Q. Which of the following statements is true regarding the complex [Cr(NH3)6]3+? (2023)
A.
It is tetrahedral
B.
It is octahedral
C.
It is square planar
D.
It has a coordination number of 4
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Solution
The complex [Cr(NH3)6]3+ is octahedral with a coordination number of 6, as it is surrounded by six ammonia ligands.
Correct Answer: B — It is octahedral
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Q. Which of the following statements is true regarding the complex [Cu(NH3)4]SO4?
A.
Cu is in +1 oxidation state
B.
Cu is in +2 oxidation state
C.
NH3 is a monodentate ligand
D.
All of the above
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Solution
In [Cu(NH3)4]SO4, copper is in +2 oxidation state, NH3 is a monodentate ligand, making the statement 'All of the above' incorrect.
Correct Answer: D — All of the above
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Q. Which of the following statements is true regarding the data represented in the mixed graph? (2023)
A.
The data is consistent across all variables.
B.
There are outliers affecting the overall trend.
C.
The data is skewed towards higher values.
D.
All variables are equally represented.
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Solution
The presence of outliers is evident in the graph, which affects the overall trend of the data.
Correct Answer: B — There are outliers affecting the overall trend.
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Q. Which of the following statements is true regarding the Earth's magnetic field?
A.
It is uniform everywhere
B.
It has a magnetic north and south pole
C.
It is only present at the equator
D.
It does not affect compass needles
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Solution
The Earth's magnetic field has a magnetic north and south pole and affects compass needles, causing them to align with the field.
Correct Answer: B — It has a magnetic north and south pole
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Q. Which of the following statements is true regarding the energy levels of molecular orbitals?
A.
σ orbitals are always lower in energy than π orbitals.
B.
π orbitals are always lower in energy than σ orbitals.
C.
For second period elements, σ2p is lower than π2p.
D.
Bonding orbitals are higher in energy than antibonding orbitals.
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Solution
For second period elements, σ2p is lower in energy than π2p.
Correct Answer: C — For second period elements, σ2p is lower than π2p.
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Q. Which of the following statements is true regarding the equilibrium constant (K) for a reaction?
A.
K is temperature dependent
B.
K is pressure dependent
C.
K is concentration dependent
D.
K is always equal to 1
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Solution
The equilibrium constant (K) is dependent on temperature; it changes with temperature variations.
Correct Answer: A — K is temperature dependent
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Q. Which of the following statements is true regarding the equilibrium constant Kc?
A.
Kc is temperature dependent
B.
Kc is pressure dependent
C.
Kc is concentration dependent
D.
Kc is independent of the reaction
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Solution
The equilibrium constant Kc is dependent on temperature; changing the temperature will change the value of Kc.
Correct Answer: A — Kc is temperature dependent
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Q. Which of the following statements is true regarding the equilibrium constant? (2020)
A.
Kc is temperature dependent
B.
Kc is pressure dependent
C.
Kc is concentration dependent
D.
Kc is independent of temperature
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Solution
The equilibrium constant Kc is dependent on temperature; changing the temperature will change the value of Kc.
Correct Answer: A — Kc is temperature dependent
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Q. Which of the following statements is true regarding the first law of thermodynamics?
A.
It applies only to closed systems.
B.
It is a statement of conservation of energy.
C.
It can be violated under certain conditions.
D.
It only applies to mechanical systems.
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Solution
The first law of thermodynamics is a statement of conservation of energy, applicable to all thermodynamic systems.
Correct Answer: B — It is a statement of conservation of energy.
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Q. Which of the following statements is true regarding the Freundlich adsorption isotherm? (2020) 2020
A.
It is applicable to monolayer adsorption.
B.
It assumes a uniform surface.
C.
It is a linear relationship.
D.
It describes heterogeneous adsorption.
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Solution
The Freundlich adsorption isotherm describes heterogeneous adsorption on surfaces with varying affinities, making it suitable for real-world applications.
Correct Answer: D — It describes heterogeneous adsorption.
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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) = 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 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 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
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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.
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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 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.
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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 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
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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 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
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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 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
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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.
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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.
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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 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
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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.
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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
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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 photoelectric effect?
A.
Electrons are emitted only if the light is of high intensity
B.
Electrons are emitted regardless of the frequency of light
C.
There is a threshold frequency below which no electrons are emitted
D.
The photoelectric effect can occur with any type of electromagnetic radiation
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Solution
The photoelectric effect requires a minimum threshold frequency; below this frequency, no electrons are emitted regardless of the intensity of the light.
Correct Answer: C — There is a threshold frequency below which no electrons are emitted
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