Q. What is the oxidation state of phosphorus in H3PO4?
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Solution
In H3PO4, phosphorus has an oxidation state of +5.
Correct Answer: A — +5
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Q. What is the oxidation state of phosphorus in phosphoric acid (H3PO4)?
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Solution
In phosphoric acid, phosphorus has an oxidation state of +5.
Correct Answer: B — +5
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Q. What is the oxidation state of sulfur in H2SO4?
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Solution
In H2SO4, the oxidation state of sulfur is +6.
Correct Answer: C — +6
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Q. What is the oxidation state of Uranium in Uranium Hexafluoride (UF6)?
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Solution
In UF6, Uranium is in the +6 oxidation state as it forms six bonds with fluorine.
Correct Answer: B — +6
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Q. What is the particular solution of dy/dx = 4x with the initial condition y(0) = 1?
A.
y = 2x^2 + 1
B.
y = 4x^2 + 1
C.
y = 2x^2
D.
y = 4x^2 + C
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Solution
Integrating gives y = 2x^2 + C. Using the initial condition, C = 1.
Correct Answer: A — y = 2x^2 + 1
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Q. What is the particular solution of the equation dy/dx = 2y with the initial condition y(0) = 1?
A.
y = e^(2x)
B.
y = e^(2x) + 1
C.
y = 1 + e^(2x)
D.
y = 1 + 2x
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Solution
The general solution is y = Ce^(2x). Using the initial condition y(0) = 1, we find C = 1.
Correct Answer: A — y = e^(2x)
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Q. What is the particular solution of the equation dy/dx = 2y with y(0) = 5?
A.
y = 5e^(2x)
B.
y = 2e^(2x)
C.
y = 5e^(-2x)
D.
y = 5 + 2x
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Solution
The general solution is y = Ce^(2x). Using y(0) = 5 gives C = 5.
Correct Answer: A — y = 5e^(2x)
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Q. What is the path difference for light waves from two coherent sources at an angle of 45° to the line joining them?
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Solution
Path difference = d sin θ = d sin(45°) = d(√2/2). For d = λ, path difference = √2λ.
Correct Answer: C — √2λ
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Q. What is the path difference for light waves from two coherent sources at an angle of 45° to the line joining the sources at a distance of 1 m?
A.
0.5 m
B.
0.707 m
C.
1 m
D.
0.25 m
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Solution
Path difference = d sin θ = 1 m * sin(45°) = 1 m * √2/2 = 0.707 m.
Correct Answer: B — 0.707 m
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Q. What is the path difference for the first minimum in a double-slit experiment?
A.
λ/2
B.
λ
C.
3λ/2
D.
2λ
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Solution
The path difference for the first minimum is λ/2, which leads to destructive interference.
Correct Answer: A — λ/2
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Q. What is the percentage by mass of a solution containing 20 grams of solute in 180 grams of solution?
A.
10%
B.
20%
C.
15%
D.
25%
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Solution
Percentage by mass = (mass of solute / mass of solution) * 100 = (20 g / (20 g + 180 g)) * 100 = 20%.
Correct Answer: B — 20%
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Q. What is the percentage by mass of a solution containing 5 g of NaCl in 95 g of water?
A.
5%
B.
10%
C.
15%
D.
20%
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Solution
Percentage by mass = (mass of solute / total mass) × 100 = (5 g / (5 g + 95 g)) × 100 = 5%.
Correct Answer: A — 5%
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Q. What is the percentage composition of carbon in glucose (C6H12O6)?
A.
40%
B.
50%
C.
60%
D.
30%
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Solution
Molar mass of glucose = 6(12) + 12(1) + 6(16) = 180 g. Percentage of carbon = (72/180) x 100 = 40%.
Correct Answer: A — 40%
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Q. What is the period number of the element with atomic number 20?
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Solution
The element with atomic number 20 is Calcium, which is in period 4.
Correct Answer: C — 4
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Q. What is the period of a pendulum that is 1 meter long?
A.
1 s
B.
2 s
C.
0.5 s
D.
3 s
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Solution
The period T of a simple pendulum is given by T = 2π√(L/g). For L = 1 m and g ≈ 9.8 m/s², T = 2π√(1/9.8) ≈ 2 s.
Correct Answer: B — 2 s
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Q. What is the period of a satellite in a circular orbit at a height of 300 km above the Earth's surface?
A.
90 minutes
B.
