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.
Special Announcement!
Before you move on to see the solution, we have something for you.
Top 5 students of APSEd, which include all our subscribers will be rewarded hugely on the basis of GATE 2021 results.
Other than this, all the GATE top 1000 rankers are eligible to get the APSEd interview course for FREE.
Note: A special surprise reward is waiting for the students who get a top 100 AIR.
For any sort of queries, just hit us an email to support@apsed.in
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
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.
Comments