Q. If J = [[1, 2], [2, 4]], what is det(J)? (2022)
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Solution
Det(J) = (1*4) - (2*2) = 4 - 4 = 0.
Correct Answer:
A
— 0
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Q. If J = [[3, 1], [2, 4]], find det(J). (2023)
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Solution
Det(J) = (3*4) - (1*2) = 12 - 2 = 10.
Correct Answer:
A
— 10
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Q. If one root of the equation x² - 6x + k = 0 is 2, find k. (2022)
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Solution
Using the root 2 in the equation: 2² - 6*2 + k = 0, we find k = 10.
Correct Answer:
B
— 10
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Q. If one root of the equation x² - 7x + k = 0 is 3, find k. (2023)
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Solution
Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 10.
Correct Answer:
A
— 10
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Q. If one root of the equation x² - 7x + k = 0 is 3, what is the value of k? (2020)
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Solution
Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 9.
Correct Answer:
D
— 9
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Q. If one root of the equation x² - 7x + p = 0 is 3, what is the value of p? (2020)
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Solution
Using the root, substitute x = 3: 3² - 7*3 + p = 0, which gives p = 6.
Correct Answer:
B
— 9
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Q. If sin(θ) = 0.5, what is θ in degrees? (2014)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
sin(30°) = 0.5, so θ = 30°.
Correct Answer:
A
— 30°
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Q. If sin(θ) = 0.6, what is the approximate value of θ in degrees? (2019)
A.
36.87°
B.
45°
C.
53.13°
D.
60°
Show solution
Solution
Using inverse sine, θ ≈ 36.87°
Correct Answer:
C
— 53.13°
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Q. If sin(θ) = 0.8, what is cos(θ) using Pythagorean identity? (2020)
A.
0.6
B.
0.8
C.
0.4
D.
0.2
Show solution
Solution
Using sin²(θ) + cos²(θ) = 1, cos²(θ) = 1 - 0.64 = 0.36, cos(θ) = 0.6
Correct Answer:
A
— 0.6
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Q. If sin(θ) = 0.8, what is cos(θ)? (2022)
A.
0.6
B.
0.8
C.
0.4
D.
0.2
Show solution
Solution
Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.
Correct Answer:
A
— 0.6
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Q. If sin(θ) = 0.866, what is θ in degrees? (2020)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
sin(60°) = √3/2 ≈ 0.866, so θ = 60°.
Correct Answer:
C
— 60°
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Q. If sin(θ) = 0.866, what is θ? (2022)
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
sin(60°) = √3/2 ≈ 0.866, so θ = 60°.
Correct Answer:
C
— 60°
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Q. If sin(θ) = 1, what is the value of θ in degrees? (2019)
A.
0°
B.
45°
C.
90°
D.
180°
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Solution
sin(90°) = 1, so θ = 90°.
Correct Answer:
C
— 90°
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Q. If sin(θ) = 1, what is the value of θ? (2023)
A.
0°
B.
90°
C.
180°
D.
270°
Show solution
Solution
sin(90°) = 1, so θ = 90°.
Correct Answer:
B
— 90°
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Q. If sin(θ) = 1, what is θ? (2023)
A.
0°
B.
30°
C.
90°
D.
180°
Show solution
Solution
sin(90°) = 1, so θ = 90°.
Correct Answer:
C
— 90°
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Q. If sin(θ) = 1/2, what is the possible value of θ? (2022)
A.
30°
B.
60°
C.
90°
D.
45°
Show solution
Solution
sin(30°) = 1/2, so θ = 30°.
Correct Answer:
A
— 30°
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Q. If sin(θ) = 1/√2, what is cos(θ)? (2022)
A.
1/√2
B.
0
C.
√2/2
D.
1
Show solution
Solution
Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - (1/√2)²) = √(1/2) = √2/2
Correct Answer:
C
— √2/2
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Q. If sin(θ) = 1/√2, what is θ in degrees?
A.
30°
B.
45°
C.
60°
D.
90°
Show solution
Solution
sin(45°) = 1/√2, so θ = 45°
Correct Answer:
B
— 45°
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Q. If tan(θ) = 1, what is the value of θ? (2020)
A.
0°
B.
30°
C.
45°
D.
60°
Show solution
Solution
tan(45°) = 1, so θ = 45°.
Correct Answer:
C
— 45°
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Q. If the amplitude of a simple harmonic oscillator is increased, what happens to its total energy? (2021)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
Show solution
Solution
The total energy (E) in a simple harmonic oscillator is given by E = (1/2)kA². If amplitude (A) increases, energy increases.
Correct Answer:
A
— Increases
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Q. If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Remains the same
Show solution
Solution
Total energy in SHM is proportional to the square of the amplitude. If amplitude is tripled, energy increases by 3^2 = 9 times.
Correct Answer:
C
— Increases by 9 times
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Q. If the amplitude of a wave is doubled, how does it affect the energy of the wave? (2020)
A.
Remains the same
B.
Doubles
C.
Increases by four times
D.
Halves
Show solution
Solution
Energy of a wave is proportional to the square of the amplitude. If amplitude is doubled, energy increases by (2^2) = 4 times.
Correct Answer:
C
— Increases by four times
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Q. If the amplitude of a wave is doubled, how does this affect the energy carried by the wave? (2021)
A.
Energy is halved
B.
Energy remains the same
C.
Energy is doubled
D.
Energy is quadrupled
Show solution
Solution
The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.
Correct Answer:
D
— Energy is quadrupled
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Q. If the area of a circle is 78.5 cm², what is the radius? (2021)
A.
5 cm
B.
7 cm
C.
10 cm
D.
6 cm
Show solution
Solution
Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.
Correct Answer:
B
— 7 cm
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Q. If the area of a coil is doubled while keeping the magnetic field constant, what happens to the magnetic flux through the coil? (2023)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Magnetic flux (Φ) is given by the product of magnetic field (B) and area (A). If the area is doubled and the magnetic field remains constant, the magnetic flux also doubles.
Correct Answer:
A
— It doubles
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Q. If the area of a loop in a magnetic field is doubled while keeping the magnetic field strength constant, what happens to the magnetic flux through the loop?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Magnetic flux (Φ) is given by Φ = B * A. If the area (A) is doubled and the magnetic field (B) remains constant, the magnetic flux also doubles.
Correct Answer:
A
— It doubles
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Q. If the capacitance in an AC circuit is increased, what happens to the capacitive reactance? (2023)
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
Show solution
Solution
Capacitive reactance XC = 1/(ωC). If capacitance C increases, XC decreases.
Correct Answer:
B
— It decreases
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Q. If the charge on a capacitor is doubled, what happens to the energy stored? (2019)
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
Show solution
Solution
The energy stored in a capacitor is proportional to the square of the charge (U = Q^2/(2C)). Doubling the charge increases the energy by a factor of 4.
Correct Answer:
C
— It quadruples
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Q. If the circumference of a circle is 31.4 cm, what is its radius? (2022)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the circumference of a circle is 31.4 cm, what is its radius? (Use π = 3.14) (2015)
A.
5 cm
B.
7 cm
C.
10 cm
D.
8 cm
Show solution
Solution
Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.
Correct Answer:
A
— 5 cm
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