Undergraduate
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 - 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) 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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Q. What is the molecular formula of butan-2-one?
A.
C4H8O
B.
C4H10O
C.
C4H6O
D.
C4H12O
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Solution
The molecular formula of butan-2-one is C4H8O.
Correct Answer: A — C4H8O
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Q. What is the molecular formula of butanoic acid?
A.
C3H6O2
B.
C4H8O2
C.
C5H10O2
D.
C6H12O2
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Solution
The molecular formula of butanoic acid is C4H8O2.
Correct Answer: B — C4H8O2
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Q. What is the molecular formula of cyclohexane? (2022)
A.
C6H12
B.
C6H10
C.
C6H14
D.
C6H6
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Solution
Cyclohexane is a cyclic alkane with the formula C6H12.
Correct Answer: A — C6H12
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Q. What is the molecular formula of formaldehyde?
A.
C2H4O
B.
CH2O
C.
C3H6O
D.
C4H8O
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Solution
The molecular formula of formaldehyde is CH2O.
Correct Answer: B — CH2O
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Q. What is the molecular formula of glucose? (2022)
A.
C6H12O6
B.
C5H10O5
C.
C6H10O5
D.
C6H14O6
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Solution
Glucose is a simple sugar with the molecular formula C6H12O6.
Correct Answer: A — C6H12O6
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Q. What is the molecular formula of glucose? (2022) 2022
A.
C6H12O6
B.
C5H10O5
C.
C6H10O5
D.
C6H14O6
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Solution
Glucose is a simple sugar with the molecular formula C6H12O6.
Correct Answer: A — C6H12O6
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Q. What is the molecular formula of the simplest alkyne? (2022)
A.
C2H2
B.
C2H4
C.
C3H4
D.
C3H6
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Solution
The simplest alkyne is ethyne (acetylene) with the molecular formula C2H2.
Correct Answer: A — C2H2
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Q. What is the momentum of a 3 kg object moving at a velocity of 4 m/s? (2017)
A.
12 kg·m/s
B.
7 kg·m/s
C.
15 kg·m/s
D.
10 kg·m/s
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Solution
Momentum (p) = mass × velocity = 3 kg × 4 m/s = 12 kg·m/s.
Correct Answer: A — 12 kg·m/s
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Q. What is the monomer of nucleic acids? (2023)
A.
Amino acid
B.
Nucleotide
C.
Monosaccharide
D.
Fatty acid
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Solution
Nucleotides are the monomers that make up nucleic acids.
Correct Answer: B — Nucleotide
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Q. What is the monomer of polyethylene?
A.
Ethylene
B.
Propylene
C.
Butylene
D.
Styrene
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Solution
Polyethylene is made from the polymerization of ethylene monomers.
Correct Answer: A — Ethylene
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Q. What is the monomer of polystyrene?
A.
Ethylene
B.
Styrene
C.
Propylene
D.
Vinyl chloride
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Solution
The monomer of polystyrene is styrene, which polymerizes to form polystyrene.
Correct Answer: B — Styrene
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Q. What is the nature of the image formed by a concave mirror when the object is placed between the focal point and the mirror? (2021)
A.
Real and inverted
B.
Virtual and erect
C.
Real and erect
D.
Virtual and inverted
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Solution
When the object is placed between the focal point and the mirror, the image formed is virtual and erect.
Correct Answer: B — Virtual and erect
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Q. What is the Nernst equation for a cell at 298 K with E° = 0.77 V and [Zn²⁺] = 0.01 M?
A.
E = 0.77 - 0.0591 log(0.01)
B.
E = 0.77 + 0.0591 log(0.01)
C.
E = 0.77 - 0.0591 log(100)
D.
E = 0.77 + 0.0591 log(100)
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Solution
Using the Nernst equation: E = E° - (0.0591/n) log([Zn²⁺]), where n=2.
Correct Answer: A — E = 0.77 - 0.0591 log(0.01)
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Q. What is the Nernst equation used for calculating the cell potential at non-standard conditions? (2023)
A.
E = E° - (RT/nF)lnQ
B.
E = E° + (RT/nF)lnQ
C.
E = E° - (nF/RT)lnQ
D.
E = E° + (nF/RT)lnQ
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Solution
The Nernst equation is E = E° - (RT/nF)lnQ, where E is the cell potential, E° is the standard potential, R is the gas constant, T is the temperature, n is the number of moles of electrons, and F is Faraday's constant.
Correct Answer: A — E = E° - (RT/nF)lnQ
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Q. What is the Nernst equation used for? (2023) 2023
A.
Calculating pH
B.
Determining cell potential
C.
Measuring current
D.
Finding resistance
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Solution
The Nernst equation is used to determine the cell potential under non-standard conditions.
Correct Answer: B — Determining cell potential
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Q. What is the net force acting on a 12 kg object moving with a constant velocity? (2023)
A.
0 N
B.
12 N
C.
24 N
D.
36 N
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Solution
According to Newton's first law, if the object is moving with constant velocity, the net force is 0 N.
Correct Answer: A — 0 N
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Q. What is the net force acting on a 15 kg object moving with a constant velocity? (2021)
A.
0 N
B.
15 N
C.
30 N
D.
45 N
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Solution
If the object is moving with constant velocity, net force is 0 N (Newton's first law).
Correct Answer: A — 0 N
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Q. What is the net gain of ATP molecules from one molecule of glucose during aerobic respiration? (2023)
A.
2
B.
18
C.
30-32
D.
36
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Solution
The net gain of ATP molecules from one molecule of glucose during aerobic respiration is approximately 30-32 ATP.
Correct Answer: C — 30-32
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Q. What is the normal pH range of human blood? (2019)
A.
6.8 - 7.2
B.
7.35 - 7.45
C.
7.0 - 7.5
D.
7.8 - 8.0
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Solution
The normal pH range of human blood is tightly regulated between 7.35 and 7.45, which is essential for proper physiological function.
Correct Answer: B — 7.35 - 7.45
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