Q. What is the rank of the matrix E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2023)
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Solution
The rank of E is 2 because the rows are linearly dependent (the third row is a linear combination of the first two).
Correct Answer: B — 2
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Q. What is the rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
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Solution
The rank of the matrix is 2, as the rows are linearly dependent.
Correct Answer: B — 2
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Q. What is the rate constant of a first-order reaction if the half-life is 10 minutes? (2021)
A.
0.0693 min⁻¹
B.
0.1 min⁻¹
C.
0.693 min⁻¹
D.
0.5 min⁻¹
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Solution
For a first-order reaction, k = 0.693 / t₁/₂. Here, t₁/₂ = 10 min, so k = 0.693 / 10 = 0.0693 min⁻¹.
Correct Answer: A — 0.0693 min⁻¹
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Q. What is the rate law expression for a reaction that is first order with respect to reactant A? (2022)
A.
Rate = k[A]
B.
Rate = k[A]^2
C.
Rate = k[A]^0
D.
Rate = k[A]^[1/2]
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Solution
For a first order reaction, the rate law is directly proportional to the concentration of the reactant, hence Rate = k[A].
Correct Answer: A — Rate = k[A]
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Q. What is the rate law expression for a reaction that is first order with respect to A and second order with respect to B? (2022)
A.
Rate = k[A][B]^2
B.
Rate = k[A]^2[B]
C.
Rate = k[A]^2[B]^2
D.
Rate = k[A][B]
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Solution
The rate law for a reaction is determined by the order with respect to each reactant. For a first order with respect to A and second order with respect to B, the rate law is Rate = k[A][B]^2.
Correct Answer: A — Rate = k[A][B]^2
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Q. What is the rate law expression for a reaction that is second order with respect to reactant A? (2023)
A.
Rate = k[A]
B.
Rate = k[A]^2
C.
Rate = k[A]^2[B]
D.
Rate = k[A][B]
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Solution
For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.
Correct Answer: B — Rate = k[A]^2
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Q. What is the rate law expression for a reaction with the rate equation rate = k[A]^2[B]?
A.
rate = k[A][B]
B.
rate = k[A]^2
C.
rate = k[A]^2[B]
D.
rate = k[B]
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Solution
The rate law expression is derived directly from the rate equation, which is given as rate = k[A]^2[B].
Correct Answer: C — rate = k[A]^2[B]
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Q. What is the rate law for a reaction that is first order with respect to A and second order with respect to B? (2022) 2022
A.
Rate = k[A][B]^2
B.
Rate = k[A]^2[B]
C.
Rate = k[A]^2[B]^2
D.
Rate = k[A][B]
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Solution
The rate law is determined by the order of the reaction with respect to each reactant. For first order in A and second order in B, the rate law is Rate = k[A][B]^2.
Correct Answer: A — Rate = k[A][B]^2
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Q. What is the rate law for a reaction that is second order with respect to reactant A? (2023)
A.
Rate = k[A]
B.
Rate = k[A]^2
C.
Rate = k[A]^2[B]
D.
Rate = k[A][B]
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Solution
For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.
Correct Answer: B — Rate = k[A]^2
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Q. What is the reactance of an inductor at a frequency of 50 Hz if the inductance is 0.1 H? (2023)
A.
31.4 Ω
B.
6.28 Ω
C.
157 Ω
D.
12.56 Ω
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Solution
Reactance (X_L) = 2πfL = 2π(50)(0.1) = 31.4 Ω.
Correct Answer: A — 31.4 Ω
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Q. What is the reactance of an inductor in an AC circuit with frequency f? (2023)
A.
2πfL
B.
1/(2πfL)
C.
L/(2πf)
D.
0
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Solution
The reactance of an inductor in an AC circuit is given by the formula X_L = 2πfL.
Correct Answer: A — 2πfL
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Q. What is the real part of the complex number 4 + 5i? (2023)
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Solution
The real part of the complex number 4 + 5i is 4.
Correct Answer: A — 4
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Q. What is the real part of the complex number 5 - 7i?
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Solution
The real part of 5 - 7i is 5.
Correct Answer: A — 5
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Q. What is the real part of the complex number 7 - 4i? (2023)
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Solution
The real part of the complex number 7 - 4i is 7.
Correct Answer: A — 7
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Q. What is the real part of the complex number z = 2e^(iπ/3)?
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Solution
The real part is 2 * cos(π/3) = 2 * 1/2 = 1.
Correct Answer: B — 2
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Q. What is the real part of the complex number z = 4 + 5i? (2022)
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Solution
The real part of z = 4 + 5i is 4.
