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1. What is the SI unit of work?
ⓐ. Joule
ⓑ. Newton
ⓒ. Watt
ⓓ. Erg
Correct Answer: Joule
Explanation: The SI unit of work is the joule, defined as the amount of work done when a force of one newton displaces an object by one meter in the direction of the force.
2. Which of the following statements is true about kinetic energy?
ⓐ. It is directly proportional to the mass and velocity of an object
ⓑ. It is directly proportional to the square of the velocity
ⓒ. It is inversely proportional to the mass of the object
ⓓ. It is inversely proportional to the velocity of the object
Correct Answer: It is directly proportional to the square of the velocity
Explanation: Kinetic energy (KE) is given by the formula KE = (1/2)mv², indicating it is directly proportional to the mass (m) and the square of the velocity (v) of an object.
3. What is the work done by a force if there is no displacement?
ⓐ. Zero
ⓑ. Maximum
ⓒ. Minimum
ⓓ. Infinite
Correct Answer: Zero
Explanation: Work is defined as the product of the force and the displacement in the direction of the force. If there is no displacement, the work done is zero, regardless of the force applied.
4. Which form of energy is associated with an object’s position in a gravitational field?
ⓐ. Kinetic energy
ⓑ. Potential energy
ⓒ. Thermal energy
ⓓ. Mechanical energy
Correct Answer: Potential energy
Explanation: Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. It is given by the formula U = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above the reference point.
5. The power of an engine is defined as:
ⓐ. The amount of force it applies
ⓑ. The amount of work it does per unit time
ⓒ. The amount of energy it consumes
ⓓ. The maximum force it can exert
Correct Answer: The amount of work it does per unit time
Explanation: Power is the rate at which work is done or energy is transferred. It is measured in watts (W), where one watt equals one joule per second.
6. Which of the following is a non-conservative force?
ⓐ. Gravitational force
ⓑ. Electrostatic force
ⓒ. Frictional force
ⓓ. Magnetic force
Correct Answer: Frictional force
Explanation: Non-conservative forces, such as friction, cause energy dissipation (usually in the form of heat), and the work done by these forces depends on the path taken, not just the initial and final positions.
7. What is the total mechanical energy of a system?
ⓐ. The sum of kinetic energy and potential energy
ⓑ. The difference between kinetic energy and potential energy
ⓒ. Only the kinetic energy
ⓓ. Only the potential energy
Correct Answer: The sum of kinetic energy and potential energy
Explanation: The total mechanical energy of a system is the sum of its kinetic energy (KE) and potential energy (PE). It is a conserved quantity in the absence of non-conservative forces.
8. Which principle states that the total energy of an isolated system remains constant?
ⓐ. Law of conservation of mass
ⓑ. Law of conservation of momentum
ⓒ. Law of conservation of energy
ⓓ. Law of universal gravitation
Correct Answer: Law of conservation of energy
Explanation: The law of conservation of energy states that the total energy of an isolated system remains constant over time, implying that energy cannot be created or destroyed, only transformed from one form to another.
9. A body is said to be in equilibrium if:
ⓐ. It has zero velocity
ⓑ. It has constant acceleration
ⓒ. The net force acting on it is zero
ⓓ. It is moving in a circular path
Correct Answer: The net force acting on it is zero
Explanation: A body is in equilibrium if the sum of all the forces acting on it is zero, resulting in no acceleration. This can be static equilibrium (at rest) or dynamic equilibrium (moving with constant velocity).
10. What is the relationship between power (P), force (F), and velocity (v)?
ⓐ. P = F / v
ⓑ. P = F × v
ⓒ. P = F + v
ⓓ. P = F – v
Correct Answer: P = F × v
Explanation: Power is the rate of doing work. If a force is applied to move an object with a certain velocity, power can be calculated using the formula P = F × v, where F is the force and v is the velocity.
11. What is the definition of work in physics?
ⓐ. The energy required to move an object
ⓑ. The force applied to an object
ⓒ. The product of force and displacement in the direction of the force
ⓓ. The distance an object is moved
Correct Answer: The product of force and displacement in the direction of the force
Explanation: In physics, work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. Mathematically, it is expressed as \( W = F \times d \times \cos(\theta) \), where \( \theta \) is the angle between the force and the displacement vector.
12. Which of the following conditions must be met for work to be done on an object?
ⓐ. The object must move
ⓑ. The force must be constant
ⓒ. The force and displacement must be in opposite directions
ⓓ. The object must have constant velocity
Correct Answer: The object must move
Explanation: For work to be done on an object, there must be a displacement of the object. If the object does not move, no work is done, regardless of the amount of force applied.
13. What happens to the work done if the angle between the force and displacement is 90 degrees?
ⓐ. The work done is maximum
ⓑ. The work done is zero
ⓒ. The work done is negative
ⓓ. The work done is positive
Correct Answer: The work done is zero
Explanation: When the angle between the force and displacement is 90 degrees, the work done is zero because \( \cos(90^\circ) = 0 \). This means the force does not contribute to the displacement in the direction of the force.
14. How is work calculated when the force is applied at an angle to the direction of displacement?
ⓐ. \( W = F \times d \)
ⓑ. \( W = F \times d \times \cos(\theta) \)
ⓒ. \( W = F \times d \times \sin(\theta) \)
ⓓ. \( W = F / d \times \cos(\theta) \)
Correct Answer: \( W = F \times d \times \cos(\theta) \)
Explanation: When a force is applied at an angle \( \theta \) to the direction of displacement, the work done is calculated using \( W = F \times d \times \cos(\theta) \), where \( \theta \) is the angle between the force and the displacement vectors.
15. If a force of 10 N moves an object 5 meters in the direction of the force, what is the work done?
ⓐ. 2 Joules
ⓑ. 50 Joules
ⓒ. 5 Joules
ⓓ. 100 Joules
Correct Answer: 50 Joules
Explanation: The work done is calculated using the formula \( W = F \times d \). Here, \( F = 10 \) N and \( d = 5 \) m, so \( W = 10 \times 5 = 50 \) Joules.
16. A person pushes a wall with a force of 100 N but the wall does not move. How much work is done on the wall?
ⓐ. 100 Joules
ⓑ. 50 Joules
ⓒ. 0 Joules
ⓓ. 1000 Joules
Correct Answer: 0 Joules
Explanation: No work is done on the wall because there is no displacement. Work is only done when a force causes displacement in the direction of the force.
