Q. What is the relationship between the rate of a reaction and the concentration of reactants according to the rate law? (2019)
A.
Directly proportional
B.
Inversely proportional
C.
Exponential
D.
No relationship
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Solution
The rate of a reaction is directly proportional to the concentration of reactants raised to their respective powers in the rate law.
Correct Answer:
A
— Directly proportional
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Q. What is the relationship between the rate of reaction and temperature according to the Arrhenius equation? (2022)
A.
Inversely proportional
B.
Directly proportional
C.
Exponential
D.
Linear
Show solution
Solution
According to the Arrhenius equation, the rate of reaction increases exponentially with temperature.
Correct Answer:
C
— Exponential
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Q. What is the relationship between the RMS and average value of a sinusoidal AC current? (2023)
A.
RMS = Average
B.
RMS = Average × √2
C.
RMS = Average / √2
D.
RMS = Average × 2
Show solution
Solution
For a sinusoidal AC current, the relationship is RMS = Average / √2.
Correct Answer:
C
— RMS = Average / √2
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Q. What is the relationship between the root mean square speed of gas molecules and the temperature of the gas?
A.
It is independent of temperature.
B.
It is directly proportional to the square root of temperature.
C.
It is inversely proportional to temperature.
D.
It is directly proportional to temperature.
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Solution
The root mean square speed of gas molecules is directly proportional to the square root of the absolute temperature of the gas.
Correct Answer:
B
— It is directly proportional to the square root of temperature.
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Q. What is the relationship between the sections of the CAT exam as described in the passage?
A.
They are independent and do not affect each other.
B.
They are interrelated and require a balanced approach.
C.
They focus solely on quantitative reasoning.
D.
They are designed to confuse the test-taker.
Show solution
Solution
The passage highlights that the sections are interrelated, necessitating a balanced preparation strategy.
Correct Answer:
B
— They are interrelated and require a balanced approach.
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Q. What is the relationship between the sides of a rhombus?
A.
All sides are equal.
B.
Opposite sides are equal.
C.
Adjacent sides are equal.
D.
No sides are equal.
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Solution
In a rhombus, all sides are equal in length.
Correct Answer:
A
— All sides are equal.
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Q. What is the relationship between the slit separation and the angle of diffraction in a double-slit experiment?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Quadratic relationship
Show solution
Solution
The angle of diffraction is inversely proportional to the slit separation; as the slit separation increases, the angle decreases.
Correct Answer:
B
— Inversely proportional
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Q. What is the relationship between the slit width and the angle of diffraction in a single-slit experiment?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
Show solution
Solution
The angle of diffraction is inversely proportional to the slit width; as the slit width decreases, the angle increases.
Correct Answer:
B
— Inversely proportional
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Q. What is the relationship between the slit width and the angular position of the first minimum in single-slit diffraction?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
Show solution
Solution
The angular position of the first minimum is inversely proportional to the slit width; as the slit width decreases, the angle increases.
Correct Answer:
B
— Inversely proportional
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Q. What is the relationship between the slit width and the angular width of the central maximum in single-slit diffraction?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Exponential
Show solution
Solution
The angular width of the central maximum is inversely proportional to the slit width; as the slit width increases, the angular width decreases.
Correct Answer:
B
— Inversely proportional
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Q. What is the relationship between the speed of gas molecules and temperature?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
Show solution
Solution
The average speed of gas molecules is directly proportional to the square root of the absolute temperature.
Correct Answer:
A
— Directly proportional
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Q. What is the relationship between the stopping potential and the maximum kinetic energy of the emitted electrons in the photoelectric effect?
A.
Stopping potential is directly proportional to the work function
B.
Stopping potential is inversely proportional to the maximum kinetic energy
C.
Stopping potential is equal to the maximum kinetic energy
D.
Stopping potential has no relation to the photoelectric effect
Show solution
Solution
The stopping potential (V) is related to the maximum kinetic energy (KE) of the emitted electrons by the equation KE = eV, where e is the charge of the electron.
Correct Answer:
C
— Stopping potential is equal to the maximum kinetic energy
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Q. What is the relationship between the stopping potential and the maximum kinetic energy of emitted electrons in the photoelectric effect?
A.
Stopping potential is directly proportional to the work function
B.
Stopping potential is directly proportional to the maximum kinetic energy
C.
Stopping potential is inversely proportional to the frequency
D.
Stopping potential has no relation to kinetic energy
Show solution
Solution
The stopping potential (V) is directly proportional to the maximum kinetic energy (KE) of the emitted electrons, given by the equation KE = eV, where e is the charge of the electron.
Correct Answer:
B
— Stopping potential is directly proportional to the maximum kinetic energy
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Q. What is the relationship between the sum of the interior angles and the exterior angles of a polygon?
A.
Interior angles sum to 180 degrees
B.
Exterior angles sum to 360 degrees
C.
Both sum to 360 degrees
D.
Interior angles sum to 360 degrees
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Solution
The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides.
Correct Answer:
B
— Exterior angles sum to 360 degrees
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Q. What is the relationship between the sum of the interior angles of a triangle and the angles formed by a transversal cutting through two parallel lines? (2022)
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are unrelated
Show solution
Solution
The sum of the interior angles of a triangle is 180 degrees, and the angles formed by a transversal cutting through two parallel lines are supplementary, meaning they add up to 180 degrees.
