AOA

I am starting this thread in order to solve problems in Applied Mathematics. I want all the members and specially seniors who have opted Applied Mathematics to solve the past papers and also check the solutions made by others.

Plz participate in this task.


Regards

Select the best answer and fill in the appropriate box in the answer sheet.


1. The two non zero vectors A and Bare parallel if

(a) AxB = 0 (b)|AxB|=1
(c) A.B=0 (d) |A|=|B|
(e) none of these

2. The displacement of a point moving in a straight line is S=8t^2+3t-5, S is measured in meters and t in seconds. The velocity if displacement is zero,is
(a) 3 m/s (b) 13 m/s
(c) 16 m/s (d) 12 m/s
(e) none of these (if displacement is zero then velocity should also b zero)
_ _ _
3. The volume of the parallelO'piped with sides A=6i'-2j' , B=j' +2k', C =i'+j'+k' is
(a) 5 cubic units (b) 10 cubic units
(c) 15 cubic units (d) 20 cubic units
(e) none of these
_ _ _
4. Three vectors A, B, C are coplanar, the value of their scalar triple product is
(a) 0 (b) 1
(c) 2 (d) 3
(e) none of these

5. If a is the angle between two vectors A, B such that |AxB|=|A.B| then a is

(a) 0 (b) 45
(c) 120 (d) 180
(e) none of these

6. Which two of the following vectors are perpendicular to eachother P=3i'+2j'+4k', Q=12i'+8j'+16k', R=2i'-11j'+4k'.
(a) R,P (b) P,Q
(c) Q,R (d) none of these

7. A force F is conservative if
(a) div F=0 (b) curl F=0
(C) div(curl F)=0 (d) curl(curl F)=0
(e) none of these

8. If M,L,F denote the dimensions of mass, length, force respectively. then the dimensions of time is.
(a) L(MF)^1/2 (b) (LM)^1/2 F^(-1/2)
(c) L^1/2 M F^1/2 (d) LM F^(-1/2)
(e) none of these

9. If F is magnitude of friction, R that of normal reaction and U(mu) the coefficient of friction then
(a) U=F R (b) U=F/R
(c) U=FR^(-1/2) (d) U=F/R^2
(e) none of these

10. If A is any differentiable vector function then Grad(div A) is
(a) Zero (b) curl(curl A) + del^2 A(its ans is (div A) del which is not equal to given)
(c) del^2 A (d) curl A
(e) none of these

11. If r is position vector then div r is
(a) 0 (b) 1
(C) 3 (d) undefined
(e) none of these

12. In CGS system unit of angular momentum is
(a) g cm/s^3 (b) g^2 cm/s^3
(C) g cm^2/s (d) g cm^2/s^2
(e) none of these

13. The workdone by the force F=4i'-6j'+3k', through distance r=3i'-10j'-3k' is
(a) 57 (b) 60
(c) 61 (d) 63
(e) none of these

16. If Q is a force and AB the arm of couple then moment of couple is
(a) AB x Q (b) Q x AB
(c) 2 AB x Q (d) AB x 2 Q
(e) none of these

17. The magnitude of a vector is never
(a) positive (b) negative
(c) Zero (d) unity
(e) none of these

18. vectors (p,q) and (5,1) are parellel only if
(a) p+q=5 (b) pq=5
(c) 5p=q (d) p=5q
(e) none of these

19. The points whose position vectors are 2a+3b-c, a-2b+3c, 3a+4b-2c, a-6b+6c form a
(a) trapezium (b) tetrahedron
(c) square (d) parallelogram
(e) none of these

20. The vector i' x (a x i') + j' x (a x j') + k' x (a x k') equals
(a) 2 a (b) 3 a
(c) 0 (d) a
(e) none of these

21. For three vectors u, v, w which of the following expressions is not equal to the remaining three
(a) u.( v x w) (b) v.( u x w)
(c) (v x w).u (d) u.(v.w)
(e) none of these

22. For vectors a,b,c in three dimensional space a. ( b x c) is
(a) a vector perpendicular to plane of b , c.
(b) a vector lying in the plane of b , c.
(c) same as a x ( b x c)
(d) same as a . ( b x c)( as its not a vector)
(e) none of these

23. The resultant R of two like forces Q and P is
(a) PQ (b) P-Q
(c) P+Q (d) Q-P
(e) none of these

24. Coefficient of friction is

(a) normal reaction/ limiting friction
(b) limiting friction/ normal reaction
(c) normal reaction/ angle of friction
(d) limiting friction/ angle of friction
(e) none of these

25. If M,L,T denote the dimensions of mass, length, time respectively. then dimension of work is
(a) M L^2/T (b) M L^2 T^2
(c) M L^2/T^2 (d) M L^2/T
(e) none of these

Although I can't, as yet, help you in answering/checking questions as I am yet to go through the complete syllabus yet. However, I was wondering if you could help me with this questions:

Intro to Mechanics: Q.K. Ghori

Question 4

I can get to the first part of the result that is:

4r cos2(Theta) = L cos(theta)

However, it is the second part i.e. L > {(2(6)^0.5 . r) / 3

I look forward to your response.

Did you study all the chapters of Q.k Ghori and solved all the exercises or just the relevant topics as per to syllabus. Can You Please bestow me with all of your conclusions regardin to your CSS experience. I've Physics, app math and indo pak as my optional subjects. Thanks

I am opting for applied mathematics and physics for appearing in 2013. I am starting my studies now. Is the time enough for me to cover all the subjects. Please help me regarding books of applied mathematics and physics and topics to be covered from these books. Also share your experience of both subjects.