[free]Gate 2022 CE solved paper with explantion Q21 to Q30 pdf

Below the Gate 2022 Civil Engineering solved question paper(forenoon session ) which were held on 12-02-2022. The total number of questions are 65, 10 from aptitude and 55 from Civil Engineering. Question paper is cover in 7 pages and each page have 10 questions. Question on this page from 21 to 30.

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10 questions of Aptitude 55 questions of Civil Engineering

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Q 21.

A rectangular channel with Gradually Varied Flow (GVF ) has a changing bed slope. If the change is from a steeper slope to a sleep slope, the resulting GVF profile is

S_3

S_1

S_2

either

S_1 \; \textrm{or} \; S_2

, depending on the magnitude of the slopes

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Detailed Explanation

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As per given data,

Flow is changed from steeper to sleep. So the normal depth of flow will increase in a steep slope, as the slope is decreased. CDL will remain the same for both the slope.

Sleeper slope $\to$ More bed slope than steep

Correct option is: S₃

Q 22.

The total hardness in raw water is 500 milligram per liter as CaCo₃ . The total hardness of this raw water, expressed in milligram equivalent per liter, is

(Consider the atomic weights of Ca, C, and O as 40 g/mol, 12 g/mol, and 16 g/mol. respectively.)

100

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Q 23.

An aerial photograph is taken from a flight at a height of 3.5 km above mean sea level, using a camera of focal length 152 mm. If the average ground elevation is 460 m above mean sea level, then the scale of the photograph is

1 : 20000

1: 20

1 : 2800

1 : 100000

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Q 24.

A Line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m.

The corrected horizontal length (in m) of the line PQ will be

342.52

349.30

356.20

350.70

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Q 25.

The matrix M is defined as

M = $\begin {bmatrix} 1 & 3 \\ 4 & 2 \end {bmatrix}$

and has eigenvalues 5 and -2 . The matrix Q is formed as

Q = M³ – 4 M² – 2 M

which of the following is/are the eigenvalue (s) of matrix Q ?

-20

-30

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Given; Eigen values of M are 5, -2

so eigen value of Q = $M^3 - 4 M^2 - 2M$ are

using 5 = $5^3 - 4 \times 5^2 - 2 \times 5 = 15$

using -2= $(-2)^3 -4 \times (-2)^2 -2 \times -2 = -20$

So the both 15 and -20 are Correct options.

Learn more : Previous year Gate papers of Civil Engineering with detailed solution

Learn more : GATE 2022 All branches Aptitude Questions with detailed Solution

Q 26.

For wastewater coming from a wood pulping industry. Chemical Oxygen Demand (COD) and 5 -day Biochemical Oxygen Demand (BOD₅) were determined.

For this wastewater, which of the following statement(s) is/are correct ?

COD > BOD5

COD ≠ BOD5

COD < BOD5

COD = BOD5

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Q 27.

Which of the following process (es) can be used for conversion of salt water into fresh water ?

Electrodialysis

Reverse osmosis

Ultrafiltration

Microfiltration

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Q 28.

A horizontal curve is to be designed in a region with limited space. Which of the following measure (s) can be used to decrease the radius of curvature ?

Decrease the design speed

Increase the super elevation

Increase the design speed

Restrict vehicles with higher weight from using the facility

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Learn more : Gate syllabus for Civil Engineering

Q 29.

Consider the following recursive iteration scheme for different values of variable P with the initial guess $x_1 = 1$

$X_{n +1} = \dfrac {1}{2} \left ( x_n + \dfrac {P}{x_n} \right), \qquad n = 1,2,3,4,5$

For $P = 2, x_5$ is obtained to be 1.414, rounded-off to three decimal places. For $P = 3 , x_5$ is obtained to be 1.732 , rounded-off to three decimal places.

If $P = 10$ , the numerical value of x₅ is ________. (round off to three decimal places.

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Q 30.

The Fourier cosine series of a function is given by :

$f(x) = \sum_{n=0}^{\infty} f_n\, cos nx$

For $f(x) = cos^4 x$ , the numerical value of $( f_4 + f _5 )$ is ______. (round off to three decimal places )

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Gate 2022 Civil Engineering solved paper with full explanation forenoon Q21 to Q30

A rectangular channel with Gradually Varied Flow (GVF ) has a changing bed slope. If the change is from a steeper slope to a sleep slope, the resulting GVF profile is

Detailed Explanation

The total hardness in raw water is 500 milligram per liter as CaCo₃ . The total hardness of this raw water, expressed in milligram equivalent per liter, is

(Consider the atomic weights of Ca, C, and O as 40 g/mol, 12 g/mol, and 16 g/mol. respectively.)

Detailed Explanation

An aerial photograph is taken from a flight at a height of 3.5 km above mean sea level, using a camera of focal length 152 mm. If the average ground elevation is 460 m above mean sea level, then the scale of the photograph is

Detailed Explanation

A Line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m.