Correct Answer: A — 4
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Q. What is the real part of the complex number z = 4e^(iπ/3)?
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Solution
The real part is Re(z) = 4 * cos(π/3) = 4 * 1/2 = 2.
Correct Answer: C — 2√3
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Q. What is the real part of the complex number z = 5 - 2i?
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Solution
The real part of z = 5 - 2i is 5.
Correct Answer: A — 5
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Q. What is the real part of the complex number z = 5 - 4i?
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Solution
The real part of z = 5 - 4i is 5.
Correct Answer: A — 5
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Q. What is the real part of the complex number z = 5 - 6i?
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Solution
The real part of z = 5 - 6i is 5.
Correct Answer: A — 5
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Q. What is the real part of the complex number z = 5e^(iπ/3)?
A.
5/2
B.
5/√3
C.
5√3/2
D.
5
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Solution
The real part is Re(z) = 5cos(π/3) = 5 * 1/2 = 5/2.
Correct Answer: A — 5/2
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Q. What is the recommended daily intake of fruits and vegetables for a healthy diet?
A.
1-2 servings
B.
3-5 servings
C.
5-7 servings
D.
7-10 servings
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Solution
The recommended daily intake is 5-7 servings of fruits and vegetables for optimal health.
Correct Answer: B — 3-5 servings
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Q. What is the reducing agent in the reaction 2MnO4- + 5C2O4^2- + 6H+ → 2Mn^2+ + 10CO2 + 3H2O?
A.
MnO4-
B.
C2O4^2-
C.
H+
D.
CO2
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Solution
C2O4^2- is the reducing agent as it donates electrons.
Correct Answer: B — C2O4^2-
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Q. What is the reducing agent in the reaction Zn + CuSO4 → ZnSO4 + Cu?
A.
Zn
B.
Cu
C.
CuSO4
D.
ZnSO4
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Solution
Zinc (Zn) is the reducing agent as it donates electrons to copper.
Correct Answer: A — Zn
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Q. What is the reduction half-reaction for the conversion of MnO4- to Mn2+ in acidic medium?
A.
MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
B.
MnO4- + 5e- → Mn2+ + 8H+ + 4H2O
C.
MnO4- + 4H2O + 5e- → Mn2+ + 8H+
D.
MnO4- + 5e- + 4H2O → Mn2+ + 8H+
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Solution
The correct reduction half-reaction in acidic medium is MnO4- + 8H+ + 5e- → Mn2+ + 4H2O.
Correct Answer: A — MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
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Q. What is the reduction half-reaction for the reaction 2MnO4- + 16H+ + 10e- → 2Mn2+ + 8H2O?
A.
MnO4- + 8H2O + 10e- → Mn2+ + 16H+
B.
MnO4- + 10e- + 8H+ → Mn2+ + 4H2O
C.
MnO4- + 10e- → Mn2+ + 8H2O
D.
MnO4- + 16H+ → Mn2+ + 10e- + 8H2O
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Solution
The correct reduction half-reaction shows the gain of electrons and protons.
Correct Answer: B — MnO4- + 10e- + 8H+ → Mn2+ + 4H2O
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Q. What is the reduction half-reaction for the reaction of copper(II) ions with zinc?
A.
Cu^2+ + 2e^- → Cu
B.
Zn → Zn^2+ + 2e^-
C.
Cu → Cu^2+ + 2e^-
D.
Zn^2+ + 2e^- → Zn
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Solution
The reduction half-reaction is Cu^2+ + 2e^- → Cu.
Correct Answer: A — Cu^2+ + 2e^- → Cu
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Q. What is the reduction half-reaction for the reaction of MnO4- in acidic medium?
A.
MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
B.
MnO4- + 3e- → MnO2 + 2H2O
C.
MnO4- + 2e- → MnO2 + 4H+
D.
MnO4- + 4e- + 8H+ → MnO2 + 4H2O
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Solution
In acidic medium, MnO4- is reduced to Mn2+.
Correct Answer: A — MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
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Q. What is the reduction potential of the half-reaction 2H⁺ + 2e⁻ → H₂?
A.
0.00 V
B.
0.34 V
C.
0.76 V
D.
1.23 V
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Solution
The standard reduction potential for 2H⁺ + 2e⁻ → H₂ is 0.00 V.
Correct Answer: D — 1.23 V
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Q. What is the refractive index of a medium if the critical angle for total internal reflection is 30°?
A.
1.00
B.
1.15
C.
1.73
D.
2.00
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Solution
Using the formula n = 1/sin(θc), where θc = 30°, we find n = 1/sin(30°) = 1/0.5 = 2.00.
Correct Answer: C — 1.73
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