Q. Which of the following statements is true regarding the Freundlich adsorption isotherm? (2020)
A.
It applies only to monolayer adsorption.
B.
It is applicable to heterogeneous surfaces.
C.
It predicts a constant adsorption capacity.
D.
It is a linear relationship.
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Solution
The Freundlich adsorption isotherm is applicable to heterogeneous surfaces and describes how adsorption varies with pressure or concentration, indicating that it is not limited to monolayer adsorption.
Correct Answer:
B
— It is applicable to heterogeneous surfaces.
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Q. Which of the following statements is true regarding the function f(x) = 1/(x-3)?
A.
Continuous at x = 3
B.
Discontinuous at x = 3
C.
Continuous everywhere
D.
Discontinuous everywhere
Show solution
Solution
The function f(x) = 1/(x-3) is discontinuous at x = 3 because it is undefined at that point.
Correct Answer:
B
— Discontinuous at x = 3
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Q. Which of the following statements is true regarding the function f(x) = x^2?
A.
It is a linear function.
B.
It is a quadratic function.
C.
It is a constant function.
D.
It is an exponential function.
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Solution
The function f(x) = x^2 is a quadratic function because it can be expressed in the form ax^2 + bx + c.
Correct Answer:
B
— It is a quadratic function.
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Q. Which of the following statements is true regarding the function f(x) = |x|?
A.
Continuous everywhere
B.
Discontinuous at x = 0
C.
Continuous only for x > 0
D.
Discontinuous for x < 0
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Solution
The function f(x) = |x| is continuous everywhere, including at x = 0.
Correct Answer:
A
— Continuous everywhere
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Q. Which of the following statements is true regarding the graph of a linear equation?
A.
It can be a curve.
B.
It is always a straight line.
C.
It can have multiple slopes.
D.
It can intersect the x-axis at multiple points.
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Solution
The graph of a linear equation is always a straight line.
Correct Answer:
B
— It is always a straight line.
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Q. Which of the following statements is true regarding the graph of a quadratic function?
A.
It is always a straight line.
B.
It can open upwards or downwards.
C.
It has no intercepts.
D.
It is always increasing.
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Solution
The graph of a quadratic function is a parabola that can open upwards (if a > 0) or downwards (if a < 0).
Correct Answer:
B
— It can open upwards or downwards.
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Q. Which of the following statements is true regarding the graph of the equation 3x + 4y = 12? (2023)
A.
It intersects the x-axis at (4, 0).
B.
It intersects the y-axis at (0, 3).
C.
It has a positive slope.
D.
It is a vertical line.
Show solution
Solution
Setting y = 0 gives x = 4, indicating that the graph intersects the x-axis at (4, 0).
Correct Answer:
A
— It intersects the x-axis at (4, 0).
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Q. Which of the following statements is true regarding the graph of the equation 5x + 2y = 10?
A.
It is a vertical line.
B.
It is a horizontal line.
C.
It has a positive slope.
D.
It has a negative slope.
Show solution
Solution
Rearranging the equation to y = -5/2x + 5 shows that the slope is negative.
Correct Answer:
D
— It has a negative slope.
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Q. Which of the following statements is true regarding the graph of the equation y = mx + b?
A.
The graph is always a circle.
B.
The slope m indicates the steepness of the line.
C.
The y-intercept b is always negative.
D.
The graph can never be horizontal.
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Solution
In the equation y = mx + b, m represents the slope, which indicates how steep the line is.
Correct Answer:
B
— The slope m indicates the steepness of the line.
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Q. Which of the following statements is true regarding the graph of the equation y = 2x + 1?
A.
It is a vertical line.
B.
It has a positive slope.
C.
It intersects the y-axis at -1.
D.
It has a negative slope.
Show solution
Solution
The equation y = 2x + 1 has a positive slope of 2 and intersects the y-axis at 1.
Correct Answer:
B
— It has a positive slope.
