat of hydration

__Hint__

Gypsum is added to prevent quick setting.

### Memory Based Questions - GATE Civil 2021 Afternoon Session

### Question 1

If k is a constant, the general solution of dy/dx − y/x = 1 will be of the form

__Hint__

This is in linear equation form, dy/dx +Py = Q

The solution would be,

y x IF = integrate(Q.IF dx)

### Question 2

Relationship between traffic speed and density is described using a negatively sloped straight line. If Vf is free to flow speed then the speed at which maximum flow will occur?

(A) Vf/y

(B) Vf

(C) 0

(D) Vf/2

__Hint__

The speed density relation is,

v = Vf(1-k/kj)

Vf: free flow speed, k: density, kj: jam density

At maximum flow condition, k =kj/2

So, v = Vf(1-0.5) = Vf/2

### Question 3

In an aggregate mix, percentage weight of coarse aggregate, fine aggregate, mineral fillers are 55%, 40%, 5% respectively. Bulk specific gravities of coarse aggregate, fine aggregate and mineral filler are 2.55, 2.65, 2.70. the theoretical specific gravity of aggregate mix is ____________ (round off to two decimal places)

__Hint__

The bulk specific gravity of aggregate mix(GT = 100/(C1/G1+C2/G2+C3/G3)

Where C: Contribution and G: Specific gravity

### Question 4

The softening point of bitumen has the same unit is that of

(A) Viscosity

(B) Temperature

(C) Time

(D) distance

__Hint__

The softening point of bitumen is expressed in degree celsius, which is a unit of temperature.

### Question 5

Two unbiased dice are thrown simultaneously. The probability of getting both even is ___________.

__Hint__

Probability = 3/6 x 3/6 = 1/4

### Question 6

The rank of the matrix is __.

__Hint__

3 is the answer.

### Question 7

If A is orthogonal, A x Transpose(A) is

__Hint__

For an orthogonal matrix, A = Transpose(A)

So, A x Transpose(A) is always a unit matrix.

### Question 8

For a split spoon sampler, the internal diameter= 48 mm and the external diameter= 52 mm.

Find the area ratio in percentage?

__Hint__

Area ratio, Ar = (do^2 - di^2)/di^2 x 100 %

### Question 9

Seasoning of timber is done for?

__Hint__

Seasoning of timber is done for strength and durability.

### Question 10

There was a numerical asking the cant deficiency.

__Hint__

Cant Deficiency = emax - e = GVmax²/127R - GV²/127R

### Question 11

Trapezoidal rule numerical (a=0 to b=0.5, f(x) = 10x - 20x, Calculate h/2[(y0+yn)+2(y1+y2+....)]

### Question 12

There was a numerical on duty in irrigation

__Hint__

We can use D = 8.64x (B/𝚫)

𝚫 = Volume/Area

### Question 13

There was a numerical on open channel flow asking the critical depth

__Hint__

Use the formula, critical depth, yc = (q²/g)^1/3)

### Question 14

For long term stability of clay: what triaxial test is used?

(A) Consolidated drained test (Answer)

(B) Unconsolidated undrained test

(C) Consolidated undrained test

(D) Unconfined compressive test

*Disclaimer: All the questions are memory-based and taken from some of our students who appeared for GATE 2021. The official notification for the same will be out soon and we will spread it across then. *

We are keeping on updating its article based on memory-based questions. Keep coming back for more. The official key will be out soon on the GATE official website.