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Q. What is the particular solution of dy/dx = 4y with the initial condition y(0) = 2?

A. y = 2e^(4x)
B. y = e^(4x)
C. y = 4e^(4x)
D. y = 2e^(x)

Solution

The general solution is y = Ce^(4x). Using the initial condition y(0) = 2, we find C = 2, thus y = 2e^(4x).

Correct Answer: A — y = 2e^(4x)

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Q. What is the path difference for the first minimum in a single-slit diffraction pattern? (2021)

A. λ/2
B. λ
C. 3λ/2
D. λ/4

Solution

The path difference for the first minimum in single-slit diffraction is λ/2.

Correct Answer: A — λ/2

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Q. What is the peak voltage of an AC source if its RMS voltage is 220 V? (2021)

A. 311 V
B. 220 V
C. 155 V
D. 440 V

Solution

The peak voltage (V_peak) is related to the RMS voltage (V_rms) by the formula V_peak = V_rms × √2. Therefore, V_peak = 220 V × √2 ≈ 311 V.

Correct Answer: A — 311 V

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Q. What is the peak voltage of an AC supply if its RMS voltage is 220 V? (2021)

A. 311 V
B. 220 V
C. 155 V
D. 440 V

Solution

The peak voltage (V_peak) is related to the RMS voltage (V_rms) by the formula V_peak = V_rms × √2. Therefore, V_peak = 220 V × √2 ≈ 311 V.

Correct Answer: A — 311 V

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Q. What is the percentage by mass of a solution containing 15 grams of solute in 85 grams of solvent? (2021)

A. 15%
B. 17.65%
C. 20%
D. 25%

Solution

Percentage by mass = (mass of solute / total mass) × 100 = (15 g / (15 g + 85 g)) × 100 = 17.65%.

Correct Answer: B — 17.65%

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Q. What is the percentage concentration of a solution containing 15 g of solute in 150 g of solution? (2023)

A. 10%
B. 15%
C. 20%
D. 25%

Solution

Percentage concentration = (mass of solute / mass of solution) × 100 = (15 g / 150 g) × 100 = 10%

Correct Answer: B — 15%

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Q. What is the percentage concentration of a solution containing 20 g of solute in 200 g of solution? (2021)

A. 10%
B. 20%
C. 5%
D. 15%

Solution

Percentage concentration = (mass of solute / mass of solution) × 100 = (20 g / 200 g) × 100 = 10%.

Correct Answer: A — 10%

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Q. What is the percentage error if the measured value is 10.0 and the true value is 9.5? (2021)

A. 5.26%
B. 4.76%
C. 2.5%
D. 10%

Solution

Percentage error = (|Measured - True| / True) × 100 = (|10.0 - 9.5| / 9.5) × 100 = 5.26%.

Correct Answer: B — 4.76%

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Q. What is the percentage error if the measured value is 20 and the true value is 25? (2021)

A. 20%
B. 25%
C. 5%
D. 10%

Solution

Percentage error is calculated as (|True Value - Measured Value| / True Value) * 100 = (|25 - 20| / 25) * 100 = 20%.

Correct Answer: D — 10%

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Q. What is the percentage error if the measured value is 20.0 and the true value is 19.5? (2021)

A. 2.56%
B. 1.25%
C. 3.33%
D. 5.00%

Solution

Percentage error = (|Measured - True| / True) × 100 = (|20.0 - 19.5| / 19.5) × 100 ≈ 2.56%.

Correct Answer: A — 2.56%

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Q. What is the percentage error if the true value is 50 and the measured value is 48? (2022)

A. 4%
B. 2%
C. 5%
D. 3%

Solution

Percentage error = |(True value - Measured value) / True value| * 100 = |(50 - 48) / 50| * 100 = 4%.

Correct Answer: A — 4%

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Q. What is the period number of Argon? (2020)

A. 2
B. 3
C. 4
D. 5

Solution

Argon is located in Period 3 of the periodic table.

Correct Answer: C — 4

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Q. What is the period number of Lithium in the periodic table? (2022)

A. 1
B. 2
C. 3
D. 4

Solution

Lithium is located in period 2 of the periodic table.

Correct Answer: B — 2

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Q. What is the period number of Lithium? (2016) 2016

A. 1
B. 2
C. 3
D. 4

Solution

Lithium is located in period 2 of the periodic table.

Correct Answer: B — 2

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Q. What is the period number of Sodium in the periodic table? (2017)

A. 1
B. 2
C. 3
D. 4

Solution

Sodium is in period 3 of the periodic table.

