Q.1
The vectors 3i - 2j + k and 2i + 6j + ck are perpendicular when
  • a) c=6
  • b) c=1
  • c)c=3
  • d)c=8
Q.2
If two forces are equal and their resultant is also equal to one of them, then angle between the two forces is
  • a) 60°
  • b) 120°
  • c) 90°
  • d) 0°
Q.3
A boy is hanging from a horizontal branch of tree. The tension in the arms will be maximum when angle between arms is
  • a)0°
  • b) 30°
  • c)60°
  • d)120°
Q.4
Find the value of c is A=0.4i + 0.3j+ck is a unit vector
  • a) 0.5
  • b) √(0.75)
  • c)1
  • d)can not be calculated
Q.5
A bird is flying towards south with velocity 40km/hr and a train is moving with a velocity 40km/hr towards east. What is the velocity of the bird w.r.t. an observer in train
  • a) 40√2 km/hr north-east
  • b) 40√2 km/hr south-east
  • c)40√2 km/hr south-west
  • d)40√2 km/hr north-west
Q.6
The area of a parallelogram formed from the vector A=i + 2j + 3k and B=3i - 2j + k as adjacent sides is
  • a) 8√3 units
  • b) 64 units
  • c) 32 units
  • d) √3 units
Q.7
The resultant of two forces has magnitude 20 Newton. One of the forces is of magnitude 20√3 Newton and makes an angle of 30° with the resultant. Then, the other force must be of magnitude
  • a)10N
  • b) 20 N
  • c)20√3 N
  • d)10√3 N
Q.8
Two forces, one of 10N and other 6N act upon a body. The direction of the forces are unknown, the resultant force on the body is
  • a) Not less than 4N and not more than 16N
  • b) More than 15N always
  • c)More than 6N
  • d)More than 10N
Q.9
The vector sum of N coplanar forces each of magnitude F, when each force is making an angle of 2π/N with the preceding one is
  • a) N F
  • b)N (F/2)
  • c)F/2
  • d)zero
Q.10
A boat moves with speed of 5km/hr relative to water in river flowing with speed of 3 km/hr and having a width of 1km. The time taken around trip is
  • a) 5 min
  • b) 60 min
  • c) 20 min
  • d) 30 min
Q.11
A vector A of magnitude 10 units and another vector of magnitude 6 units are acting at 60° to each other. The magnitude of vector product of two vector is
  • a)30 units
  • b) 60 unit
  • c)30√3 unit
  • d)none of the above
Q.12
The magnitude of vector can not be
  • a) unity
  • b) positive
  • c)negative
  • d)zero
Q.13
A river is flowing at the rate of 6 km/hr. A swimmer swims across with a velocity of 9 km/hr. The resultant velocity of the man will be in(km/hr)
  • a) √(117)
  • b) √(340)
  • c)√(17)
  • d)3√(40)
Q.14
The area of parallelogram with sides as A=2i + 3j and B=i + 4j
  • a) 5 units
  • b) 10 units
  • c) 15 units
  • d) 20 units
Q.15
To a person going east in a car with velocity of 25 km/hr a train appearing to move towards north with velocity of 25√3 km/hr. The actual velocity of the train will be
  • a)25 km/hr
  • b) 50km/hr
  • c)5 km/hr
  • d)5√3 km/hr
Q.16
At what angle two forces 2F and √2F acts, so that the resultant force is F√(10) N
  • a) 45°
  • b) 60°
  • c)120°
  • d)90°
Q.17
A stone is dropped from the window of a train moving along a horizontal straight track, the path of the stone as observed by an observer on ground is
  • a) straight line
  • b) parabolic
  • c)circular
  • d)hyperbolic
Q.18
A grasshopper can jump a maximum horizontal distance of 20 cm. If it spends negligible time on the ground, what is its speed of travel along the road
  • a) √2 m/s
  • b) 1 m/s
  • c) (1/√2) m/s
  • d) can not be calculated
Q.19
A particle is projected such that the horizontal range and vertical height are same. Then the angle of projection is
  • a)π/4
  • d)π/3
  • b) tan⁻¹(4)
  • c)tan⁻¹(1/4)
Q.20
The height y and the distance x along the horizontal plane of projectile on a certain planet ( with no surrounding atmosphere) are given by y=(8t-5t2) m and x=6t metre where t is in seconds. The velocity with which the projectile is projected is
  • a) 8 m/sec
  • b) 6 m/sec
  • c) 10 m/sec
  • d) not obtainable from the data
Q.21
A gun fires two bullets at 60° and 30° with horizontal. The bullets strikes at same horizontal distance. The ratio of maximum height for the two bullets is in the ratio
  • a)2:1
  • b) 3:1
  • c)4:1
  • d)1:1
Q.22
A hose pipe lying on the ground shoots a stream of water upward at an angle of 60° to the horizontal. The speed of the water is 20m/sec as it leaves the hose. It will strike the wall 10 m away at a height of
  • a) 10.5 m
  • b) 12.32 m
  • c)10.0 m
  • d)20.0 m
Q.23
A particle having a mass 0.5 kg is projected under gravity with speed of 98m/s at an angle of 60°. The magnitude of the change of momentum of the particle after 10 seconds is
  • a) 0.5 N-sec
  • b) 49 N-sec
  • c)98 N-sec
  • d)490 N-sec
Q.24
The range of a particle when launched at an angle of 15° with horizontal is 1.5km. What is the range of the projectile when launched at an angle of 45° to the horizontal.
  • a) 1.5 km
  • b) 3.0 km
  • c) 6.0 km
  • d) 0.75 km
Q.25
A projectile of mass m is fired with velcoity v from a point A at an angle of 45°. Neglecting air resistance, the magnitude of change in momentum between the starting point A and the arriving point B is
  • a)mv(√2)
  • b) 2mv
  • c)(1/2) mv
  • d)√(mv)
Q.26
An areoplane is flying at a speed of 144 km/hr at an altitude of 1000 m. How far froma given target should a bomb be released from it to hit the target
  • a) 571.43 m
  • b) 671.43 m
  • c)471.34 m
  • d)371.34 m
Q.27
The maximum range of a gun on a horizontal terrain is 16 km. If g=10 m/s2, the muzzle velocity of the shell must be
  • a)400 m/sec
  • b) 160√(10) m/sec
  • c)1600 m/sec
  • d)200√2 m/sec
Q.28
The greatest range of rifle bullet on level ground is 6000 m. Its maximum range up to an incline of 30° is
  • a) 1000 m
  • b) 2000 m
  • c) 4000 m
  • d) 6000 m
Q.29
Minimum number of equal forces required for a zero resultant is
  • a)2
  • b) 3
  • c)4
  • d)1
Q.30
Minimum number of unequal forces required for a zero resultant is
  • a) 2
  • b) 3
  • c)4
  • d)1
0 h : 0 m : 1 s