Q. In a survey, 70% of people like tea and 30% like coffee. If a person is chosen at random, what is the probability that they like tea given that they do not like coffee?
A.
1/3
B.
2/3
C.
1/2
D.
1
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Solution
If a person does not like coffee, they must like tea. Therefore, P(Tea | Not Coffee) = 1.
Correct Answer: D — 1
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Q. In a survey, 70% of people like tea and 40% like coffee. If 30% like both, what is the probability that a person likes coffee given that they like tea?
A.
0.4
B.
0.3
C.
0.5
D.
0.6
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Solution
Using conditional probability, P(C|T) = P(C ∩ T) / P(T) = 0.3 / 0.7 = 3/7.
Correct Answer: A — 0.4
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Q. In a survey, 70% of people like tea, and 40% like coffee. If 30% like both tea and coffee, what is the probability that a person likes tea given that they like coffee?
A.
0.5
B.
0.7
C.
0.3
D.
0.4
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Solution
Using conditional probability, P(Tea | Coffee) = P(Tea and Coffee) / P(Coffee) = 0.3 / 0.4 = 0.75.
Correct Answer: A — 0.5
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Q. In a survey, 70% of people like tea, and 40% like coffee. If 30% like both tea and coffee, what is the probability that a person likes coffee given that they like tea?
A.
0.4
B.
0.3
C.
0.5
D.
0.6
Show solution
Solution
Using conditional probability, P(Coffee|Tea) = P(Coffee and Tea) / P(Tea) = 0.3 / 0.7 = 3/7.
Correct Answer: A — 0.4
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Q. In a survey, 70% of people prefer tea over coffee. If 10 people are surveyed, what is the probability that exactly 7 prefer tea?
A.
0.193
B.
0.200
C.
0.250
D.
0.300
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Solution
Using binomial probability: P(X=7) = C(10,7) * (0.7)⁷ * (0.3)³ = 120 * 0.0823543 * 0.027 = 0.193.
Correct Answer: A — 0.193
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Q. In a survey, 70% of people prefer tea over coffee. If 10 people are surveyed, what is the expected number of tea drinkers?
Show solution
Solution
Expected number = 70% of 10 = 0.7 * 10 = 7.
Correct Answer: B — 7
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Q. In a survey, 70% of people prefer tea over coffee. If 50 people are surveyed, how many prefer tea?
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Solution
Number of people preferring tea = 70% of 50 = 0.7 * 50 = 35.
Correct Answer: D — 45
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Q. In a system at equilibrium, if the concentration of reactants is increased, what will happen to the equilibrium position?
A.
Shift to the right
B.
Shift to the left
C.
No change
D.
Depends on temperature
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Solution
According to Le Chatelier's principle, increasing the concentration of reactants will shift the equilibrium position to the right to favor the formation of products.
Correct Answer: A — Shift to the right
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Q. In a system of two blocks connected by a spring, if the spring is compressed, what is the condition for equilibrium?
A.
Net force acting on the system is zero
B.
Net momentum of the system is constant
C.
Kinetic energy is maximized
D.
Potential energy is minimized
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Solution
For equilibrium, the net force acting on the system must be zero.
Correct Answer: A — Net force acting on the system is zero
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Q. In a system of two particles, if one particle has an angular momentum of L1 and the other has L2, what is the total angular momentum of the system?
A.
L1 + L2
B.
L1 - L2
C.
L1 * L2
D.
L1 / L2
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Solution
Total angular momentum of the system is the vector sum of individual angular momenta: L_total = L1 + L2.
Correct Answer: A — L1 + L2
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Q. In a system of two rotating bodies, if one body has twice the moment of inertia of the other, how does their angular momentum compare if they rotate with the same angular velocity?
A.
The same
B.
Twice as much
C.
Half as much
D.
Four times as much
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Solution
Angular momentum L = Iω; if one has twice the moment of inertia, it will have twice the angular momentum at the same angular velocity.
Correct Answer: B — Twice as much
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Q. In a system of two rotating disks, if disk A has twice the moment of inertia of disk B and they are both rotating with the same angular velocity, what can be said about their angular momentum?
A.
LA = LB
B.
LA = 2LB
C.
LA = 4LB
D.
LA = 1/2 LB
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Solution
Angular momentum L = Iω; since IA = 2IB and ωA = ωB, LA = 2LB.
Correct Answer: B — LA = 2LB
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Q. In a system where two forces act at an angle of 90 degrees, how do you find the resultant force?
A.
By adding the forces algebraically
B.
Using the Pythagorean theorem
C.
By taking the average of the two forces
D.
By subtracting the smaller force from the larger force
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Solution
The resultant force can be found using the Pythagorean theorem since the forces are perpendicular.
Correct Answer: B — Using the Pythagorean theorem
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Q. In a temperature-resistivity graph, what does the slope represent for a metallic conductor?
A.
Resistivity
B.
Temperature coefficient of resistivity
C.
Resistance
D.
Conductivity
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Solution
The slope of the temperature-resistivity graph represents the temperature coefficient of resistivity.
Correct Answer: B — Temperature coefficient of resistivity
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Q. In a tensile test, if a material exhibits a linear stress-strain relationship, what type of deformation is it undergoing?
A.
Elastic deformation
B.
Plastic deformation
C.
Brittle fracture
D.
Ductile fracture
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Solution
A linear stress-strain relationship indicates that the material is undergoing elastic deformation.
Correct Answer: A — Elastic deformation
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Q. In a tensile test, if a material shows a linear relationship between stress and strain up to a certain point, this point is known as:
A.
Yield point
B.
Ultimate tensile strength
C.
Elastic limit
D.
Fracture point
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Solution
The elastic limit is the maximum stress that a material can withstand while still returning to its original shape.
Correct Answer: C — Elastic limit
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Q. In a tensile test, if a material shows a linear relationship between stress and strain, it is said to be in which region?
A.
Plastic region
B.
Elastic region
C.
Yield point
D.
Fracture point
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Solution
The linear relationship between stress and strain indicates that the material is in the elastic region.
Correct Answer: B — Elastic region
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Q. In a tensile test, if the stress-strain curve of a material shows a linear relationship, what does this indicate?
A.
The material is elastic
B.
The material is plastic
C.
The material has failed
D.
The material is brittle
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Solution
A linear relationship in the stress-strain curve indicates that the material behaves elastically within that range.
Correct Answer: A — The material is elastic
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Q. In a tensile test, if the stress-strain curve shows a linear relationship, what does this indicate about the material?
A.
It is inelastic
B.
It is elastic
C.
It has reached its yield point
D.
It will break immediately
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Solution
A linear relationship in the stress-strain curve indicates that the material behaves elastically within that range.
Correct Answer: B — It is elastic
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Q. In a thermodynamic cycle, if the net work done by the system is 200 J and the heat absorbed is 300 J, what is the change in internal energy?
A.
100 J
B.
200 J
C.
300 J
D.
500 J
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Solution
According to the First Law of Thermodynamics, ΔU = Q - W. Here, ΔU = 300 J - 200 J = 100 J.
Correct Answer: A — 100 J
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Q. In a thermodynamic cycle, the net work done is equal to the:
A.
Net heat added to the system
B.
Net heat removed from the system
C.
Change in internal energy
D.
Change in entropy
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Solution
In a thermodynamic cycle, the net work done is equal to the net heat added to the system, according to the first law of thermodynamics.
Correct Answer: A — Net heat added to the system
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Q. In a thermodynamic cycle, the net work done is equal to which of the following?
A.
Net heat added to the system
B.
Net heat rejected by the system
C.
Change in internal energy
D.
Change in enthalpy
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Solution
In a thermodynamic cycle, the net work done is equal to the net heat added to the system, according to the first law of thermodynamics.
Correct Answer: A — Net heat added to the system
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Q. In a thermodynamic cycle, the net work done is equal to:
A.
Net heat added to the system
B.
Net change in internal energy
C.
Net heat removed from the system
D.
None of the above
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Solution
In a thermodynamic cycle, the net work done is equal to the net heat added to the system, as the internal energy change is zero.
Correct Answer: A — Net heat added to the system
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Q. In a thermodynamic process, if the internal energy of a system increases, which of the following could be true?
A.
Heat is added to the system
B.
Work is done by the system
C.
Both heat is added and work is done by the system
D.
Work is done on the system
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Solution
The internal energy of a system increases if heat is added to the system or work is done on the system.
Correct Answer: A — Heat is added to the system
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Q. In a thermodynamic process, if the pressure of a gas is held constant and the volume decreases, what happens to the temperature?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes negative
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Solution
According to Gay-Lussac's Law, if the volume decreases at constant pressure, the temperature must increase.
Correct Answer: B — It decreases
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Q. In a thermodynamic process, if the volume of a gas is doubled while keeping the temperature constant, what happens to the pressure?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
According to Boyle's Law, for a constant temperature, pressure is inversely proportional to volume. If volume doubles, pressure halves.
Correct Answer: B — It halves
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Q. In a thin film interference pattern, what happens to the colors observed as the angle of incidence increases?
A.
Colors become more vivid
B.
Colors disappear
C.
Colors shift
D.
Colors remain unchanged
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Solution
As the angle of incidence increases, the effective path difference changes, causing a shift in the observed colors.
Correct Answer: C — Colors shift
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Q. In a thin film interference, if the film is denser than the medium it is placed in, what happens to the phase of the reflected wave?
A.
No phase change
B.
Phase change of π
C.
Phase change of 2π
D.
Phase change of π/2
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Solution
When light reflects off a denser medium, it undergoes a phase change of π (180 degrees).
Correct Answer: B — Phase change of π
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Q. In a thin film interference, if the film is of thickness t and the refractive index is n, what is the condition for constructive interference?
A.
2nt = (m + 1/2)λ
B.
2nt = mλ
C.
2nt = (m - 1/2)λ
D.
2nt = mλ/2
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Solution
For constructive interference in thin films, the condition is 2nt = mλ, where m is an integer.
Correct Answer: B — 2nt = mλ
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Q. In a thin film interference, if the film is of thickness t and the refractive index is n, what is the condition for the first dark fringe?
A.
2nt = (m + 1/2)λ
B.
2nt = mλ
C.
2nt = (m - 1/2)λ
D.
2nt = 0
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Solution
For the first dark fringe in thin film interference, the condition is 2nt = (m + 1/2)λ, where m = 0.
Correct Answer: A — 2nt = (m + 1/2)λ
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