Undergraduate
Q. In the context of atomic structure, what does the term 'isotope' refer to? (2021)
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A.
Atoms with the same number of protons but different neutrons
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B.
Atoms with different numbers of protons
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C.
Atoms with the same mass number
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D.
Atoms that are chemically identical
Solution
Isotopes are defined as atoms that have the same number of protons but different numbers of neutrons.
Correct Answer: A — Atoms with the same number of protons but different neutrons
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^0?
Solution
The coefficient of x^0 is given by 4C4 * (2x)^0 * (3)^4 = 1 * 81 = 81.
Correct Answer: A — 81
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^2? (2021)
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A.
-150
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B.
-300
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C.
300
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D.
150
Solution
The coefficient of x^2 is C(6,2) * (2)^2 * (-5)^4 = 15 * 4 * 625 = -37500.
Correct Answer: A — -150
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^3? (2020)
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A.
-600
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B.
-720
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C.
720
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D.
600
Solution
The coefficient of x^3 is C(6,3)(2)^3(-5)^3 = 20 * 8 * -125 = -20000.
Correct Answer: B — -720
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Q. In the expansion of (3x - 4)^4, what is the coefficient of x^2? (2023)
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A.
-144
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B.
-216
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C.
216
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D.
144
Solution
The coefficient of x^2 is C(4,2)(3)^2(-4)^2 = 6 * 9 * 16 = -864.
Correct Answer: B — -216
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Q. In the kinetic theory of gases, the term 'elastic collision' means: (2019)
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A.
Kinetic energy is conserved
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B.
Momentum is conserved
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C.
Both kinetic energy and momentum are conserved
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D.
Neither kinetic energy nor momentum is conserved
Solution
In elastic collisions, both kinetic energy and momentum are conserved, which is a key assumption in the kinetic theory of gases.
Correct Answer: C — Both kinetic energy and momentum are conserved
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Q. In the Langmuir adsorption isotherm, which assumption is NOT made? (2019)
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A.
Adsorption occurs on a surface with a finite number of identical sites
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B.
Adsorption is reversible
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C.
There is no interaction between adsorbed molecules
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D.
Adsorption occurs only at high pressures
Solution
The Langmuir isotherm assumes that adsorption occurs at all pressures, not just high pressures.
Correct Answer: D — Adsorption occurs only at high pressures
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Q. In the reaction 2Ag+ + Zn → 2Ag + Zn2+, what is the oxidation state of zinc after the reaction?
Solution
Zinc (Zn) is oxidized to Zn2+, so its oxidation state is +2.
Correct Answer: B — +2
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Q. In the reaction 2Fe + 3Cl2 → 2FeCl3, which element is oxidized?
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A.
Fe
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B.
Cl2
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C.
FeCl3
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D.
None of the above
Solution
Iron (Fe) is oxidized as it loses electrons to form FeCl3.
Correct Answer: A — Fe
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Q. In the reaction 2Fe2O3 + 3C → 4Fe + 3CO2, what is being reduced? (2020) 2020
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A.
Fe2O3
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B.
C
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C.
CO2
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D.
Fe
Solution
Fe2O3 is reduced to Fe, as it gains electrons during the reaction.
Correct Answer: A — Fe2O3
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Q. In the reaction 2Fe²⁺ + Cl2 → 2Fe³⁺ + 2Cl⁻, what is being oxidized? (2021)
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A.
Fe²⁺
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B.
Cl2
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C.
Fe³⁺
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D.
Cl⁻
Solution
In this reaction, Fe²⁺ is being oxidized to Fe³⁺ as it loses electrons.
Correct Answer: A — Fe²⁺
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Q. In the reaction 2Mg + O2 → 2MgO, which element is oxidized? (2021)
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A.
Magnesium
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B.
Oxygen
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C.
Both Magnesium and Oxygen
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D.
Neither Magnesium nor Oxygen
Solution
Magnesium is oxidized as it loses electrons and its oxidation state increases from 0 to +2.
Correct Answer: A — Magnesium
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Q. In the reaction 3H2 + N2 → 2NH3, which element is reduced? (2022)
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A.
H2
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B.
N2
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C.
NH3
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D.
None
Solution
N2 is reduced to NH3 as it gains electrons.
Correct Answer: B — N2
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Q. In the reaction 4Fe + 3O2 → 2Fe2O3, which element is oxidized?
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A.
Fe
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B.
O2
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C.
Fe2O3
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D.
None of the above
Solution
Iron (Fe) is oxidized as it loses electrons to form Fe2O3.
Correct Answer: A — Fe
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Q. In the reaction Zn + CuSO4 → ZnSO4 + Cu, which species is reduced?
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A.
Zn
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B.
CuSO4
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C.
ZnSO4
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D.
Cu
Solution
Copper (Cu) is reduced as it gains electrons from zinc.
