# GATE CE 2013

 Question 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
 A 0.5 B 1.5 C 2 D 4
Engineering Mathematics   Linear Algebra
 Question 2
What is the minimum number of multiplications involved in computing the matrix product PQR?
MatrixP has 4 rows and 2 columns, matrixQ has 2 rows and 4 columns, and matrixR has 4 rows and 1 column. __________
 A 256 B 32 C 16 D 128
Engineering Mathematics   Linear Algebra
Question 2 Explanation:
If we multiply QR first then,
$Q_{2\times 4}\times R_{\left ( 2\times 1 \right )}$ having multiplication number 8.
Therefore $P_{\left ( 4\times 2 \right )}QR_{\left ( 2\times 1 \right )}$ will have minimum number of multiplication =(8+8)=16.

 Question 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
Engineering Hydrology   Flood Routing and Flood Control
Question 3 Explanation:
Return period of rainfall,
 T&=50 years
$\therefore$ probability of occurrence once in 50 years,
p&=$\frac{1}{50}$&=0.02
Probability of occurrence in each of 2 successive year $=p^{2}=\left ( 0.02 \right )^{2}=0.0004$
 Question 4
Maximum possible value of Compacting Factor for fresh (green) concrete is:
 A 0.5 B 1 C 1.5 D 2
RCC Structures   Working Stress and Limit State Method
 Question 5
As per IS 800:2007, the cross-section in which the extreme fiber can reach the yield stress, but cannot develop the plastic moment of resistance due to failure by local buckling is classified as
 A plastic section B compact section C semi-compact section D slender section
Design of Steel Structures   Plastic Analysis
Question 5 Explanation:
As per clause 3.7.2 of IS 800:2007

There are 5 questions to complete.