Correct Answer:
B
— They are supplementary
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Q. What is the relationship between the terms of a harmonic progression and their reciprocals?
A.
They are in geometric progression.
B.
They are in arithmetic progression.
C.
They are in quadratic progression.
D.
They are in exponential progression.
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Solution
The terms of a harmonic progression are the reciprocals of the terms of an arithmetic progression.
Correct Answer:
B
— They are in arithmetic progression.
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Q. What is the relationship between the two main concepts discussed in the passage?
A.
They are mutually exclusive.
B.
They complement each other.
C.
They are unrelated.
D.
They are contradictory.
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Solution
The two main concepts discussed in the passage complement each other, as they work together to address the issue.
Correct Answer:
B
— They complement each other.
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Q. What is the relationship between the two main ideas presented in the passage?
A.
They are contradictory.
B.
They complement each other.
C.
They are unrelated.
D.
They are sequential.
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Solution
The two main ideas in the passage complement each other, providing a holistic view of the topic discussed.
Correct Answer:
B
— They complement each other.
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Q. What is the relationship between the two studies mentioned in the passage?
A.
They are completely unrelated.
B.
One study supports the findings of the other.
C.
They contradict each other.
D.
They were conducted by the same researchers.
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Solution
The passage indicates that one study provides evidence that supports the findings of the other, establishing a relationship.
Correct Answer:
B
— One study supports the findings of the other.
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Q. What is the relationship between the units of energy (Joule) and force (Newton)? (2021)
A.
1 J = 1 N·m
B.
1 J = 1 N/m
C.
1 J = 1 m/N
D.
1 J = 1 N^2
Show solution
Solution
1 Joule is defined as the work done when a force of one Newton moves an object one meter, hence 1 J = 1 N·m.
Correct Answer:
A
— 1 J = 1 N·m
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Q. What is the relationship between the units of energy and work?
A.
They are the same
B.
Energy is greater than work
C.
Work is greater than energy
D.
They are different
Show solution
Solution
Energy and work are measured in the same unit, which is Joules (J).
Correct Answer:
A
— They are the same
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Q. What is the relationship between the units of pressure in SI? (2019)
A.
1 Pa = 1 N/m²
B.
1 Pa = 1 kg/m·s²
C.
Both are correct
D.
None of the above
Show solution
Solution
Both statements are correct; 1 Pascal (Pa) is defined as 1 Newton per square meter.
Correct Answer:
C
— Both are correct
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Q. What is the relationship between the units of work and energy?
A.
They are the same
B.
Work is a subset of energy
C.
Energy is a subset of work
D.
They are unrelated
Show solution
Solution
Work and energy are measured in the same unit, which is Joules (J) in the SI system.
Correct Answer:
A
— They are the same
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Q. What is the relationship between the vapor pressure of a solution and the mole fraction of the solvent? (2023)
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
Show solution
Solution
The vapor pressure of a solution is directly proportional to the mole fraction of the solvent.
Correct Answer:
A
— Directly proportional
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Q. What is the relationship between the wavelength and frequency of a wave?
A.
Wavelength is directly proportional to frequency
B.
Wavelength is inversely proportional to frequency
C.
Wavelength is equal to frequency
D.
Wavelength and frequency are unrelated
Show solution
Solution
The relationship is given by the equation v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. Thus, wavelength is inversely proportional to frequency.
Correct Answer:
B
— Wavelength is inversely proportional to frequency
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Q. What is the relationship between the wavelength of light and the angle of diffraction in a diffraction grating?
A.
Longer wavelengths diffract less
B.
Longer wavelengths diffract more
C.
Wavelength has no effect
D.
Only the slit width matters
Show solution
Solution
Longer wavelengths diffract more, leading to larger angles of diffraction in a diffraction grating.
Correct Answer:
B
— Longer wavelengths diffract more
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Q. What is the relationship between the wavelength of light and the angle of diffraction in a grating? (2023)
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
Show solution
Solution
The angle of diffraction is directly proportional to the wavelength of light used in a diffraction grating, as described by the grating equation.
Correct Answer:
A
— Directly proportional
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Q. What is the relationship between the wavelength of light and the angle of diffraction in a single-slit experiment? (2023)
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
Show solution
Solution
The angle of diffraction is inversely proportional to the wavelength; as the wavelength increases, the angle of diffraction decreases.
Correct Answer:
B
— Inversely proportional
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Q. What is the relationship between the wavelength of light and the energy of the emitted electrons in the photoelectric effect?
A.
Energy is directly proportional to wavelength
B.
Energy is inversely proportional to wavelength
C.
Energy is independent of wavelength
D.
Energy is proportional to the square of wavelength
Show solution
Solution
The energy of the emitted electrons is inversely proportional to the wavelength of the incident light, as given by E = hc/λ.
Correct Answer:
B
— Energy is inversely proportional to wavelength
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Q. What is the relationship between the width of the central maximum and the wavelength in a single-slit diffraction pattern?
A.
Directly proportional
B.
Inversely proportional
C.
No relationship
D.
Exponential relationship
Show solution
Solution
The width of the central maximum is inversely proportional to the slit width and directly proportional to the wavelength.
Correct Answer:
B
— Inversely proportional
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