the mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)ⁿ and (average velocity)^m of the liquid. which one of the following relations is correct?

• m=n

• m=-n

• m²= n

• m = -n²

the ratio of the dimensions of Plank's constant and that of the moment of inertia has the dimensions of

• angular momentum

• time

• velocity

• frequency

if the absolute errors in two physical quantities A and B are a and b respectively, then the absolute error in the value of A-B is

• b-a

• a/b

• a+b

• a-b

A vector a is turned without a change in its length through a small angle  $d\theta$  , the value of  $\left|\Delta a\right|$  is 

•  $a.d\theta$  

•  $2a\ \sin\left(\frac{d\theta}{2}\right)$  

• 0

• none of these

the resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. the angle between the two forces is

• 120^o

• 135^o

• 90^o

• 150^o

if A and B are two non-zero vectors having equal magnitude, the angle between the vectors A and A-B is

• 0^o

• 90^o

• 180^o

• dependent on the orientation of A and B

which of the following statement is true?

• when the coordinate axes have translated the component of a vector in a plane changes.

• when the coordinate axes are rotated through some angle components of the vectors change but the vector's magnitude remains constant.

• the sum of a and b is R. if the magnitude of a alone is increased angle between b and R decreases.

• the cross product of vectors 3i and 4j is 12.

In one dimensional motion, instantaneous speed v satisfies 0 ≤ v < v₀

• The displacement in time T must always take non-negative values.

• The displacement x in time T satisfies – v_o T < x < v_o T.

• The acceleration is always a non-negative number.

• The motion has no turning points.

the displacement (x) of a particle depends on time I as

The motion has no turning points  $x\ =\ \alpha t^2-\beta t^3$  . choose the incorrect statements from the following-

• the particle never returns to the starting point.

• the particle comes to the rest after time  $\frac{2\alpha}{3\beta}$  

• the initial velocity of the particle is zero.

• the initial acceleration of the particle is zero. 

The displacement - time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point :

• E

• F

• C

• D