17. What is the work done by gravity when an object falls freely under the influence of gravity?
ⓐ. Zero
ⓑ. Negative
ⓒ. Positive
ⓓ. Infinite
Correct Answer: Positive
Explanation: When an object falls freely under the influence of gravity, the work done by gravity is positive because the force of gravity and the displacement of the object are in the same direction.
18. If an object is displaced at an angle to the applied force, which component of the force is used to calculate work done?
ⓐ. The entire force
ⓑ. The perpendicular component of the force
ⓒ. The horizontal component of the force
ⓓ. The component of the force in the direction of displacement
Correct Answer: The component of the force in the direction of displacement
Explanation: Only the component of the force that is in the direction of the displacement contributes to the work done. This is calculated as \( F \cos(\theta) \), where \( \theta \) is the angle between the force and the displacement.
19. Which of the following best describes negative work?
ⓐ. Work done by a force in the opposite direction to the displacement
ⓑ. Work done by a force in the same direction as the displacement
ⓒ. Work done when no displacement occurs
ⓓ. Work done when displacement is perpendicular to the force
Correct Answer: Work done by a force in the opposite direction to the displacement
Explanation: Negative work occurs when the force applied to an object is in the opposite direction to its displacement. This means the force is resisting the movement, such as friction or air resistance.
20. An object is moved 4 meters to the right while a constant force of 5 N acts to the left. What is the work done by this force?
ⓐ. 20 Joules
ⓑ. -20 Joules
ⓒ. 0 Joules
ⓓ. 10 Joules
Correct Answer: -20 Joules
Explanation: The work done by the force is negative because the force and displacement are in opposite directions. Using the formula \( W = F \times d \times \cos(180^\circ) \), where \( \cos(180^\circ) = -1 \), we get \( W = 5 \times 4 \times -1 = -20 \) Joules.
21. What type of energy is associated with the motion of an object?
ⓐ. Potential energy
ⓑ. Thermal energy
ⓒ. Kinetic energy
ⓓ. Chemical energy
Correct Answer: Kinetic energy
Explanation: Kinetic energy is the energy possessed by an object due to its motion. It is given by the formula \( KE = \frac{1}{2} mv^2 \), where \( m \) is the mass and \( v \) is the velocity of the object.
22. Which of the following is an example of potential energy?
ⓐ. A car moving at a constant speed
ⓑ. Water held behind a dam
ⓒ. A spinning wheel
ⓓ. A hot cup of coffee
Correct Answer: Water held behind a dam
Explanation: Potential energy is the energy stored in an object due to its position or state. Water held behind a dam has gravitational potential energy due to its elevated position.
23. Thermal energy is also known as:
ⓐ. Electrical energy
ⓑ. Heat energy
ⓒ. Chemical energy
ⓓ. Nuclear energy
Correct Answer: Heat energy
Explanation: Thermal energy, also known as heat energy, is the energy that comes from the temperature of matter. The faster the particles in an object move, the more thermal energy they produce.
24. Which type of energy is stored in the bonds of chemical compounds?
ⓐ. Kinetic energy
ⓑ. Thermal energy
ⓒ. Chemical energy
ⓓ. Nuclear energy
Correct Answer: Chemical energy
Explanation: Chemical energy is the energy stored in the bonds of chemical compounds, such as molecules and atoms. This energy is released during chemical reactions.
25. What type of energy is exhibited by a compressed spring?
ⓐ. Kinetic energy
ⓑ. Potential energy
ⓒ. Thermal energy
ⓓ. Electrical energy
Correct Answer: Potential energy
Explanation: A compressed spring has elastic potential energy due to its deformation. This energy can be released when the spring returns to its original shape.
26. The energy possessed by an object due to its height above the ground is called:
ⓐ. Kinetic energy
ⓑ. Thermal energy
ⓒ. Gravitational potential energy
ⓓ. Chemical energy
Correct Answer: Gravitational potential energy
Explanation: Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is given by the formula \( U = mgh \), where \( m \) is mass, \( g \) is the acceleration due to gravity, and \( h \) is the height above the ground.
27. What type of energy is associated with the random motion of particles in a substance?
ⓐ. Kinetic energy
ⓑ. Potential energy
ⓒ. Thermal energy
ⓓ. Electrical energy
Correct Answer: Thermal energy
Explanation: Thermal energy is the total kinetic energy of the particles in a substance due to their random motion. It is related to the temperature of the substance.
28. Which type of energy transformation occurs in a battery-powered flashlight?
ⓐ. Chemical to electrical to light
ⓑ. Electrical to thermal to light
ⓒ. Thermal to chemical to light
ⓓ. Kinetic to electrical to light
Correct Answer: Chemical to electrical to light
Explanation: In a battery-powered flashlight, chemical energy stored in the battery is converted to electrical energy, which then powers the light bulb to produce light energy.
29. A pendulum at its highest point has:
ⓐ. Maximum kinetic energy
ⓑ. Maximum potential energy
ⓒ. Minimum potential energy
ⓓ. Minimum thermal energy
Correct Answer: Maximum potential energy
Explanation: At the highest point of its swing, a pendulum has maximum potential energy and minimum kinetic energy. As it swings down, potential energy is converted into kinetic energy.
30. Which of the following statements is true about the conservation of energy?
ⓐ. Energy can be created and destroyed
ⓑ. The total energy of an isolated system remains constant
ⓒ. Potential energy is always greater than kinetic energy
ⓓ. Thermal energy cannot be converted into other forms of energy
Correct Answer: The total energy of an isolated system remains constant
Explanation: The law of conservation of energy states that the total energy of an isolated system remains constant over time. Energy can be transformed from one form to another but cannot be created or destroyed.
31. Which of the following is an example of kinetic energy?
ⓐ. A wound-up clock spring
ⓑ. A stretched rubber band
ⓒ. A rolling ball
ⓓ. A charged battery
Correct Answer: A rolling ball
Explanation: Kinetic energy is the energy an object possesses due to its motion. A rolling ball has kinetic energy because it is moving.