Correct Answer: C — 3

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Q. What is the pH of a 0.001 M acetic acid solution (Ka = 1.8 x 10^-5)?

A. 2.87
B. 3.87
C. 4.87
D. 5.87

Solution

Using the formula for weak acids, pH = 0.5(pKa - logC) = 0.5(4.74 - log(0.001)) = 3.87.

Correct Answer: B — 3.87

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Q. What is the pH of a 0.001 M solution of hydrochloric acid?

A. 3
B. 4
C. 5
D. 6

Solution

pH = -log(0.001) = 3.

Correct Answer: A — 3

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Q. What is the pH of a 0.01 M HCl solution? (2021) 2021

A. 1
B. 2
C. 3
D. 4

Solution

For a strong acid like HCl, pH = -log[H+] = -log(0.01) = 2.

Correct Answer: A — 1

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Q. What is the pH of a 0.01 M solution of Na2CO3?

A. 10
B. 11
C. 12
D. 9

Solution

Na2CO3 is a basic salt, pH is approximately 11.5.

Correct Answer: C — 12

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Q. What is the pH of a 0.01 M solution of NaOH?

A. 12
B. 13
C. 14
D. 11

Solution

pOH = -log(0.01) = 2; pH = 14 - pOH = 14 - 2 = 12.

Correct Answer: B — 13

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Q. What is the pH of a 0.01 M solution of phosphoric acid (H3PO4)?

A. 1.0
B. 2.0
C. 3.0
D. 4.0

Solution

H3PO4 is a triprotic acid; for a dilute solution, the first dissociation dominates, giving pH ≈ 2.

Correct Answer: B — 2.0

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Q. What is the pH of a 0.05 M acetic acid solution (Ka = 1.8 x 10^-5)? (2023)

A. 2.9
B. 3.1
C. 4.0
D. 4.7

Solution

Using the formula for weak acids, pH = 0.5(pKa - log[C]) where pKa = -log(1.8 x 10^-5) ≈ 4.74. pH = 0.5(4.74 - log(0.05)) ≈ 4.7.

Correct Answer: D — 4.7

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Q. What is the pH of a 0.05 M solution of NaCl?

A. 7
B. 6
C. 8
D. 5

Solution

NaCl is a neutral salt, so the pH remains 7.

Correct Answer: A — 7

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Q. What is the pH of a 0.1 M solution of ammonium chloride (NH4Cl)? (2019) 2019

A. 5.10
B. 4.75
C. 6.00
D. 7.00

Solution

NH4Cl is a salt of a weak base and strong acid, pH < 7. Calculate using hydrolysis: pH ≈ 4.75.

Correct Answer: B — 4.75

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Q. What is the pH of a 0.1 M solution of K2CO3?

A. 9.0
B. 10.0
C. 11.0
D. 12.0

Solution

K2CO3 is a salt of a weak acid (H2CO3) and strong base (KOH), resulting in a basic solution with pH around 10.

Correct Answer: B — 10.0

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Q. What is the pH of a 0.1 M solution of K2SO4? (2023)

A. 7
B. 6
C. 8
D. 5

Solution

K2SO4 is a neutral salt formed from a strong acid (H2SO4) and a strong base (KOH). Therefore, the pH of the solution is 7.

Correct Answer: A — 7

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Q. What is the pH of a 0.1 M solution of NH4Cl?

A. 5
B. 6
C. 7
D. 8

Solution

NH4Cl is an acidic salt, pH is approximately 5.1.

Correct Answer: B — 6

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Q. What is the pH of a 0.1 M solution of sodium acetate (Ka for acetic acid = 1.8 x 10^-5)?

A. 4.75
B. 5.25
C. 9.25
D. 10.25

Solution

Using the formula for salt of weak acid, pH = 14 + 0.5(pKa + logC) = 14 + 0.5(4.74 + log(0.1)) = 9.25.

Correct Answer: C — 9.25

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Q. What is the pH of a 0.1 M solution of sodium bicarbonate (NaHCO3)? (2022) 2022

A. 8.00
B. 9.00
C. 7.00
D. 6.00

Solution

NaHCO3 is a weak base, pH ≈ 8.00 due to its bicarbonate ion acting as a weak base.

Correct Answer: A — 8.00

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Q. What is the pH of a 0.1 M solution of sulfuric acid (H2SO4)?

A. 1
B. 2
C. 3
D. 4

Solution

H2SO4 is a strong acid; it dissociates completely, so [H+] = 0.1 M; pH = -log(0.1) = 1.

Correct Answer: B — 2

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