The corrected horizontal length (in m) of the line PQ will be

Detailed Explanation

The matrix M is defined as

M = $\begin {bmatrix} 1 & 3 \\ 4 & 2 \end {bmatrix}$

and has eigenvalues 5 and -2 . The matrix Q is formed as

Q = M³ – 4 M² – 2 M

which of the following is/are the eigenvalue (s) of matrix Q ?

Detailed Explanation

For wastewater coming from a wood pulping industry. Chemical Oxygen Demand (COD) and 5 -day Biochemical Oxygen Demand (BOD₅) were determined.

For this wastewater, which of the following statement(s) is/are correct ?

Detailed Explanation

Which of the following process (es) can be used for conversion of salt water into fresh water ?

Detailed Explanation

A horizontal curve is to be designed in a region with limited space. Which of the following measure (s) can be used to decrease the radius of curvature ?

Detailed Explanation

Consider the following recursive iteration scheme for different values of variable P with the initial guess $x_1 = 1$

$X_{n +1} = \dfrac {1}{2} \left ( x_n + \dfrac {P}{x_n} \right), \qquad n = 1,2,3,4,5$

For $P = 2, x_5$ is obtained to be 1.414, rounded-off to three decimal places. For $P = 3 , x_5$ is obtained to be 1.732 , rounded-off to three decimal places.

If $P = 10$ , the numerical value of x₅ is ________. (round off to three decimal places.

Detailed Explanation

The Fourier cosine series of a function is given by :

$f(x) = \sum_{n=0}^{\infty} f_n\, cos nx$

For $f(x) = cos^4 x$ , the numerical value of $( f_4 + f _5 )$ is ______. (round off to three decimal places )

Detailed Explanation

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A rectangular channel with Gradually Varied Flow (GVF ) has a changing bed slope. If the change is from a steeper slope to a sleep slope, the resulting GVF profile is

Detailed Explanation

The total hardness in raw water is 500 milligram per liter as CaCo3 . The total hardness of this raw water, expressed in milligram equivalent per liter, is

(Consider the atomic weights of Ca, C, and O as 40 g/mol, 12 g/mol, and 16 g/mol. respectively.)

Detailed Explanation

An aerial photograph is taken from a flight at a height of 3.5 km above mean sea level, using a camera of focal length 152 mm. If the average ground elevation is 460 m above mean sea level, then the scale of the photograph is

Detailed Explanation

A Line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m.

The corrected horizontal length (in m) of the line PQ will be

Detailed Explanation

The matrix M is defined as

M = \begin {bmatrix} 1 & 3 \\ 4 & 2 \end {bmatrix}

and has eigenvalues 5 and -2 . The matrix Q is formed as

Q = M3 – 4 M2 – 2 M

which of the following is/are the eigenvalue (s) of matrix Q ?

Detailed Explanation

For wastewater coming from a wood pulping industry. Chemical Oxygen Demand (COD) and 5 -day Biochemical Oxygen Demand (BOD5) were determined.

For this wastewater, which of the following statement(s) is/are correct ?

Detailed Explanation

Which of the following process (es) can be used for conversion of salt water into fresh water ?

Detailed Explanation

A horizontal curve is to be designed in a region with limited space. Which of the following measure (s) can be used to decrease the radius of curvature ?

Detailed Explanation

Consider the following recursive iteration scheme for different values of variable P with the initial guess x_1 = 1

X_{n +1} = \dfrac {1}{2} \left ( x_n + \dfrac {P}{x_n} \right), \qquad n = 1,2,3,4,5

For P = 2, x_5 is obtained to be 1.414, rounded-off to three decimal places. For P = 3 , x_5 is obtained to be 1.732 , rounded-off to three decimal places.

If P = 10 , the numerical value of x5 is ________. (round off to three decimal places.

Detailed Explanation

The Fourier cosine series of a function is given by :

f(x) = \sum_{n=0}^{\infty} f_n\, cos nx

For f(x) = cos^4 x , the numerical value of ( f_4 + f _5 ) is ______. (round off to three decimal places )

Detailed Explanation

Leave a Comment Cancel reply

The total hardness in raw water is 500 milligram per liter as CaCo₃ . The total hardness of this raw water, expressed in milligram equivalent per liter, is

M = $\begin {bmatrix} 1 & 3 \\ 4 & 2 \end {bmatrix}$

Q = M³ – 4 M² – 2 M

For wastewater coming from a wood pulping industry. Chemical Oxygen Demand (COD) and 5 -day Biochemical Oxygen Demand (BOD₅) were determined.

Consider the following recursive iteration scheme for different values of variable P with the initial guess $x_1 = 1$

$X_{n +1} = \dfrac {1}{2} \left ( x_n + \dfrac {P}{x_n} \right), \qquad n = 1,2,3,4,5$

For $P = 2, x_5$ is obtained to be 1.414, rounded-off to three decimal places. For $P = 3 , x_5$ is obtained to be 1.732 , rounded-off to three decimal places.

If $P = 10$ , the numerical value of x₅ is ________. (round off to three decimal places.

$f(x) = \sum_{n=0}^{\infty} f_n\, cos nx$

For $f(x) = cos^4 x$ , the numerical value of $( f_4 + f _5 )$ is ______. (round off to three decimal places )