32. What type of energy conversion occurs when burning wood in a campfire?
ⓐ. Chemical to thermal and light
ⓑ. Thermal to chemical and light
ⓒ. Electrical to chemical and thermal
ⓓ. Kinetic to potential and thermal
Correct Answer: Chemical to thermal and light
Explanation: When wood burns in a campfire, the chemical energy stored in the wood is converted into thermal energy (heat) and light energy.
33. What type of energy does a rock at the edge of a cliff have?
ⓐ. Kinetic energy
ⓑ. Chemical energy
ⓒ. Potential energy
ⓓ. Thermal energy
Correct Answer: Potential energy
Explanation: A rock at the edge of a cliff has gravitational potential energy due to its elevated position above the ground. This energy can be converted into kinetic energy if the rock falls.
34. What happens to the kinetic energy of an object if its mass is doubled while its velocity remains constant?
ⓐ. It stays the same
ⓑ. It is halved
ⓒ. It is doubled
ⓓ. It is quadrupled
Correct Answer: It is doubled
Explanation: Kinetic energy is given by \( KE = \frac{1}{2} mv^2 \). If the mass \( m \) is doubled while the velocity \( v \) remains constant, the kinetic energy also doubles.
35. In which form of energy do we classify the energy stored in food?
ⓐ. Kinetic energy
ⓑ. Potential energy
ⓒ. Thermal energy
ⓓ. Chemical energy
Correct Answer: Chemical energy
Explanation: The energy stored in food is classified as chemical energy. This energy is released during digestion and used by the body to perform various functions.
36. What type of energy is primarily involved when water at the top of a waterfall flows to the bottom?
ⓐ. Thermal energy
ⓑ. Chemical energy
ⓒ. Potential energy to kinetic energy
ⓓ. Electrical energy
Correct Answer: Potential energy to kinetic energy
Explanation: Water at the top of a waterfall has gravitational potential energy. As it flows to the bottom, this potential energy is converted into kinetic energy.
37. A stretched bow possesses which type of energy?
ⓐ. Kinetic energy
ⓑ. Chemical energy
ⓒ. Elastic potential energy
ⓓ. Thermal energy
Correct Answer: Elastic potential energy
Explanation: A stretched bow has elastic potential energy due to its deformation. When released, this energy is converted into kinetic energy as the arrow is launched.
38. Which form of energy is transferred by electromagnetic waves?
ⓐ. Kinetic energy
ⓑ. Potential energy
ⓒ. Radiant energy
ⓓ. Chemical energy
Correct Answer: Radiant energy
Explanation: Radiant energy is the energy transferred by electromagnetic waves, such as light and radio waves. It is a form of energy that can travel through the vacuum of space.
39. How does the kinetic energy of an object change if its velocity is tripled?
ⓐ. It stays the same
ⓑ. It is tripled
ⓒ. It increases nine times
ⓓ. It is halved
Correct Answer: It increases nine times
Explanation: Kinetic energy is given by \( KE = \frac{1}{2} mv^2 \). If the velocity \( v \) is tripled, the kinetic energy increases by a factor of \( 3^2 = 9 \).
40. Which of the following statements is true about thermal energy?
ⓐ. It can only be transferred through conduction
ⓑ. It is the total kinetic and potential energy of the particles in an object
ⓒ. It can only be transferred through radiation
ⓓ. It is not related to the temperature of an object
Correct Answer: It is the total kinetic and potential energy of the particles in an object
Explanation: Thermal energy is the total kinetic and potential energy of the particles in an object. It is related to the temperature of the object and can be transferred through conduction, convection, and radiation.
41. Which type of energy is most important for the operation of electrical appliances?
ⓐ. Kinetic energy
ⓑ. Potential energy
ⓒ. Thermal energy
ⓓ. Electrical energy
Correct Answer: Electrical energy
Explanation: Electrical energy is crucial for the operation of electrical appliances as it powers their functions and enables them to perform their tasks.
42. In which of the following systems is chemical energy most critical?
ⓐ. Solar panels
ⓑ. Internal combustion engines
ⓒ. Wind turbines
ⓓ. Hydroelectric dams
Correct Answer: Internal combustion engines
Explanation: Internal combustion engines rely on chemical energy stored in fuels, such as gasoline or diesel, which is converted into mechanical energy to power vehicles.
43. How does the human body utilize chemical energy?
ⓐ. It converts it directly into thermal energy
ⓑ. It stores it as potential energy in muscles
ⓒ. It converts it into electrical energy to power cells
ⓓ. It converts it into kinetic and thermal energy through metabolism
Correct Answer: It converts it into kinetic and thermal energy through metabolism
Explanation: The human body metabolizes chemical energy from food, converting it into kinetic energy for movement and thermal energy to maintain body temperature.
44. What type of energy is crucial for plants during photosynthesis?
ⓐ. Chemical energy
ⓑ. Thermal energy
ⓒ. Kinetic energy
ⓓ. Radiant energy
Correct Answer: Radiant energy
Explanation: During photosynthesis, plants use radiant energy from sunlight to convert carbon dioxide and water into glucose and oxygen, storing chemical energy.
45. Which type of energy transformation occurs in a hydroelectric power plant?
ⓐ. Kinetic to electrical
ⓑ. Chemical to electrical
ⓒ. Thermal to electrical
ⓓ. Potential to electrical
Correct Answer: Potential to electrical
Explanation: In a hydroelectric power plant, the potential energy of stored water is converted into kinetic energy as it flows through turbines, generating electrical energy.
46. In a wind turbine, which form of energy is converted into electrical energy?
ⓐ. Potential energy
ⓑ. Kinetic energy
ⓒ. Chemical energy
ⓓ. Thermal energy
Correct Answer: Kinetic energy
Explanation: Wind turbines convert the kinetic energy of moving air (wind) into mechanical energy, which is then transformed into electrical energy.
47. Why is thermal energy important in climate systems?
ⓐ. It drives ocean currents and weather patterns
ⓑ. It powers solar panels
ⓒ. It stores chemical energy
ⓓ. It converts into electrical energy directly
Correct Answer: It drives ocean currents and weather patterns
Explanation: Thermal energy from the sun heats the Earth’s surface and atmosphere, driving ocean currents and weather patterns, influencing the climate system.
48. What role does kinetic energy play in transportation systems?
ⓐ. It stores potential energy
ⓑ. It powers the movement of vehicles
ⓒ. It is converted into chemical energy
ⓓ. It generates electrical energy directly
Correct Answer: It powers the movement of vehicles
Explanation: Kinetic energy is essential in transportation systems, as it powers the movement of vehicles, such as cars, trains, and airplanes, enabling them to travel from one place to another.
