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.

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