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