49. In a geothermal power plant, what type of energy is harnessed from the Earth?
ⓐ. Electrical energy
ⓑ. Kinetic energy
ⓒ. Chemical energy
ⓓ. Thermal energy
Correct Answer: Thermal energy
Explanation: Geothermal power plants harness thermal energy from the Earth’s interior, using it to generate steam that drives turbines and produces electrical energy.
50. Why is energy conservation important in modern society?
ⓐ. It reduces the availability of energy resources
ⓑ. It increases the cost of energy
ⓒ. It helps to sustain energy resources for future generations
ⓓ. It limits technological advancements
Correct Answer: It helps to sustain energy resources for future generations
Explanation: Energy conservation is crucial for sustaining energy resources, reducing environmental impact, and ensuring that future generations have access to necessary energy supplies.
51. What is the scalar product (dot product) of two vectors \(\mathbf{A}\) and \(\mathbf{B}\)?
ⓐ. A vector perpendicular to both \(\mathbf{A}\) and \(\mathbf{B}\)
ⓑ. A scalar quantity equal to the product of their magnitudes and the cosine of the angle between them
ⓒ. A scalar quantity equal to the product of their magnitudes and the sine of the angle between them
ⓓ. A vector parallel to both \(\mathbf{A}\) and \(\mathbf{B}\)
Correct Answer: A scalar quantity equal to the product of their magnitudes and the cosine of the angle between them
Explanation: The scalar product, or dot product, of two vectors \(\mathbf{A}\) and \(\mathbf{B}\) is defined as \( \mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cos \theta \), where \(\theta\) is the angle between the vectors.
52. If vectors \(\mathbf{A} = 2\mathbf{i} + 3\mathbf{j}\) and \(\mathbf{B} = 4\mathbf{i} – \mathbf{j}\), what is \(\mathbf{A} \cdot \mathbf{B}\)?
ⓐ. 5
ⓑ. 7
ⓒ. 8
ⓓ. 1
Correct Answer: 8
Explanation: The dot product \(\mathbf{A} \cdot \mathbf{B} = (2)(4) + (3)(-1) = 8 – 3 = 5\).
53. Which of the following is true about the scalar product of orthogonal vectors?
ⓐ. It is equal to the product of their magnitudes
ⓑ. It is equal to zero
ⓒ. It is always negative
ⓓ. It is equal to the sum of their magnitudes
Correct Answer: It is equal to zero
Explanation: The scalar product of orthogonal (perpendicular) vectors is zero because the cosine of the angle \(90^\circ\) between them is zero.
54. For vectors \(\mathbf{A}\) and \(\mathbf{B}\) with a scalar product \(\mathbf{A} \cdot \mathbf{B} = 0\), what can be inferred about the vectors?
ⓐ. They are parallel
ⓑ. They are orthogonal
ⓒ. They have the same magnitude
ⓓ. They are collinear
Correct Answer: They are orthogonal
Explanation: If the scalar product of two vectors is zero, it means that the cosine of the angle between them is zero, indicating that the vectors are orthogonal (perpendicular).
55. What is the scalar product of a vector \(\mathbf{A}\) with itself?
ⓐ. Zero
ⓑ. The square of its magnitude
ⓒ. Twice its magnitude
ⓓ. The negative of its magnitude
Correct Answer: The square of its magnitude
Explanation: The scalar product of a vector \(\mathbf{A}\) with itself is \(\mathbf{A} \cdot \mathbf{A} = |\mathbf{A}|^2\).
56. If vectors \(\mathbf{A} = a\mathbf{i} + b\mathbf{j}\) and \(\mathbf{B} = c\mathbf{i} + d\mathbf{j}\), what is the general expression for \(\mathbf{A} \cdot \mathbf{B}\)?
ⓐ. \(ac + bd\)
ⓑ. \(a + b + c + d\)
ⓒ. \(ad + bc\)
ⓓ. \(ab + cd\)
Correct Answer: \(ac + bd\)
Explanation: The dot product of \(\mathbf{A} = a\mathbf{i} + b\mathbf{j}\) and \(\mathbf{B} = c\mathbf{i} + d\mathbf{j}\) is \(\mathbf{A} \cdot \mathbf{B} = ac + bd\).
57. What does the scalar product (dot product) of two vectors represent geometrically?
ⓐ. The area of the parallelogram formed by the vectors
ⓑ. The projection of one vector onto the other
ⓒ. The volume of the parallelepiped formed by the vectors
ⓓ. The length of the vector perpendicular to both vectors
Correct Answer: The projection of one vector onto the other
Explanation: Geometrically, the dot product represents the projection of one vector onto the other, scaled by the magnitude of the second vector.
58. How is the scalar product (dot product) used in calculating work done by a force?
ⓐ. Work is the cross product of force and displacement
ⓑ. Work is the sum of the magnitudes of force and displacement
ⓒ. Work is the dot product of force and displacement
ⓓ. Work is the difference of the magnitudes of force and displacement
Correct Answer: Work is the dot product of force and displacement
Explanation: Work done by a force is calculated as the dot product of the force vector and the displacement vector: \( W = \mathbf{F} \cdot \mathbf{d} \).
59. If \(\mathbf{A} = 5\mathbf{i} + 2\mathbf{j}\) and \(\mathbf{B} = 3\mathbf{i} + 4\mathbf{j}\), what is the angle \(\theta\) between \(\mathbf{A}\) and \(\mathbf{B}\) given that \(\mathbf{A} \cdot \mathbf{B} = 23\)?
ⓐ. \(30^\circ\)
ⓑ. \(45^\circ\)
ⓒ. \(60^\circ\)
ⓓ. \(90^\circ\)
Correct Answer: \(45^\circ\)
Explanation: \(\cos \theta = \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|} = \frac{23}{\sqrt{5^2 + 2^2} \sqrt{3^2 + 4^2}} = \frac{23}{\sqrt{29} \sqrt{25}} = \frac{23}{\sqrt{725}}\). Solving for \(\theta\) gives approximately \(45^\circ\).