60 minutes
C.
120 minutes
D.
30 minutes
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Solution
The period of a satellite in a circular orbit at a height of 300 km is approximately 90 minutes.
Correct Answer: A — 90 minutes
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Q. What is the period of a satellite in a low Earth orbit (LEO) compared to a satellite in a geostationary orbit?
A.
Longer than a geostationary orbit
B.
Shorter than a geostationary orbit
C.
Equal to a geostationary orbit
D.
Depends on the mass of the satellite
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Solution
Satellites in low Earth orbit have a much shorter orbital period compared to geostationary satellites due to their proximity to Earth.
Correct Answer: B — Shorter than a geostationary orbit
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Q. What is the periodic trend for electronegativity across a period?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Varies irregularly
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Solution
Electronegativity increases across a period from left to right.
Correct Answer: A — Increases
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Q. What is the pH of a 0.01 M HCl solution?
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Solution
The pH of a 0.01 M HCl solution is 2, as HCl is a strong acid and fully dissociates.
Correct Answer: B — 2
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Q. What is the pH of a 0.01 M NaOH solution?
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Solution
For NaOH, which is a strong base, pOH = -log[OH-]. [OH-] = 0.01 M, so pOH = 2. Therefore, pH = 14 - pOH = 14 - 2 = 12.
Correct Answer: A — 12
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Q. What is the pH of a 0.01 M solution of sodium acetate (CH3COONa)?
A.
4.76
B.
7.00
C.
9.24
D.
10.00
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Solution
Sodium acetate is a salt of a weak acid (acetic acid) and a strong base (sodium hydroxide). The pH can be calculated using the formula pH = 7 + 0.5(pKa - log[C]), where pKa of acetic acid is 4.76.
Correct Answer: C — 9.24
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Q. What is the pH of a 0.01 M solution of sodium hydroxide (NaOH)?
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Solution
pH = 14 - pOH; pOH = -log[OH-] = -log(0.01) = 2; pH = 14 - 2 = 12.
Correct Answer: A — 12
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Q. What is the pH of a 0.01 M solution of sulfuric acid (H2SO4)?
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Solution
H2SO4 is a strong acid and dissociates completely, so pH = -log(0.01) = 2.
Correct Answer: A — 1
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Q. What is the pH of a 0.05 M solution of sulfuric acid (H2SO4)?
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Solution
H2SO4 is a strong acid and dissociates completely; [H+] = 0.05 M, so pH = -log(0.05) ≈ 1.3
Correct Answer: B — 1.3
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Q. What is the pH of a 0.1 M NaOH solution?
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Solution
pOH = -log[OH-] = -log(0.1) = 1; pH = 14 - pOH = 14 - 1 = 13
Correct Answer: C — 12
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Q. What is the pH of a 0.1 M solution of acetic acid (CH3COOH) given its Ka is 1.8 x 10^-5?
A.
2.87
B.
4.76
C.
3.87
D.
5.00
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Solution
Using the formula for weak acids, pH = 0.5(pKa - log[C]) = 0.5(4.74 - log(0.1)) = 4.76.
Correct Answer: B — 4.76
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Q. What is the pH of a 0.1 M solution of ammonium chloride (NH4Cl)?
A.
5.1
B.
5.5
C.
6.1
D.
6.5
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Solution
NH4Cl is a salt of a weak base and a strong acid; it hydrolyzes to give H+, resulting in a pH < 7.
Correct Answer: C — 6.1
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Q. What is the pH of a 0.1 M solution of hydrochloric acid (HCl)?
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Solution
The pH of a strong acid like HCl is calculated using the formula pH = -log[H+]. For 0.1 M HCl, [H+] = 0.1 M, so pH = -log(0.1) = 1.
Correct Answer: A — 1
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Q. What is the pH of a 0.1 M solution of potassium hydrogen phthalate (KHP)?
A.
4.0
B.
5.0
C.
6.0
D.
7.0
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Solution
KHP is a weak acid; its pKa is approximately 5.0, so the pH of a 0.1 M solution is around 5.0.
Correct Answer: B — 5.0
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Q. What is the pH of a 0.1 M solution of sodium acetate (CH3COONa)?
A.
4.76
B.
7
C.
9.24
D.
10
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Solution
pH = 7 + 0.5(pKa + log[C]) = 7 + 0.5(4.76 + log(0.1)) = 9.24
Correct Answer: C — 9.24
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