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1.
If the sum of the two unit vectors is also a unit vector, then magnitude of their difference is
2.
A force 
(where 
is a positive constant) acts on a particle moving in the 
plane. Starting from the origin, the particle is taken along the positive 
-axis to the point (
) and then parallel to the 
-axis to the 
. The total work done by the force 
on the particle is
(where is a positive constant) acts on a particle moving in the plane. Starting from the origin, the particle is taken along the positive -axis to the point () and then parallel to the -axis to the . The total work done by the force on the particle is
3.
A projectile can have the same range 
for two angles of projection. If 
and 
be the times of flights in the two cases, then the product of the two times of flights is directly proportional to
for two angles of projection. If and be the times of flights in the two cases, then the product of the two times of flights is directly proportional to
4.
A projectile shot into air at some angle with the horizontal has a range of 200 m. If the time of flight is 5 s, then the horizontal component of the velocity of the projectile at the highest point of trajectory is
5.
If 
=
and 
, then angle between and 
is
= and , then angle between and is
6.
A body slides down a frictionless track which ends in a circular loop of diameter 
. Then the minimum height 
of the body in terms of so that it may just complete the loop, is
. Then the minimum height of the body in terms of so that it may just complete the loop, is
7.
A particle moves in a circular path with decreasing speed. Choose the correct statement
8.
A stone of mass 
tied to a light inextensible string of length 
is whirling in a circular path of radius 
in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if 
is taken to be 
the speed of the stone at the highest point of the circle is
tied to a light inextensible string of length is whirling in a circular path of radius in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if is taken to be the speed of the stone at the highest point of the circle is
9.
A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of path and the body is 0.5. The angular velocity, in radians/sec, with which the body should move so that it does not leave the path is 
10.
Two particles of equal mass are connected to a rope 
of negligible mass such that one is at end 
and other dividing the length of rope in the ratio 
from 
. The rope is rotated about end in a horizontal plane. Ratio of tensions in the smaller part to the other is (ignore effect of gravity)
of negligible mass such that one is at end and other dividing the length of rope in the ratio from . The rope is rotated about end in a horizontal plane. Ratio of tensions in the smaller part to the other is (ignore effect of gravity)