60. Which of the following statements is true regarding the scalar product of two parallel vectors?
ⓐ. It is zero
ⓑ. It is negative
ⓒ. It is equal to the product of their magnitudes
ⓓ. It is always one
Correct Answer: It is equal to the product of their magnitudes
Explanation: When two vectors are parallel, the angle between them is \(0^\circ\), and the cosine of \(0^\circ\) is 1. Thus, their scalar product is equal to the product of their magnitudes.
61. The scalar product of two vectors \(\mathbf{A}\) and \(\mathbf{B}\) can be geometrically interpreted as which of the following?
ⓐ. The volume of the parallelepiped formed by the vectors
ⓑ. The length of the perpendicular vector
ⓒ. The area of the parallelogram formed by the vectors
ⓓ. The product of the magnitudes of the vectors and the cosine of the angle between them
Correct Answer: The product of the magnitudes of the vectors and the cosine of the angle between them
Explanation: Geometrically, the scalar product (dot product) of two vectors \(\mathbf{A}\) and \(\mathbf{B}\) is equal to \(|\mathbf{A}| |\mathbf{B}| \cos \theta\), where \(\theta\) is the angle between the vectors.
62. If the scalar product of two non-zero vectors \(\mathbf{A}\) and \(\mathbf{B}\) is zero, what does this imply about the vectors?
ⓐ. They are parallel
ⓑ. They are perpendicular
ⓒ. They have the same magnitude
ⓓ. They are anti-parallel
Correct Answer: They are perpendicular
Explanation: If the scalar product of two vectors is zero, the cosine of the angle between them is zero, implying that the vectors are perpendicular (orthogonal).
63. For vectors \(\mathbf{A}\) and \(\mathbf{B}\) with an angle \(\theta\) between them, which of the following represents the dot product \(\mathbf{A} \cdot \mathbf{B}\)?
ⓐ. \(|\mathbf{A}| |\mathbf{B}| \sin \theta\)
ⓑ. \(|\mathbf{A}| |\mathbf{B}| \cos \theta\)
ⓒ. \(|\mathbf{A}|^2 + |\mathbf{B}|^2\)
ⓓ. \(\sqrt{|\mathbf{A}|^2 + |\mathbf{B}|^2}\)
Correct Answer: \(|\mathbf{A}| |\mathbf{B}| \cos \theta\)
Explanation: The dot product of two vectors is given by the formula \(\mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cos \theta\), where \(\theta\) is the angle between the vectors.
64. What does a positive scalar product of two vectors indicate about the angle between them?
ⓐ. The angle is less than \(90^\circ\)
ⓑ. The angle is exactly \(90^\circ\)
ⓒ. The angle is greater than \(90^\circ\)
ⓓ. The angle is exactly \(180^\circ\)
Correct Answer: The angle is less than \(90^\circ\)
Explanation: A positive scalar product indicates that the cosine of the angle between the vectors is positive, meaning the angle is less than \(90^\circ\).
65. Which of the following scenarios would result in a negative scalar product?
ⓐ. The vectors are parallel
ⓑ. The vectors are perpendicular
ⓒ. The vectors form an angle greater than \(90^\circ\)
ⓓ. The vectors form an angle of \(0^\circ\)
Correct Answer: The vectors form an angle greater than \(90^\circ\)
Explanation: A negative scalar product occurs when the cosine of the angle between the vectors is negative, meaning the angle is greater than \(90^\circ\).
66. When two vectors \(\mathbf{A}\) and \(\mathbf{B}\) are aligned in the same direction, what is their scalar product?
ⓐ. Zero
ⓑ. Positive
ⓒ. Negative
ⓓ. Cannot be determined
Correct Answer: Positive
Explanation: When two vectors are aligned in the same direction, the angle between them is \(0^\circ\), and the cosine of \(0^\circ\) is 1, resulting in a positive scalar product.
67. How is the scalar product related to the projection of one vector onto another?
ⓐ. The scalar product equals the projection of the first vector onto the second
ⓑ. The scalar product is unrelated to the projection
ⓒ. The scalar product is the sum of the magnitudes of the vectors
ⓓ. The scalar product is the projection of one vector onto the other, multiplied by the magnitude of the other vector
Correct Answer: The scalar product is the projection of one vector onto the other, multiplied by the magnitude of the other vector
Explanation: The scalar product \(\mathbf{A} \cdot \mathbf{B}\) can be interpreted as the projection of \(\mathbf{A}\) onto \(\mathbf{B}\), multiplied by the magnitude of \(\mathbf{B}\).
68. If vectors \(\mathbf{A}\) and \(\mathbf{B}\) are orthogonal, what is their scalar product?
ⓐ. Equal to \(|\mathbf{A}| |\mathbf{B}|\)
ⓑ. Equal to zero
ⓒ. Equal to the magnitude of \(\mathbf{A}\)
ⓓ. Equal to the magnitude of \(\mathbf{B}\)
Correct Answer: Equal to zero
Explanation: When vectors \(\mathbf{A}\) and \(\mathbf{B}\) are orthogonal, the angle between them is \(90^\circ\), and the cosine of \(90^\circ\) is zero, resulting in a scalar product of zero.
69. Which of the following represents the geometric interpretation of the scalar product in terms of angle?
ⓐ. \(\sin \theta\) between the vectors
ⓑ. \(\cos \theta\) between the vectors
ⓒ. \(\tan \theta\) between the vectors
ⓓ. The product of the angles between the vectors
Correct Answer: \(\cos \theta\) between the vectors
Explanation: The scalar product of two vectors is directly related to the cosine of the angle between them, providing a geometric interpretation.
70. What is the effect on the scalar product if one of the vectors is scaled by a factor of 2?
ⓐ. The scalar product is halved
ⓑ. The scalar product remains the same
ⓒ. The scalar product is doubled
ⓓ. The scalar product becomes zero
Correct Answer: The scalar product is doubled
Explanation: If one of the vectors is scaled by a factor of 2, the scalar product is also scaled by the same factor, resulting in the product being doubled.
71. Which of the following properties does the scalar product of two vectors satisfy?
ⓐ. Commutativity
ⓑ. Anti-commutativity
ⓒ. Distributivity over scalar addition
ⓓ. Distributivity over vector subtraction
Correct Answer: Commutativity
Explanation: The scalar product of two vectors is commutative, meaning \(\mathbf{A} \cdot \mathbf{B} = \mathbf{B} \cdot \mathbf{A}\).
