Q. 1
What would be the scalar product between two vectors -3î + 2ĵ - 4k̂ and 5ĵ - 7k̂?
• a. 37
• b. 38
• c. -38
• d. -37
• e. 36

• Explaination: Explanation: Scalar product is given by A – B
A – B = (-3î + 2ĵ - 4k̂) – (0î + 5ĵ - 7k̂)
A – B = (-3î ― 0î) + (2ĵ ― 5ĵ) + (- 4k̂ ―-7k̂)
A – B = 0 + 10 + (28)
A – B = 38
Therefore, B is the correct answer option.
Q. 2
A train at rest starts from station A and travels to station B at a distance of 2 km in 4 minutes? Consider the following statements.
1. Instantaneous speed of the train is 8.33 m/s
2. Average speed of the train is 8.33 m/s
3. Instantaneous acceleration of the train is 8.33 m/s2
Which of the following statement(s) is/are true?
• a. 1
• b. 2
• c. 3
• d. Both 1 and 3
• e. Both 2 and 3

• Explaination: Explanation: Average speed = (Total distance) / (Total time) -------------- (1)
Total distance = 2 km and total time = 4 minutes.
Since, distance and time are given in kilometers and minutes we need to convert them into meters and seconds.
Average speed = 2000/240 = 8.33 m/s
Instantaneous acceleration is related to instantaneous speed. Hence, instantaneous acceleration cannot be found here. Thus, B is the correct answer option.
Q. 3
Consider the figure given below for a system of two iron blocks connected with a common pulley. If the block A weighs 200 N, what would be the mass of the iron block B to keep the whole system in static equilibrium?
• a. 20.41 kg
• b. 15.57 kg
• c. 22.23 kg
• d. 34.45 kg
• e. 21.45 kg

• Explaination: Explanation: As the whole system is in static equilibrium, there will be no motion in the blocks. Therefore,
Weight of A = Weight of B = 200 N
Weight of a body is given as
W = mg
200 = m * 9.8
M = 20.41 kg
Therefore, A is the correct answer option.
Q. 4
A boy of 45 kg jumps out of a window and just before reaching the ground his speed is 2 m/s. After he hits the ground he stops and total time taken during this process is 1 s. What is the force exerted by the ground on the boy?
• a. 45 N
• b. 22.5 N
• c. 180 N
• d. 90 N
• e. 85 N

• Explaination: Explanation: F = p/t and p = mv
p = 45*2
p = 90 kg m/s
F = 90/1 Or, F = 90N
Therefore, D is the correct answer option.
Q. 5
If a ferry-wheel completes 100 rotations in 15 s, with what velocity is it rotating?

• Explaination: Explanation: Velocity with which the ferry-wheel is rotating is its angular velocity. It is given as
ω = (N*2Π)/t ------------ (1)
Putting the values is equation 1 we get
ω = (100*2Π)/15
Therefore, A is the correct answer option.
Q. 6
A 5 kg block of ice, kept at some height, has the potential energy of 1000 Joules. What is the height at which the block has been kept?
• a. 20.4 m
• b. 21.2 m
• c. 10.5 m
• d. 11.4 m
• e. 24.3 m

• Explaination: Explanation: Potential energy is given as
PE = mgh
1000 = 5*9.8*h
[1000/(5*9.8)] = h
h = 20.4 m
Hence, A is the correct answer option.
Q. 7
For a body in SHM, the maximum displacement of the body on either sides of the equilibrium is known as
• a. Amplitude
• b. Wavelength
• c. Period
• d. Frequency
• e. Speed