Q. What is the particular solution of dy/dx = 4x with the initial condition y(0) = 1?
-
A.
y = 2x^2 + 1
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B.
y = 4x^2 + 1
-
C.
y = 2x^2
-
D.
y = 4x^2 + C
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 dy/dx = 4y with the initial condition y(0) = 2?
-
A.
y = 2e^(4x)
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B.
y = e^(4x)
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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 particular solution of the equation dy/dx = 2y with the initial condition y(0) = 1?
-
A.
y = e^(2x)
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B.
y = e^(2x) + 1
-
C.
y = 1 + e^(2x)
-
D.
y = 1 + 2x
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)
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B.
y = 2e^(2x)
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C.
y = 5e^(-2x)
-
D.
y = 5 + 2x
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 past tense of 'run'? (2021)
-
A.
Runed
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B.
Ran
-
C.
Runned
-
D.
Running
Solution
The past tense of 'run' is 'ran'.
Correct Answer: B — Ran
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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?
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
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
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B.
λ
-
C.
3λ/2
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D.
2λ
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 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
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B.
220 V
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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%
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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 by mass of a solution containing 20 grams of solute in 180 grams of solution?
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A.
10%
-
B.
20%
-
C.
15%
-
D.
25%
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%
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%
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B.
50%
-
C.
60%
-
D.
30%
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 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)
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 percentage increase in sales of Product A from Q1 to Q3?
-
A.
20%
-
B.
25%
-
C.
30%
-
D.
35%
Solution
The percentage increase in sales of Product A from Q1 to Q3 is 25%.
Correct Answer: B — 25%
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Q. What is the perimeter of a rectangle with length 10 cm and width 5 cm? (2021)
-
A.
30 cm
-
B.
25 cm
-
C.
20 cm
-
D.
15 cm
Solution
The perimeter of a rectangle is given by P = 2(length + width). Here, P = 2(10 + 5) = 30 cm.
Correct Answer: B — 25 cm
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Q. What is the perimeter of a rectangle with length 8 units and width 3 units?
-
A.
22 units
-
B.
24 units
-
C.
20 units
-
D.
18 units
Solution
Perimeter = 2 * (length + width) = 2 * (8 + 3) = 22 units.
Correct Answer: A — 22 units
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Q. What is the perimeter of a square with a side length of 4 cm?
-
A.
8 cm
-
B.
12 cm
-
C.
16 cm
-
D.
20 cm
Solution
Perimeter of a square = 4 × side = 4 × 4 cm = 16 cm.
Correct Answer: C — 16 cm
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Q. What is the period number of Argon? (2020)
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)
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
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)
Solution
Sodium is in period 3 of the periodic table.
Correct Answer: C — 3
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Q. What is the period number of the element with atomic number 20?
Solution
The element with atomic number 20 is Calcium, which is in period 4.
Correct Answer: C — 4
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