 |
1. Express the matrix A as a sum of symmetric and a skew symmetric matrix
4 2 -3
A = 1 3 -6
-5 0 -7
2. Determine the rank of the following matrix:
0 1 -3 -1
0 0 1 1
A = 3 1 0 2
1 1 -2 0
3. Find the div F and curl F where F = grad (x3 + y3 + z3 – 3xyz)
4. If F = 3xyi – y2j, evaluate line integral (F. dr) where C is the curve in the xy plane y = 2x2 from (0,0) to (1,2).
5. Solve (D2 + 1) y = sin x
6. A certain number of articles manufactured in one batch were classified into 3 categories according to a particular characteristic, being
less than 50
between 50 and 60
greater than 60
if this characteristic is known to be normally distributed, determine the mean, standard deviation for this batch if 60%, 35% and 5% were found in these categories
7. Given x, y as real variables and x > 0, xy = 1 find minima of x + y
Find minima of sin x + cos x
8. Find the integration of the following:
dx / sqrt (1 + sin x)
1 / sqrt (x2 + x + 1)
log x
1 / {(x -1)(x - 2)}
sqrt (x2 + 2x)
(sin x + cos x) / (2sin x + 3cos x)
9. What is displayed when the following program is run: #include
void f(int x) { if (x == 4) cout << "hello\n"; else { cout << "goodbye\n";f(x - 1);
}cout << "xxx"; // note no \n in this string
}
void main() { f(6); cout << "okay\n";
}
10. Write a C
program to find if a number is a prime number or not. The programme should be
efficient in finding the factors of the number.
11. What do you understand by “fire load” of a building? How do you determine it?
12. Explain the following in the context of building science:
Thermal conductivity
Surface resistance
Total thermal resistance
Thermal transmittance
Thermal damping
Thermal time constant
13. What is the wavelength of the wave in the figure, where each segment of the wave has length d?
d
14. The audible frequency range for normal hearing is from 20Hz to 20KHz. What are the wavelengths at these frequencies?
15. Define glare in buildings. How many types has glare been classified into?
16. State Lambert’s Law for reflection of light. Is mirror a true lambertian surface?
17. With respect to reflection of light differentiate between specular, diffused and spread reflection.
18. What do you understand by “critical thickness of insulation”?
19. What is reverberence in buildings? What is the difference between reverberence and echo?
20. Draw the network of the following activities. Indicate the critical path. Node 1 denotes start and node 5 denotes end. Calculate float values.
Activity Duration (days) Depends upon
1-2 3 none
1-3 5 none
2-4 4 1-2
4-5 5 1-3 and 2-4
3-5 8 1-3
21. Find the stiffness matrix K and the load vector f in the matrix equation Ku = f
where u denotes the displacement of the nodes for the truss.
d e
15KN f 15KN
3m
a b c
4m 4m
22. The following two statements are made with reference to a simply supported under reinforced RCC beam
Failure takes place by crushing of concrete below the steel has yielded
The neutral axis moves up as the load is increased
With reference to the above statements which of the following applies
Both the statements are false
Both the statements are true
One is true and second is false
One is false and second is true
23. Draw BMD and SFD for the following loading:
5 kN 4kN/m 5 kN 3 kN
24. Draw the shear stress diagrams for the given sections:
