Q. The potential energy stored in a capacitor is directly proportional to which of the following? (2023)
A.
Charge and Voltage
B.
Charge only
C.
Voltage only
D.
Capacitance only
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Solution
The potential energy (U) stored in a capacitor is given by U = 1/2 CV^2, which shows it is directly proportional to both charge and voltage.
Correct Answer:
A
— Charge and Voltage
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Q. The potential energy stored in a capacitor is given by which of the following formulas? (2020)
A.
1/2 CV^2
B.
CV
C.
Q^2/2C
D.
1/2 QV
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Solution
The potential energy (U) stored in a capacitor is given by U = 1/2 CV^2.
Correct Answer:
A
— 1/2 CV^2
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Q. The pressure of a gas is inversely proportional to its volume at constant temperature is known as: (2022)
A.
Charles's Law
B.
Boyle's Law
C.
Avogadro's Law
D.
Ideal Gas Law
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Solution
Boyle's Law states that the pressure of a gas is inversely proportional to its volume at constant temperature.
Correct Answer:
B
— Boyle's Law
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Q. The pressure of an ideal gas is directly proportional to its temperature when: (2022)
A.
Volume is constant
B.
Number of moles is constant
C.
Both volume and number of moles are constant
D.
None of the above
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Solution
According to Gay-Lussac's law, the pressure of an ideal gas is directly proportional to its temperature when the volume is held constant.
Correct Answer:
A
— Volume is constant
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Q. The pressure of an ideal gas is inversely proportional to its volume at constant temperature. This relationship is known as: (2022)
A.
Charles's Law
B.
Boyle's Law
C.
Avogadro's Law
D.
Ideal Gas Law
Show solution
Solution
This relationship is known as Boyle's Law, which states that the pressure of an ideal gas is inversely proportional to its volume at constant temperature.
Correct Answer:
B
— Boyle's Law
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Q. The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)
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Solution
The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.
Correct Answer:
B
— 1
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Q. The rate constant of a reaction is affected by which of the following? (2023)
A.
Nature of the reactants
B.
Temperature
C.
Catalysts
D.
All of the above
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Solution
The rate constant of a reaction is affected by the nature of the reactants, temperature, and the presence of catalysts.
Correct Answer:
D
— All of the above
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Q. The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. What is the general form of the rate equation? (2023)
A.
Rate = k[A]^n
B.
Rate = k[A][B]
C.
Rate = k[A]^2[B]
D.
Rate = k[A] + [B]
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Solution
The general form of the rate equation is Rate = k[A]^n, where n is the order of the reaction.
Correct Answer:
A
— Rate = k[A]^n
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Q. The rate of a reaction is directly proportional to the concentration of one reactant raised to the power of 2. What is the order of the reaction? (2022)
A.
Zero order
B.
First order
C.
Second order
D.
Third order
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Solution
If the rate is proportional to the concentration of one reactant raised to the power of 2, the reaction is second order.
Correct Answer:
C
— Second order
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Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This statement defines which of the following? (2020)
A.
Rate law
B.
Equilibrium constant
C.
Le Chatelier's principle
D.
Reaction mechanism
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Solution
This statement defines the rate law of a reaction.
Correct Answer:
A
— Rate law
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Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This statement defines:
A.
Rate law
B.
Equilibrium constant
C.
Reaction quotient
D.
Catalytic efficiency
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Solution
This statement defines the rate law of a reaction.
Correct Answer:
A
— Rate law
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Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This statement defines which law?
A.
Law of conservation of mass
B.
Rate law
C.
Le Chatelier's principle
D.
Gibbs free energy
Show solution
Solution
This statement defines the rate law of a chemical reaction.
Correct Answer:
B
— Rate law
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Q. The rate of a reaction is given by the equation rate = k[A]^2[B]. What is the overall order of the reaction? (2020)
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Solution
The overall order of the reaction is 2 (from [A]^2) + 1 (from [B]) = 3.
Correct Answer:
C
— 3
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Q. The resonant frequency of an RLC circuit is given by which formula? (2022)
A.
f = 1/(2π√(LC))
B.
f = 2π√(LC)
C.
f = LC
D.
f = R/(2πL)
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Solution
The resonant frequency f of an RLC circuit is given by f = 1/(2π√(LC)).
Correct Answer:
A
— f = 1/(2π√(LC))
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Q. The restoring force in a simple harmonic oscillator is directly proportional to what? (2022)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
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Solution
The restoring force (F) is directly proportional to the displacement (x) and acts in the opposite direction, F = -kx.
Correct Answer:
A
— Displacement
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Q. The restoring force in simple harmonic motion is directly proportional to what? (2022)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
Show solution
Solution
The restoring force (F) is directly proportional to the displacement (x) and acts in the opposite direction, F = -kx.
Correct Answer:
A
— Displacement
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Q. The restoring force in simple harmonic motion is directly proportional to: (2023)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
Show solution
Solution
Restoring force (F) is proportional to displacement (x), F = -kx.
Correct Answer:
A
— Displacement
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Q. The roots of the equation x² + 2x + k = 0 are real and distinct if k is: (2020)
A.
< 1
B.
≥ 1
C.
≤ 1
D.
> 1
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Solution
For real and distinct roots, the discriminant must be positive: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer:
A
— < 1
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Q. The roots of the equation x² + 4x + 4 = 0 are: (2020)
A.
-2 and -2
B.
2 and 2
C.
0 and 4
D.
1 and 3
Show solution
Solution
The equation can be factored as (x + 2)² = 0, giving the double root x = -2.
Correct Answer:
A
— -2 and -2
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Q. The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)
A.
-12
B.
-8
C.
-10
D.
-14
Show solution
Solution
Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.
Correct Answer:
B
— -8
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Q. The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)
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Solution
Using the product of roots: k = 4 * 4 = 16.
Correct Answer:
A
— 16
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Q. The scientific study of classification is known as: (2022)
A.
Taxonomy
B.
Morphology
C.
Anatomy
D.
Ecology
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Solution
Taxonomy is the scientific study of classification of organisms.
Correct Answer:
A
— Taxonomy
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Q. The self-inductance of a coil depends on which of the following factors? (2021)
A.
Number of turns
B.
Area of cross-section
C.
Length of the coil
D.
All of the above
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Solution
The self-inductance of a coil depends on the number of turns, area of cross-section, and length of the coil.
Correct Answer:
D
— All of the above
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Q. The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of: (2023)
A.
1 kg of the substance by 1°C
B.
1 g of the substance by 1°C
C.
1 L of the substance by 1°C
D.
1 mole of the substance by 1°C
Show solution
Solution
The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1°C.
Correct Answer:
A
— 1 kg of the substance by 1°C
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Q. The specific heat capacity of a substance is defined as: (2023)
A.
The amount of heat required to raise the temperature by 1 degree Celsius
B.
The amount of heat required to change the phase of a substance
C.
The heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius
D.
The heat required to raise the temperature of 1 mole of the substance by 1 degree Celsius
Show solution
Solution
The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius.
Correct Answer:
C
— The heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius
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Q. The term 'adsorption' refers to: (2022)
A.
The process of a substance being taken up by a liquid.
B.
The accumulation of molecules on a surface.
C.
The mixing of two liquids.
D.
The dissolution of a solid in a liquid.
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Solution
Adsorption is the process where molecules accumulate on the surface of a solid or liquid.
Correct Answer:
B
— The accumulation of molecules on a surface.
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Q. The term 'binomial nomenclature' refers to: (2019)
A.
The two-part naming system for species
B.
The classification of organisms
C.
The study of animal behavior
D.
The grouping of organisms based on habitat
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Solution
Binomial nomenclature is the two-part naming system for species, consisting of the genus and species name.
Correct Answer:
A
— The two-part naming system for species
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Q. The theory that explains the gradual change in species over time is known as? (1972)
A.
Punctuated equilibrium
B.
Gradualism
C.
Catastrophism
D.
Uniformitarianism
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Solution
Gradualism is the theory that evolution occurs slowly and steadily over long periods of time.
Correct Answer:
B
— Gradualism
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Q. The theory that organisms can pass on traits acquired during their lifetime is known as?
A.
Natural Selection
B.
Lamarckism
C.
Mendelian Genetics
D.
Darwinism
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Solution
Lamarckism is the theory that organisms can pass on traits acquired during their lifetime, which has been largely discredited in favor of Darwinian evolution.
Correct Answer:
B
— Lamarckism
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Q. The uncertainty in a measurement is defined as: (2022)
A.
The difference between the maximum and minimum values
B.
The average of the measurements
C.
The standard deviation
D.
The range of values
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Solution
Uncertainty is often defined as the range of values within which the true value lies.
Correct Answer:
A
— The difference between the maximum and minimum values
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