Correct Answer: D — Cu
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Q. In the reaction Zn + Cu²⁺ → Zn²⁺ + Cu, which element is oxidized? (2022)
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A.
Zn
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B.
Cu²⁺
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C.
Zn²⁺
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D.
Cu
Solution
Zinc (Zn) is oxidized as it loses electrons to form Zn²⁺.
Correct Answer: A — Zn
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Q. In the redox reaction 2Ag+ + Cu → 2Ag + Cu2+, which species is oxidized? (2022) 2022
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A.
Ag+
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B.
Cu
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C.
Ag
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D.
Cu2+
Solution
Cu is oxidized to Cu2+ as it loses electrons in the reaction.
Correct Answer: B — Cu
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Q. In the redox reaction 2Ag+ + Zn → 2Ag + Zn2+, which species is oxidized? (2021)
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A.
Ag+
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B.
Zn
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C.
Ag
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D.
Zn2+
Solution
Zn is oxidized to Zn2+ as it loses electrons.
Correct Answer: B — Zn
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Q. In the redox reaction 2MnO4- + 5C2O4^2- + 16H+ → 2Mn^2+ + 10CO2 + 8H2O, what is the oxidation state of carbon in C2O4^2-?
Solution
In C2O4^2-, the oxidation state of carbon is +3.
Correct Answer: C — +4
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Q. In which of the following organisms does external fertilization occur? (2021)
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A.
Frog
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B.
Human
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C.
Dog
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D.
Cat
Solution
Frogs exhibit external fertilization where eggs and sperm are released into the water.
Correct Answer: A — Frog
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Q. In which of the following processes is adsorption utilized? (2023)
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A.
Water purification
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B.
Sublimation
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C.
Distillation
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D.
Filtration
Solution
Adsorption is widely used in water purification processes to remove impurities.
Correct Answer: A — Water purification
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Q. In which of the following processes is the enthalpy change (ΔH) equal to the heat absorbed at constant pressure? (2019)
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A.
Isothermal process
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B.
Isochoric process
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C.
Isobaric process
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D.
Adiabatic process
Solution
In an isobaric process, the enthalpy change (ΔH) is equal to the heat absorbed or released at constant pressure.
Correct Answer: C — Isobaric process
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Q. In which part of the plant does respiration primarily occur? (2020)
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A.
Roots
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B.
Leaves
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C.
Stems
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D.
All parts
Solution
Respiration occurs in all parts of the plant, including roots, leaves, and stems.
Correct Answer: D — All parts
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Q. In which phase of the cell cycle does the cell spend the majority of its life? (2021)
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A.
M phase
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B.
G1 phase
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C.
S phase
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D.
G2 phase
Solution
The G1 phase is where the cell spends most of its life, performing normal functions and growing.
Correct Answer: B — G1 phase
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Q. In which state of matter do particles have the least amount of energy?
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A.
Solid
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B.
Liquid
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C.
Gas
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D.
Plasma
Solution
Particles in a solid have the least amount of energy compared to liquids, gases, and plasma.
Correct Answer: A — Solid
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Q. In which state of matter do particles move freely and are far apart? (2021)
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A.
Solid
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B.
Liquid
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C.
Gas
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D.
None of the above
Solution
In gases, particles move freely and are far apart compared to solids and liquids.
Correct Answer: C — Gas
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Q. Solve the differential equation dy/dx = 2x + 1.
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A.
y = x^2 + x + C
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B.
y = x^2 + 2x + C
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C.
y = 2x^2 + x + C
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D.
y = x^2 + C
Solution
Integrating both sides, we get y = ∫(2x + 1)dx = x^2 + x + C.
Correct Answer: A — y = x^2 + x + C
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Q. Solve the differential equation dy/dx = 2y + 3. (2023)
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A.
y = Ce^(2x) - 3/2
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B.
y = Ce^(-2x) + 3/2
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C.
y = 3e^(2x)
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D.
y = 2e^(2x) + C
Solution
Using an integrating factor, we find the solution is y = Ce^(2x) - 3/2.
Correct Answer: A — y = Ce^(2x) - 3/2
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Q. Solve the differential equation dy/dx = y/x. (2023)
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A.
y = Cx
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B.
y = Cx^2
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C.
y = C/x
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D.
y = C ln(x)
Solution
This is a separable equation. Integrating gives y = Cx.
Correct Answer: A — y = Cx
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Q. Solve the differential equation y' = 5 - 2y.
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A.
y = 5/2 + Ce^(-2x)
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B.
y = 5 + Ce^(-2x)
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C.
y = 2 + Ce^(2x)
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D.
y = 5/2 - Ce^(-2x)
Solution
This is a linear first-order equation. The solution is y = 5/2 + Ce^(-2x).
Correct Answer: A — y = 5/2 + Ce^(-2x)
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