### (Questions with Answer Key)- GATE 2013 Civil Engineering Examination

GATE 2013 Questions and answer key for CIVIL ENGG. Q. 1 – Q. 25 carries one mark each.

Q.1 There is no value of x that can simultaneously satisfy both the given equations.Therefore, find the

‘least squares error’ solution to the two equations, i.e., find the value of x that minimizes the sum of

squares of the errors in the two equations. __________

2x = 3

4x =1

Q.2 What is the minimum number of multiplications involved in computing the matrix product PQR?

Matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and

1 column. ________Sol:__16 multiplications

Q.3 A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that

a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:

(A) 0.04 (B) 0.2 (C)0.02 (D) 0.0004 Sol: (D) p = 1/50*1/50

Q.4 Maximum possible value of Compacting Factor for fresh (green) concrete …

Q.1 There is no value of x that can simultaneously satisfy both the given equations.Therefore, find the

‘least squares error’ solution to the two equations, i.e., find the value of x that minimizes the sum of

squares of the errors in the two equations. __________

2x = 3

4x =1

Q.2 What is the minimum number of multiplications involved in computing the matrix product PQR?

Matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and

1 column. ________Sol:__16 multiplications

Q.3 A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that

a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:

(A) 0.04 (B) 0.2 (C)0.02 (D) 0.0004 Sol: (D) p = 1/50*1/50

Q.4 Maximum possible value of Compacting Factor for fresh (green) concrete …