72. If \(\mathbf{A} \cdot \mathbf{A} = |\mathbf{A}|^2\), what property of the scalar product is demonstrated?
ⓐ. Commutativity
ⓑ. Distributivity
ⓒ. Associativity
ⓓ. Self-product property
Correct Answer: Self-product property
Explanation: The self-product property states that the scalar product of a vector with itself is equal to the square of its magnitude: \(\mathbf{A} \cdot \mathbf{A} = |\mathbf{A}|^2\).
73. Which of the following is true for the scalar product of a vector with the zero vector?
ⓐ. It is equal to the magnitude of the vector
ⓑ. It is equal to one
ⓒ. It is equal to the magnitude of the zero vector
ⓓ. It is equal to zero
Correct Answer: It is equal to zero
Explanation: The scalar product of any vector with the zero vector is zero, \(\mathbf{A} \cdot \mathbf{0} = 0\).
74. If \(\mathbf{A} \cdot (\mathbf{B} + \mathbf{C}) = \mathbf{A} \cdot \mathbf{B} + \mathbf{A} \cdot \mathbf{C}\), what property of the scalar product is illustrated?
ⓐ. Commutativity
ⓑ. Distributivity
ⓒ. Associativity
ⓓ. Linearity
Correct Answer: Distributivity
Explanation: The distributive property of the scalar product states that the scalar product of a vector with the sum of two vectors is equal to the sum of the scalar products: \(\mathbf{A} \cdot (\mathbf{B} + \mathbf{C}) = \mathbf{A} \cdot \mathbf{B} + \mathbf{A} \cdot \mathbf{C}\).
75. What is the scalar product of two vectors \(\mathbf{A}\) and \(\mathbf{B}\) if the angle between them is \(180^\circ\)?
ⓐ. Zero
ⓑ. Positive
ⓒ. Negative
ⓓ. Equal to the sum of their magnitudes
Correct Answer: Negative
Explanation: The angle \(180^\circ\) corresponds to \(\cos(180^\circ) = -1\). Thus, the scalar product is negative: \(\mathbf{A} \cdot \mathbf{B} = -|\mathbf{A}| |\mathbf{B}|\).
76. Which of the following indicates that the scalar product of two vectors is a scalar quantity?
ⓐ. It is a vector
ⓑ. It is a matrix
ⓒ. It is a magnitude without direction
ⓓ. It has both magnitude and direction
Correct Answer: It is a magnitude without direction
Explanation: The scalar product results in a scalar quantity, which has magnitude but no direction.
77. How does the scalar product change if both vectors are scaled by a factor of \(k\)?
ⓐ. It is scaled by \(k\)
ⓑ. It is scaled by \(k^2\)
ⓒ. It remains the same
ⓓ. It becomes zero
Correct Answer: It is scaled by \(k^2\)
Explanation: If both vectors are scaled by a factor \(k\), the scalar product is scaled by \(k^2\): \((k\mathbf{A}) \cdot (k\mathbf{B}) = k^2 (\mathbf{A} \cdot \mathbf{B})\).
78. Which property of the scalar product is demonstrated by \(\mathbf{A} \cdot \mathbf{B} = \mathbf{B} \cdot \mathbf{A}\)?
ⓐ. Distributivity
ⓑ. Commutativity
ⓒ. Associativity
ⓓ. Linearity
Correct Answer: Commutativity
Explanation: The commutative property states that the order of the vectors in the scalar product does not matter: \(\mathbf{A} \cdot \mathbf{B} = \mathbf{B} \cdot \mathbf{A}\).
79. The scalar product of two perpendicular vectors is:
ⓐ. Positive
ⓑ. Negative
ⓒ. Zero
ⓓ. Undefined
Correct Answer: Zero
Explanation: The scalar product of two perpendicular vectors is zero because the cosine of \(90^\circ\) is zero.
80. What does the distributive property of the scalar product allow us to do?
ⓐ. Multiply vectors in any order
ⓑ. Add the magnitudes of vectors
ⓒ. Distribute the scalar product over vector addition
ⓓ. Scale the vectors independently
Correct Answer: Distribute the scalar product over vector addition
Explanation: The distributive property allows the scalar product to be distributed over vector addition: \(\mathbf{A} \cdot (\mathbf{B} + \mathbf{C}) = \mathbf{A} \cdot \mathbf{B} + \mathbf{A} \cdot \mathbf{C}\).
81. In the context of work done by a force, the scalar product is used to calculate:
ⓐ. The angle between force and displacement
ⓑ. The magnitude of the force
ⓒ. The component of the force in the direction of displacement
ⓓ. The total energy
Correct Answer: The component of the force in the direction of displacement
Explanation: The work done by a force is calculated as the scalar product of the force and the displacement, which gives the component of the force in the direction of displacement times the magnitude of the displacement.
82. How is the work done by a constant force \(\mathbf{F}\) over a displacement \(\mathbf{d}\) calculated?
ⓐ. \(\mathbf{F} \times \mathbf{d}\)
ⓑ. \(\mathbf{F} \cdot \mathbf{d}\)
ⓒ. \(\mathbf{F} + \mathbf{d}\)
ⓓ. \(\mathbf{F} / \mathbf{d}\)
Correct Answer: \(\mathbf{F} \cdot \mathbf{d}\)
Explanation: The work done by a constant force is calculated using the scalar product of the force and the displacement: \(W = \mathbf{F} \cdot \mathbf{d}\).
83. If a force \(\mathbf{F}\) acts at an angle \(\theta\) to the direction of displacement \(\mathbf{d}\), the work done is:
ⓐ. \(|\mathbf{F}| |\mathbf{d}| \sin \theta\)
ⓑ. \(|\mathbf{F}| |\mathbf{d}| \cos \theta\)
ⓒ. \(|\mathbf{F}| + |\mathbf{d}|\)
ⓓ. \(|\mathbf{F}| |\mathbf{d}| \tan \theta\)
Correct Answer: \(|\mathbf{F}| |\mathbf{d}| \cos \theta\)
Explanation: The work done by the force is given by the scalar product, which involves the cosine of the angle between the force and displacement vectors: \(W = |\mathbf{F}| |\mathbf{d}| \cos \theta\).
