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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)