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Q. Which of the following statements is true regarding the HCF and LCM of two numbers? (2023)
A.
HCF is always greater than LCM
B.
HCF is the product of the numbers
C.
LCM is always less than the product of the numbers
D.
HCF * LCM = Product of the numbers
Show solution
Solution
The correct statement is that HCF * LCM = Product of the numbers.
Correct Answer:
D
— HCF * LCM = Product of the numbers
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Q. Which of the following statements is true regarding the inductive effect?
A.
It is a temporary effect.
B.
It operates through pi bonds.
C.
It is stronger than the mesomeric effect.
D.
It decreases with distance.
Show solution
Solution
The inductive effect decreases with distance from the electronegative atom or group.
Correct Answer:
D
— It decreases with distance.
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Q. Which of the following statements is true regarding the International Date Line? (2019)
A.
It is located at 180° longitude
B.
It is a straight line
C.
It is not recognized by all countries
D.
All of the above
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Solution
The International Date Line is approximately at 180° longitude, is not a straight line, and is not recognized by all countries.
Correct Answer:
D
— All of the above
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Q. Which of the following statements is true regarding the intersection of two constraint-based sets?
A.
The intersection will always contain all elements of both sets.
B.
The intersection may contain elements that satisfy the constraints of both sets.
C.
The intersection will be empty if the sets have no common elements.
D.
Both b and c are true.
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Solution
The intersection of two constraint-based sets may contain elements that satisfy the constraints of both sets, and it will be empty if there are no common elements.
Correct Answer:
D
— Both b and c are true.
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Q. Which of the following statements is true regarding the intersection of two hybrid sets?
A.
The intersection is always empty.
B.
The intersection contains all elements from both sets.
C.
The intersection contains only the common elements.
D.
The intersection is equal to the union of the sets.
Show solution
Solution
The intersection of two hybrid sets contains only the elements that are common to both sets.
Correct Answer:
C
— The intersection contains only the common elements.
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Q. Which of the following statements is true regarding the inverse of a function?
A.
The inverse of a function is always a function.
B.
The inverse of a function is defined only for linear functions.
C.
The graph of a function and its inverse are symmetric about the line y = x.
D.
The inverse of a function can never be found.
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Solution
The graph of a function and its inverse are symmetric about the line y = x, which is a key property of inverse functions.
Correct Answer:
C
— The graph of a function and its inverse are symmetric about the line y = x.
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Q. Which of the following statements is true regarding the Langmuir adsorption isotherm?
A.
It assumes a monolayer adsorption.
B.
It applies to multilayer adsorption.
C.
It is temperature independent.
D.
It is only applicable to gases.
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Solution
The Langmuir adsorption isotherm assumes that adsorption occurs in a monolayer on a surface with a finite number of identical sites.
Correct Answer:
A
— It assumes a monolayer adsorption.
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Q. Which of the following statements is true regarding the magnetic field due to a solenoid? (2023)
A.
It is uniform inside and zero outside
B.
It is zero inside and uniform outside
C.
It is uniform both inside and outside
D.
It varies linearly with distance
Show solution
Solution
A solenoid produces a uniform magnetic field inside and negligible field outside when it is long compared to its diameter.
Correct Answer:
A
— It is uniform inside and zero outside
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Q. Which of the following statements is true regarding the magnetic field due to a long straight conductor? (2020)
A.
It is uniform and constant
B.
It decreases with distance from the conductor
C.
It is strongest at the center of the conductor
D.
It is only present when the current is alternating
Show solution
Solution
The magnetic field around a long straight conductor decreases with distance from the conductor, following the inverse relationship.
Correct Answer:
B
— It decreases with distance from the conductor
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Q. Which of the following statements is true regarding the magnetic field inside a long solenoid? (2023)
A.
It is zero
B.
It is uniform and parallel to the axis
C.
It varies with distance from the center
D.
