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
2x= 3
4x= 1
0.5 | |
1.5 | |
2 | |
4 |
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. __________
MatrixP has 4 rows and 2 columns, matrixQ has 2 rows and 4 columns, and matrixR has 4 rows and 1 column. __________
256 | |
32 | |
16 | |
128 |
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.
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:
0.04 | |
0.2 | |
0.02 | |
0.0004 |
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
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:
0.5 | |
1 | |
1.5 | |
2 |
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
plastic section | |
compact section | |
semi-compact section | |
slender section |
Question 5 Explanation:
As per clause 3.7.2 of IS 800:2007
There are 5 questions to complete.