Physics Department, Panskura Banamali College by Dr. Abhijit Kar Gupta

Physics Hons., 1st Year : Surprise Test-2006 on Vector Analysis (Tick the correct answer) 1. If the two vectors are kjiA

)))++= 43 and kjiB

)))+−= then

(a) they are orthogonal, (b) orthonormal (c) anti-parallel, (d) none of these

2. The directional derivative of 22),( yxyxf += at (1,1) along jiu ˆ23ˆ

21ˆ += is

(a) 2

32 + , (b) 0, (c) 31+ (d) 1

3. If r1

=φ , then φ2∇ is

(a) 1, (b) -1, (c) 0, (d) 2

1r

4. =

×∇ 2rr ?

(a) r , (b) 0, (c) r− , (d) r)

5. For a particle moving in a circular orbit trjtrir ωω sincos))

+= , the value of dtrdr × is

(a) riω)

, (b) 2rkω)

, (c) 2rjω)

, (d) 22 rjri ωω))

+ 6. If we have a force jxiyF

))+= , then the work done along a circular path in the xy-

plane from 0=θ to 2πθ = is

(a) π , (b) 2π , (c) 0, (d) 1 7. If rV ×= ω , and ω is a constant vector then V×∇ =? (a) ω , (b) ω2 , (c) ω− , (d) 0

8. The vector 3rr is

(a) irrotational, (b) solenoidal, (c) both irrotational and solenoidal, (d) none of these 9. If a is a constant vector and r is the radius vector then ( )=××∇ ra ?

(a) a , (b) 2a , (c) 0, (d) r 10. Find the angle between two vectors a and b if baba ⋅=×

(a) 30 o , (b) 0, (c) 45 o , (d) 90 o