It is stronger at the ends
Show solution
Solution
Inside a long solenoid, the magnetic field is uniform and parallel to the axis of the solenoid, provided the solenoid is long enough.
Correct Answer:
B
— It is uniform and parallel to the axis
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Q. Which of the following statements is true regarding the mean free path of gas molecules?
A.
It increases with increasing temperature.
B.
It decreases with increasing pressure.
C.
It is independent of the size of the gas molecules.
D.
It is constant for all gases.
Show solution
Solution
The mean free path decreases with increasing pressure because more molecules are present in a given volume, leading to more frequent collisions.
Correct Answer:
B
— It decreases with increasing pressure.
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Q. Which of the following statements is true regarding the mesomeric effect?
A.
It can only be observed in aliphatic compounds.
B.
It involves the movement of sigma electrons.
C.
It is responsible for the stability of resonance structures.
D.
It is a short-range effect.
Show solution
Solution
The mesomeric effect is responsible for the stability of resonance structures due to the delocalization of pi electrons.
Correct Answer:
C
— It is responsible for the stability of resonance structures.
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Q. Which of the following statements is true regarding the mixed graph's data distribution? (2023)
A.
The data is normally distributed.
B.
The data is skewed to the right.
C.
The data shows a uniform distribution.
D.
The data is bimodal.
Show solution
Solution
The distribution of data points shows a right skew, indicating more values on the lower end.
Correct Answer:
B
— The data is skewed to the right.
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Q. Which of the following statements is true regarding the molecular orbital configuration of O2?
A.
It has 2 unpaired electrons
B.
It has 4 unpaired electrons
C.
It is diamagnetic
D.
It has a bond order of 3
Show solution
Solution
O2 has 2 unpaired electrons in its molecular orbital configuration, making it paramagnetic.
Correct Answer:
A
— It has 2 unpaired electrons
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Q. Which of the following statements is true regarding the molecular orbital theory?
A.
It only applies to diatomic molecules.
B.
It explains the magnetic properties of molecules.
C.
It does not consider electron spin.
D.
It is less accurate than valence bond theory.
Show solution
Solution
Molecular orbital theory explains the magnetic properties of molecules, such as paramagnetism in O2.
Correct Answer:
B
— It explains the magnetic properties of molecules.
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Q. Which of the following statements is true regarding the moment of inertia?
A.
It depends on the mass distribution
B.
It is always constant
C.
It is independent of the axis of rotation
D.
It is only relevant for rigid bodies
Show solution
Solution
The moment of inertia depends on the mass distribution relative to the axis of rotation.
Correct Answer:
A
— It depends on the mass distribution
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Q. Which of the following statements is true regarding the number '0' in any number system?
A.
It is always positive
B.
It is always negative
C.
It is neither positive nor negative
D.
It is undefined
Show solution
Solution
Zero is neither positive nor negative in any number system.
Correct Answer:
C
— It is neither positive nor negative
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Q. Which of the following statements is true regarding the number '100' in base 3?
A.
It is equal to 9
B.
It is equal to 10
C.
It is equal to 12
D.
It is equal to 27
Show solution
Solution
'100' in base 3 is calculated as 1*3^2 + 0*3^1 + 0*3^0 = 9.
Correct Answer:
A
— It is equal to 9
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Q. Which of the following statements is true regarding the number 'A' in hexadecimal?
A.
A is equal to 10
B.
A is equal to 11
C.
A is equal to 12
D.
A is equal to 13
Show solution
Solution
In hexadecimal, 'A' represents the decimal value 10.
Correct Answer:
A
— A is equal to 10
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Q. Which of the following statements is true regarding the number 36?
A.
It has exactly 9 factors.
B.
It is a prime number.
C.
It is a perfect square.
D.
It is a multiple of 10.
Show solution
Solution
36 is a perfect square as it can be expressed as 6 * 6.
Correct Answer:
C
— It is a perfect square.
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