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
 Answer: B

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/s^{2}
Which of the following statement(s) is/are true?
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/s^{2}
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
 Answer: B

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
 Answer: A

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
 Answer: D

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 ferrywheel completes 100 rotations in 15 s, with what velocity is it rotating?
 a. 41.87 rad/s
 b. 42.34 rad/s
 c. 40.56 rad/s
 d. 45.45 rad/s
 e. 6.67 rad/s
 Answer: A

Explaination: Explanation: Velocity with which the ferrywheel 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
ω = 41.87 rad/s
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
 Answer: A

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
 Answer: A
 Explaination: Explanation: A body in SHM moves under a restoring force. The restoring force is always directed towards the equilibrium position. Displacement of a body in SHM is measured as the difference between the final position and the position of equilibrium. Amplitude in SHM is the maximum displacement of the body from the position of equilibrium. In other words, it can be said that amplitude is the maximum displacement of the body on either sides of the equilibrium as the body is SHM will continue performing a to and fro motion. Therefore, A is the correct answer option. Time period or period is the time taken to complete one cycle of oscillation. Hence, C is an incorrect option. Wavelength is the distance between two consecutive maxima of a wave. Therefore, B is an incorrect answer option. Frequency of a body is defined as the number of oscillations about the equilibrium position per second. Therefore, D is an incorrect option. The magnitude of velocity with which the body in SHM moves is known as its speed. Therefore, E is an incorrect option.
Q. 8
A tuning fork is making a sound between the frequency range of 200 Hz and 1000 Hz. Which of the following is a correct representation for the range of wavelength of sound that the tuning fork is making? (Speed of sound in air is 340 m/s)
 a. 0.14 m ≤ λ ≤ 0.7 m
 b. 0.54 m ≤ λ ≤ 1.7 m
 c. 0.34 m ≤ λ ≤ 1.7 m
 d. 0.24 cm
 e.
 Answer: A