84. In the context of torque, the scalar product is used to calculate which of the following?
ⓐ. The magnitude of the force
ⓑ. The perpendicular component of the force
ⓒ. The angular velocity
ⓓ. None of the above
Correct Answer: None of the above
Explanation: Torque is calculated using the vector product (cross product), not the scalar product. The scalar product is not directly used in the calculation of torque.
85. How is the work done by a variable force \(\mathbf{F}(t)\) over a displacement \(\mathbf{d}(t)\) generally calculated?
ⓐ. \(\int \mathbf{F}(t) \cdot \mathbf{d}(t) \, dt\)
ⓑ. \(\int \mathbf{F}(t) \times \mathbf{d}(t) \, dt\)
ⓒ. \(\int \mathbf{F}(t) + \mathbf{d}(t) \, dt\)
ⓓ. \(\int \mathbf{F}(t) / \mathbf{d}(t) \, dt\)
Correct Answer: \(\int \mathbf{F}(t) \cdot \mathbf{d}(t) \, dt\)
Explanation: For a variable force, the work done is calculated by integrating the scalar product of the force and the infinitesimal displacement over the path of motion: \(W = \int \mathbf{F}(t) \cdot \mathbf{d}(t) \, dt\).
86. Which physical quantity is obtained by the scalar product of the position vector and the force vector in rotational motion?
ⓐ. Torque
ⓑ. Angular momentum
ⓒ. Work
ⓓ. None of the above
Correct Answer: None of the above
Explanation: In rotational motion, torque is calculated using the cross product of the position vector and the force vector, not the scalar product.
87. In terms of work done by a force, if the angle between the force vector and the displacement vector is \(90^\circ\), what is the work done?
ⓐ. Maximum
ⓑ. Zero
ⓒ. Minimum
ⓓ. Equal to the magnitude of the force
Correct Answer: Zero
Explanation: When the angle between the force vector and the displacement vector is \(90^\circ\), the cosine of \(90^\circ\) is zero, resulting in zero work done: \(W = |\mathbf{F}| |\mathbf{d}| \cos 90^\circ = 0\).
88. Which of the following represents the scalar product in the context of work done by a force?
ⓐ. \(\mathbf{F} \cdot \mathbf{d} = |\mathbf{F}| |\mathbf{d}| \sin \theta\)
ⓑ. \(\mathbf{F} \cdot \mathbf{d} = |\mathbf{F}| |\mathbf{d}| \cos \theta\)
ⓒ. \(\mathbf{F} \cdot \mathbf{d} = |\mathbf{F}| + |\mathbf{d}|\)
ⓓ. \(\mathbf{F} \cdot \mathbf{d} = |\mathbf{F}| – |\mathbf{d}|\)
Correct Answer: \(\mathbf{F} \cdot \mathbf{d} = |\mathbf{F}| |\mathbf{d}| \cos \theta\)
Explanation: The work done by a force is calculated using the scalar product, which involves the cosine of the angle between the force and displacement vectors: \(W = \mathbf{F} \cdot \mathbf{d} = |\mathbf{F}| |\mathbf{d}| \cos \theta\).
89. In calculating the power delivered by a force, which product is used?
ⓐ. Scalar product of force and velocity
ⓑ. Vector product of force and displacement
ⓒ. Scalar product of force and displacement
ⓓ. Vector product of force and velocity
Correct Answer: Scalar product of force and velocity
Explanation: Power delivered by a force is calculated as the scalar product of the force and the velocity: \(P = \mathbf{F} \cdot \mathbf{v}\).
90. The scalar product can be used to find which of the following in the context of mechanical work?
ⓐ. The displacement vector
ⓑ. The force vector
ⓒ. The component of force along displacement
ⓓ. The perpendicular component of force
Correct Answer: The component of force along displacement
Explanation: The scalar product of the force and displacement vectors gives the component of the force in the direction of the displacement, which is used to calculate work.
91. The work done by a constant force \(\mathbf{F}\) acting on an object that undergoes a displacement \(\mathbf{d}\) is given by:
ⓐ. \(\mathbf{F} \times \mathbf{d}\)
ⓑ. \(\mathbf{F} \cdot \mathbf{d}\)
ⓒ. \(\mathbf{F} + \mathbf{d}\)
ⓓ. \(\mathbf{F} / \mathbf{d}\)
Correct Answer: \(\mathbf{F} \cdot \mathbf{d}\)
Explanation: The work done by a constant force is calculated as the scalar product of the force and displacement vectors: \(W = \mathbf{F} \cdot \mathbf{d}\).
92. If a force \(\mathbf{F}\) of 10 N acts in the direction of displacement \(\mathbf{d}\) of 5 m, what is the work done?
ⓐ. 2 J
ⓑ. 10 J
ⓒ. 15 J
ⓓ. 50 J
Correct Answer: 50 J
Explanation: Since the force and displacement are in the same direction, \(W = F \cdot d = 10 \times 5 = 50\) J.
93. When a force of magnitude \(F\) acts at an angle \(\theta\) to the direction of displacement \(d\), the work done is given by:
ⓐ. \(Fd \sin \theta\)
ⓑ. \(Fd \cos \theta\)
ⓒ. \(Fd \tan \theta\)
ⓓ. \(Fd / \cos \theta\)
Correct Answer: \(Fd \cos \theta\)
Explanation: The work done by the force is the product of the force, the displacement, and the cosine of the angle between them: \(W = Fd \cos \theta\).
94. What is the work done by a constant force if the displacement is zero?
ⓐ. Maximum
ⓑ. Minimum
ⓒ. Zero
ⓓ. Undefined
Correct Answer: Zero
Explanation: If there is no displacement, no work is done regardless of the force applied: \(W = F \cdot 0 = 0\).
95. If a force of 20 N acts perpendicular to the displacement of 4 m, what is the work done?
ⓐ. 0 J
ⓑ. 80 J
ⓒ. 20 J
ⓓ. 4 J
Correct Answer: 0 J
Explanation: The work done by a force perpendicular to the displacement is zero because \(\cos 90^\circ = 0\).
96. How is the work done by a force calculated when the force and displacement are in opposite directions?
ⓐ. Positive
ⓑ. Negative
ⓒ. Zero
ⓓ. Equal to the force times displacement
Correct Answer: Negative
Explanation: When the force and displacement are in opposite directions, the work done is negative because \(\cos 180^\circ = -1\).
