Q. What is the real part of the complex number 7 - 4i? (2023)
Solution
The real part of the complex number 7 - 4i is 7.
Correct Answer:
A
— 7
Learn More →
Q. What is the real part of the complex number z = -2 + 3i? (2020)
Solution
The real part of z is -2.
Correct Answer:
A
— -2
Learn More →
Q. What is the real part of the complex number z = 2e^(iπ/3)?
Solution
The real part is 2 * cos(π/3) = 2 * 1/2 = 1.
Correct Answer:
B
— 2
Learn More →
Q. What is the real part of the complex number z = 3 - 5i? (2019)
Solution
The real part of z is 3.
Correct Answer:
A
— 3
Learn More →
Q. What is the real part of the complex number z = 4 + 5i? (2022)
Solution
The real part of z = 4 + 5i is 4.
Correct Answer:
A
— 4
Learn More →
Q. What is the real part of the complex number z = 4 - 3i? (2023)
Solution
The real part of z is 4.
Correct Answer:
A
— 4
Learn More →
Q. What is the real part of the complex number z = 4e^(iπ/3)?
Solution
The real part is Re(z) = 4 * cos(π/3) = 4 * 1/2 = 2.
Correct Answer:
C
— 2√3
Learn More →
Q. What is the real part of the complex number z = 5 - 2i?
Solution
The real part of z = 5 - 2i is 5.
Correct Answer:
A
— 5
Learn More →
Q. What is the real part of the complex number z = 5 - 4i?
Solution
The real part of z = 5 - 4i is 5.
Correct Answer:
A
— 5
Learn More →
Q. What is the real part of the complex number z = 5 - 6i?
Solution
The real part of z = 5 - 6i is 5.
Correct Answer:
A
— 5
Learn More →
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
Solution
The real part is Re(z) = 5cos(π/3) = 5 * 1/2 = 5/2.
Correct Answer:
A
— 5/2
Learn More →
Q. What is the recommended daily intake of fiber for adults?
-
A.
10-15 grams
-
B.
20-25 grams
-
C.
25-30 grams
-
D.
30-35 grams
Solution
The recommended daily intake of fiber for adults is 25-30 grams to maintain digestive health.
Correct Answer:
C
— 25-30 grams
Learn More →
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
Solution
The recommended daily intake is 5-7 servings of fruits and vegetables for optimal health.
Correct Answer:
B
— 3-5 servings
Learn More →
Q. What is the recommended daily intake of fruits and vegetables for adults?
-
A.
1-2 servings
-
B.
3-5 servings
-
C.
5-7 servings
-
D.
7-10 servings
Solution
The recommended daily intake of fruits and vegetables for adults is 5-7 servings to ensure adequate nutrient intake.
Correct Answer:
B
— 3-5 servings
Learn More →
Q. What is the recommended daily intake of protein for an average adult? (2019)
-
A.
30 grams
-
B.
50 grams
-
C.
70 grams
-
D.
100 grams
Solution
The recommended daily intake of protein for an average adult is about 50 grams.
Correct Answer:
B
— 50 grams
Learn More →
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
Solution
C2O4^2- is the reducing agent as it donates electrons.
Correct Answer:
B
— C2O4^2-
Learn More →
Q. What is the reducing agent in the reaction Zn + CuSO4 → ZnSO4 + Cu?
-
A.
Zn
-
B.
Cu
-
C.
CuSO4
-
D.
ZnSO4
Solution
Zinc (Zn) is the reducing agent as it donates electrons to copper.
Correct Answer:
A
— Zn
Learn More →
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+
Solution
The correct reduction half-reaction in acidic medium is MnO4- + 8H+ + 5e- → Mn2+ + 4H2O.
Correct Answer:
A
— MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
Learn More →
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
Solution
The correct reduction half-reaction shows the gain of electrons and protons.
Correct Answer:
B
— MnO4- + 10e- + 8H+ → Mn2+ + 4H2O
Learn More →
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
Solution
The reduction half-reaction is Cu^2+ + 2e^- → Cu.
Correct Answer:
A
— Cu^2+ + 2e^- → Cu
Learn More →
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
Solution
In acidic medium, MnO4- is reduced to Mn2+.
Correct Answer:
A
— MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
Learn More →
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
Solution
The standard reduction potential for 2H⁺ + 2e⁻ → H₂ is 0.00 V.
Correct Answer:
D
— 1.23 V
Learn More →
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
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
Learn More →
Q. What is the refractive index of a medium if the critical angle for total internal reflection is 30° when light travels to air?
-
A.
1.73
-
B.
1.00
-
C.
1.41
-
D.
1.50
Solution
Using sin(30°) = 0.5, n = 1/sin(30°) = 1/0.5 = 2. Therefore, the refractive index is 2.
Correct Answer:
A
— 1.73
Learn More →
Q. What is the relationship between a function and its inverse?
-
A.
They are always identical.
-
B.
The inverse function undoes the action of the original function.
-
C.
They can never intersect on a graph.
-
D.
The inverse function is always a polynomial.
Solution
The inverse function undoes the action of the original function, meaning that applying a function and then its inverse returns the original input.
Correct Answer:
B
— The inverse function undoes the action of the original function.
Learn More →
Q. What is the relationship between angular momentum L and moment of inertia I for a rotating object?
-
A.
L = Iω
-
B.
L = I²ω
-
C.
L = ω/I
-
D.
L = I + ω
Solution
Angular momentum L is given by L = Iω, where ω is the angular velocity.
Correct Answer:
A
— L = Iω
Learn More →
Q. What is the relationship between biodiversity and climate change as described in the passage?
-
A.
Biodiversity is unaffected by climate change.
-
B.
Climate change enhances biodiversity.
-
C.
Biodiversity loss exacerbates climate change.
-
D.
Biodiversity and climate change are unrelated.
Solution
The passage indicates that loss of biodiversity can worsen the effects of climate change.
Correct Answer:
C
— Biodiversity loss exacerbates climate change.
Learn More →
Q. What is the relationship between biodiversity and climate change as discussed in the passage?
-
A.
Biodiversity is unaffected by climate change.
-
B.
Climate change poses a significant threat to biodiversity.
-
C.
Biodiversity can mitigate the effects of climate change.
-
D.
The passage does not address biodiversity.
Solution
The passage discusses how climate change significantly threatens biodiversity, leading to habitat loss and species extinction.
Correct Answer:
B
— Climate change poses a significant threat to biodiversity.
Learn More →
Q. What is the relationship between bulk modulus and compressibility?
-
A.
Bulk modulus is the inverse of compressibility
-
B.
Bulk modulus is equal to compressibility
-
C.
Bulk modulus is the square of compressibility
-
D.
There is no relationship
Solution
Bulk modulus is defined as the reciprocal of compressibility, indicating how incompressible a material is.
Correct Answer:
A
— Bulk modulus is the inverse of compressibility
Learn More →
Q. What is the relationship between Celsius and Kelvin?
-
A.
K = C + 273.15
-
B.
K = C - 273.15
-
C.
C = K + 273.15
-
D.
C = K - 273.15
Solution
The relationship is K = C + 273.15, where K is the temperature in Kelvin and C is the temperature in Celsius.
Correct Answer:
A
— K = C + 273.15
Learn More →
Showing 20731 to 20760 of 28492 (950 Pages)
