Q. What is the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 48? (2021)
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Solution
The maximum height occurs at t = -b/(2a) = -64/(2*-16) = 2. h(2) = -16(2^2) + 64(2) + 48 = 80.
Correct Answer: B — 64
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Q. What is the maximum number of bright fringes observed in a double-slit experiment if the wavelength of light is 500 nm and the distance between the slits is 0.1 mm? (2020)
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Solution
The maximum number of bright fringes is given by the formula n = d/λ. Here, n = 0.1 mm / 500 nm = 200, which means 20 bright fringes can be observed on either side of the central maximum.
Correct Answer: C — 20
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Q. What is the maximum number of bright fringes that can be observed in a double-slit experiment with a given wavelength? (2023)
A.
Depends on the slit width
B.
Depends on the distance to the screen
C.
Depends on the wavelength and slit separation
D.
Always infinite
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Solution
The maximum number of bright fringes depends on the wavelength and the slit separation, as it determines how many integer multiples of the wavelength fit within the observable range.
Correct Answer: C — Depends on the wavelength and slit separation
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Q. What is the maximum number of electrons in the d subshell? (2022) 2022
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Solution
The d subshell can hold a maximum of 10 electrons.
Correct Answer: C — 10
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Q. What is the maximum number of electrons in the f-subshell? (2022)
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Solution
The f-subshell can hold a maximum of 14 electrons.
Correct Answer: C — 14
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Q. What is the maximum number of electrons that can occupy the n=3 shell? (2021) 2021
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Solution
The maximum number of electrons in a shell is given by the formula 2n². For n=3, it is 2(3)² = 18.
Correct Answer: C — 18
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Q. What is the maximum number of electrons that can occupy the n=3 shell? (2022) 2022
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Solution
The maximum number of electrons in a shell is given by the formula 2n². For n=3, it is 2(3)² = 18.
Correct Answer: C — 18
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Q. What is the maximum oxidation state of phosphorus in its compounds? (2021)
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Solution
Phosphorus can exhibit a maximum oxidation state of +5 in compounds like PCl5.
Correct Answer: B — +5
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Q. What is the maximum profit if the profit function is P(x) = -x^2 + 10x - 16? (2021)
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Solution
The maximum profit occurs at x = -b/(2a) = 10/2 = 5. P(5) = -5^2 + 10*5 - 16 = 9.
Correct Answer: C — 8
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Q. What is the maximum value of f(x) = -x^2 + 4x + 1? (2023)
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Solution
The vertex occurs at x = 2. f(2) = -2^2 + 4(2) + 1 = 5.
Correct Answer: A — 5
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Q. What is the maximum value of f(x) = -x^2 + 6x - 8? (2023)
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Solution
The vertex occurs at x = 3. f(3) = -9 + 18 - 8 = 1.
Correct Answer: C — 6
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Q. What is the minimum distance from the point (3, 4) to the line 2x + 3y - 6 = 0? (2023)
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Solution
Using the distance formula from a point to a line, the minimum distance is calculated to be 2 units.
Correct Answer: A — 2
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Q. What is the minimum energy required to remove an electron from a metal surface with a work function of 2 eV? (2021)
A.
1 eV
B.
2 eV
C.
3 eV
D.
4 eV
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Solution
The minimum energy required is equal to the work function, which is 2 eV.
Correct Answer: B — 2 eV
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Q. What is the minimum thickness of a soap bubble for which the first order of constructive interference occurs for light of wavelength λ? (2019)
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
For constructive interference in a soap bubble, the minimum thickness should be λ/4, accounting for the phase change upon reflection.
Correct Answer: A — λ/4
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Q. What is the minimum value of f(x) = 3x^2 - 12x + 12? (2021)
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Solution
The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 12 = 0.
Correct Answer: B — 3
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Q. What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)
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Solution
The vertex occurs at x = 2. f(2) = -5.
Correct Answer: A — -5
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Q. What is the minimum value of f(x) = 3x^2 - 12x + 9? (2022)
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Solution
The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 9 = 0.
Correct Answer: B — 1
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Q. What is the minimum value of f(x) = x^2 - 4x + 5? (2020)
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2.
Correct Answer: A — 1
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Q. What is the minimum value of f(x) = x^2 - 4x + 6? (2022)
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Solution
The vertex occurs at x = 2. f(2) = 2.
Correct Answer: B — 3
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Q. What is the minimum value of f(x) = x^2 - 4x + 7? (2023)
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2, thus minimum value is 3.
Correct Answer: A — 3
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Q. What is the minimum value of f(x) = x^2 - 6x + 10? (2020)
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Solution
The vertex form gives the minimum at x = 3. f(3) = 3^2 - 6(3) + 10 = 1.
Correct Answer: A — 4
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Q. What is the minimum value of the function f(x) = 4x^2 - 16x + 20? (2021)
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Solution
The vertex gives the minimum at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.
Correct Answer: B — 5
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Q. What is the minimum value of the function f(x) = 4x^2 - 16x + 20? (2021) 2021
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Solution
The vertex occurs at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.
Correct Answer: B — 5
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Q. What is the modulus of the complex number 3 + 4i? (2023)
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Solution
The modulus is calculated as √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Correct Answer: A — 5
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Q. What is the molality of a solution made by dissolving 10 moles of solute in 5 kg of solvent? (2022)
A.
2 m
B.
1 m
C.
0.5 m
D.
3 m
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Solution
Molality (m) = moles of solute / kg of solvent = 10 moles / 5 kg = 2 m.
Correct Answer: A — 2 m
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Q. What is the molar mass of water (H2O)? (2023) 2023
A.
16 g/mol
B.
18 g/mol
C.
20 g/mol
D.
22 g/mol
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Solution
The molar mass of water is calculated as follows: H (1 g/mol) x 2 + O (16 g/mol) = 2 + 16 = 18 g/mol.
Correct Answer: B — 18 g/mol
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Q. What is the molarity of a solution containing 5 moles of solute in 2 liters of solution? (2021) 2021
A.
2.5 M
B.
5 M
C.
10 M
D.
1 M
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Solution
Molarity (M) = moles of solute / liters of solution = 5 moles / 2 L = 2.5 M.
Correct Answer: A — 2.5 M
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Q. What is the molarity of a solution containing 58.5 g of NaCl in 1 liter of solution? (2021)
A.
1 M
B.
0.5 M
C.
2 M
D.
0.1 M
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Solution
Molarity (M) = moles of solute / liters of solution. Moles of NaCl = 58.5 g / 58.5 g/mol = 1 mol. Therefore, M = 1 mol / 1 L = 1 M.
Correct Answer: A — 1 M
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Q. What is the molarity of a solution prepared by dissolving 5 grams of NaCl in enough water to make 250 mL of solution? (Molar mass of NaCl = 58.5 g/mol) (2023)
A.
0.34 M
B.
0.42 M
C.
0.25 M
D.
0.50 M
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Solution
Molarity (M) = moles of solute / liters of solution. Moles of NaCl = 5 g / 58.5 g/mol = 0.0855 moles. Volume of solution = 250 mL = 0.250 L. M = 0.0855 moles / 0.250 L = 0.342 M, approximately 0.34 M.
Correct Answer: A — 0.34 M
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Q. What is the molecular formula of Benzoic acid?
A.
C6H5COOH
B.
C7H6O2
C.
C6H6O
D.
C6H4O2
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Solution
The molecular formula of Benzoic acid is C7H6O2.
Correct Answer: B — C7H6O2
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