97. If a force \(\mathbf{F} = 3\mathbf{i} + 4\mathbf{j}\) N acts on an object that undergoes a displacement \(\mathbf{d} = 5\mathbf{i} + 2\mathbf{j}\) m, what is the work done?
ⓐ. 23 J
ⓑ. 17 J
ⓒ. 15 J
ⓓ. 20 J
Correct Answer: 23 J
Explanation: \(W = \mathbf{F} \cdot \mathbf{d} = (3\mathbf{i} + 4\mathbf{j}) \cdot (5\mathbf{i} + 2\mathbf{j}) = 3 \times 5 + 4 \times 2 = 15 + 8 = 23\) J.
98. The work done by a constant force is directly proportional to which of the following?
ⓐ. The magnitude of the force only
ⓑ. The magnitude of the displacement only
ⓒ. The angle between force and displacement
ⓓ. Both the magnitude of the force and the displacement
Correct Answer: Both the magnitude of the force and the displacement
Explanation: The work done is given by \(W = Fd \cos \theta\), showing that it is directly proportional to both the magnitude of the force and the displacement.
99. A force of 10 N is applied to move an object 5 m along a frictionless surface. What is the work done if the force is applied horizontally?
ⓐ. 5 J
ⓑ. 10 J
ⓒ. 50 J
ⓓ. 25 J
Correct Answer: 50 J
Explanation: Since the force is applied horizontally and the displacement is also horizontal, \(W = F \cdot d = 10 \times 5 = 50\) J.
100. Which of the following conditions results in zero work being done?
ⓐ. Force is parallel to displacement
ⓑ. Force is perpendicular to displacement
ⓒ. Force and displacement are in the same direction
ⓓ. Force and displacement are in opposite directions
Correct Answer: Force is perpendicular to displacement
Explanation: When the force is perpendicular to the displacement, the angle \(\theta = 90^\circ\) and \(\cos 90^\circ = 0\), resulting in zero work being done.
Welcome to Class 11 Physics MCQs – Chapter 6: Work, Energy, and Power (Part 1). This page is a chapter-wise question bank for the NCERT/CBSE Class 11 Physics syllabus—built for quick revision and exam speed. Practice MCQs / objective questions / Physics quiz items with solutions and explanations, ideal for CBSE Boards, JEE Main, NEET, competitive exams, and Board exams.
These MCQs are suitable for international competitive exams—physics concepts are universal.
Navigation & pages: The full chapter has 420 MCQs in 5 parts (100 + 100 + 100 + 100 + 20). Part 1 contains 100 MCQs split across 10 pages—you’ll see 10 questions per page. Use the page numbers above to view the remaining questions.
What you will learn & practice
- Introduction to Work, Energy, and Power
- Scalar product (dot product) and its use in work calculations
- Work done by a constant force and by a variable force (area under F–x)
- Kinetic energy and the Work–Energy Theorem
- Power: average and instantaneous power
- Potential energy and Conservation of Mechanical Energy
- Potential energy of a spring (elastic potential), force–extension
- Various forms of energy and Mass–energy equivalence (E = mc²)
How this practice works
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Real value: Strictly aligned to NCERT/CBSE topics, informed by previous-year paper trends, and written with concise, exam-oriented explanations—perfect for one-mark questions, quick concept checks, and last-minute revision.
The full chapter includes 420 solved multiple-choice questions in 5 parts. This page (Part 1) gives the first 100 MCQs with answers and explanations to build your foundations. Explore more with: Class 11 Physics – Chapter Index, Class 11 – Subject Index, All Classes – MCQ Library.
- 👉 Total MCQs in this chapter: 420 (100 + 100 + 100 + 100 + 20)
- 👉 This page: first 100 multiple-choice questions with answers & brief explanations (in 10 pages)
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FAQs on Work, Energy, and Power ▼
▸ What are Class 11 Physics Chapter 6 Work, Energy, and Power MCQs?
These are multiple-choice questions from Chapter 6 of NCERT Class 11 Physics – Work, Energy, and Power. They test concepts like work-energy theorem, kinetic energy, potential energy, conservation of energy, and power.
▸ How many MCQs are available in this chapter?
There are a total of 420 MCQs in Work, Energy, and Power. They are divided into 5 sets – four sets of 100 questions each and one set of 20 questions for extra practice.
▸ Are these Physics MCQs useful for NCERT and CBSE board exams?
Yes, these MCQs strictly follow the NCERT and CBSE Class 11 Physics syllabus, making them very useful for school exams, class tests, and board exam preparation.
▸ Do these MCQs help in state board exam preparation?
Yes, since the chapter Work, Energy, and Power is common across most state boards, these MCQs are also useful for state board students preparing for physics exams.
▸ Are Work, Energy, and Power MCQs important for JEE and NEET?
Absolutely! Work, Energy, and Power is a high-weightage chapter in JEE, NEET, and other competitive exams. Practicing MCQs helps in mastering problem-solving speed and accuracy.
▸ Do these MCQs include answers and explanations?
Yes, every MCQ is provided with the correct answer and detailed explanation. This helps students not just memorize but also understand the logic behind each solution.
▸ Who should practice these Physics MCQs?
These MCQs are ideal for Class 11 students, CBSE/NCERT board exam candidates, state board students, and aspirants preparing for JEE, NEET, NDA, UPSC, and other competitive entrance exams.
▸ Can I practice these Work, Energy, and Power MCQs online for free?
Yes, all MCQs on GK Aim are available for free online. You can practice them anytime on mobile, tablet, or desktop.
▸ Are these MCQs helpful for quick revision before exams?
Yes, practicing these MCQs helps with quick revision, sharpens memory recall, and boosts exam performance by improving accuracy and problem-solving speed.
▸ Do these MCQs cover both basics and advanced concepts?
Yes, the MCQs cover everything from basic concepts like work done by a force to advanced topics like conservation of mechanical energy, collisions, and power calculations.
▸ Why are the MCQs divided into 5 sets?
The MCQs are divided into 5 sets to make practice organized and systematic. Smaller sets help students focus step by step and track their progress effectively.
▸ Can teachers and coaching institutes use these MCQs?
Yes, teachers and coaching centers can use these MCQs as ready-made assignments, quizzes, and test material for students preparing for board and competitive exams.
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