Q. Under which article can a citizen approach the Supreme Court for the enforcement of Fundamental Rights? (2022)
A.
Article 32
B.
Article 226
C.
Article 19
D.
Article 21
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Solution
A citizen can approach the Supreme Court under Article 32 for the enforcement of Fundamental Rights.
Correct Answer: A — Article 32
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Q. Under which Article of the Indian Constitution is the Right to Constitutional Remedies provided?
A.
Article 21
B.
Article 32
C.
Article 19
D.
Article 14
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Solution
The Right to Constitutional Remedies is provided under Article 32, allowing individuals to approach the Supreme Court for enforcement of their rights.
Correct Answer: B — Article 32
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Q. Using Biot-Savart Law, what is the direction of the magnetic field produced by a current flowing in a straight wire?
A.
Radially inward
B.
Radially outward
C.
Perpendicular to the wire
D.
Parallel to the wire
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Solution
According to the right-hand rule, the magnetic field produced by a straight current-carrying wire is perpendicular to the wire.
Correct Answer: C — Perpendicular to the wire
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Q. Using Biot-Savart Law, what is the magnetic field at the center of a circular loop of radius R carrying current I?
A.
μ₀I/(2R)
B.
μ₀I/(4R)
C.
μ₀I/(πR)
D.
μ₀I/(2πR)
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Solution
The magnetic field at the center of a circular loop of radius R carrying current I is given by B = μ₀I/(2R) and for a complete loop, it simplifies to B = μ₀I/(2πR).
Correct Answer: D — μ₀I/(2πR)
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Q. Using Gauss's law, what is the electric field inside a uniformly charged cylindrical shell of radius R?
A.
0
B.
Q/(2πε₀R)
C.
Q/(4πε₀R²)
D.
Q/(2πε₀R²)
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Solution
Inside a uniformly charged cylindrical shell, the electric field is zero due to symmetry, as the contributions from all parts of the shell cancel out.
Correct Answer: A — 0
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Q. Using Kirchhoff's Current Law, if three currents enter a junction as 2A, 3A, and I, what is the value of I if the total current leaving the junction is 5A?
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Solution
According to KCL, I = total entering - total leaving = (2A + 3A) - 5A = 0A.
Correct Answer: B — 1A
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Q. Using Kirchhoff's Current Law, if three currents enter a junction as 3A, 2A, and I, what is the value of I if the total current leaving the junction is 5A?
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Solution
According to KCL, I = Total entering - Total leaving = (3A + 2A) - 5A = 0A.
Correct Answer: A — 4A
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Q. Using Kirchhoff's Voltage Law, if a loop in a circuit has a 12V battery and two resistors of 4Ω and 6Ω, what is the voltage across the 4Ω resistor?
A.
4.8V
B.
8V
C.
6V
D.
3.2V
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Solution
Using voltage division, V_R1 = (R1 / (R1 + R2)) * V_total = (4Ω / (4Ω + 6Ω)) * 12V = 4.8V.
Correct Answer: B — 8V
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Q. Using Kirchhoff's Voltage Law, if a loop in a circuit has a 12V battery and two resistors of 4Ω and 6Ω, what is the voltage drop across the 4Ω resistor?
A.
4.8V
B.
8V
C.
6V
D.
3.2V
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Solution
Using voltage division, V_R1 = V_total * (R1 / (R1 + R2)) = 12V * (4Ω / (4Ω + 6Ω)) = 12V * (4/10) = 4.8V.
Correct Answer: B — 8V
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Q. Using Kirchhoff's voltage law, if a loop in a circuit has a 9V battery and two resistors (2Ω and 3Ω) with voltage drops of 4V and 5V respectively, is the loop correctly analyzed?
A.
Yes
B.
No
C.
Only if the battery is 12V
D.
Only if the resistors are in series
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Solution
According to Kirchhoff's voltage law, the sum of the voltage drops must equal the source voltage. Here, 4V + 5V = 9V, which is correct.
Correct Answer: B — No
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Q. Viruses are classified as: (2020)
A.
Living organisms
B.
Non-living entities
C.
Prokaryotes
D.
Eukaryotes
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Solution
Viruses are considered non-living entities as they cannot carry out metabolic processes independently.
Correct Answer: B — Non-living entities
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Q. Water is to Drink as Food is to?
A.
Eat
B.
Cook
C.
Prepare
D.
Serve
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Solution
You drink water, just as you eat food.
Correct Answer: A — Eat
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Q. What are the building blocks of nucleic acids?
A.
Amino acids
B.
Fatty acids
C.
Nucleotides
D.
Monosaccharides
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Solution
Nucleotides are the building blocks of nucleic acids like DNA and RNA.
Correct Answer: C — Nucleotides
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Q. What are the dimensions of pressure?
A.
ML^-1T^-2
B.
ML^2T^-2
C.
ML^2T^-1
D.
M^0L^0T^0
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Solution
Pressure is defined as force per unit area. The dimensions of force are ML^1T^-2, and area is L^2, thus pressure has dimensions ML^-1T^-2.
Correct Answer: A — ML^-1T^-2
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Q. What are the roots of the equation 3x² - 12x + 12 = 0? (2019)
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Solution
Dividing the equation by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.
Correct Answer: B — 4
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Q. What are the roots of the equation x² - 2x - 8 = 0? (2022)
A.
-2 and 4
B.
2 and -4
C.
4 and -2
D.
0 and 8
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Solution
Factoring gives (x - 4)(x + 2) = 0, hence the roots are 4 and -2.
Correct Answer: C — 4 and -2
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Q. What are the roots of the equation x² - 5x + 6 = 0? (2021)
A.
1 and 6
B.
2 and 3
C.
3 and 2
D.
0 and 5
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Solution
The roots can be found using the factorization method: (x - 2)(x - 3) = 0, hence the roots are 2 and 3.
Correct Answer: B — 2 and 3
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Q. What are the solutions of the equation cos(x) + sin(x) = 1?
A.
x = 0
B.
x = π/4
C.
x = π/2
D.
x = π
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Solution
The only solution is x = 0.
Correct Answer: A — x = 0
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Q. What are the solutions of the equation cos(x) = -1/2 in the interval [0, 2π]?
A.
2π/3, 4π/3
B.
π/3, 5π/3
C.
π/2, 3π/2
D.
0, π
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Solution
The solutions are x = 2π/3 and 4π/3.
Correct Answer: A — 2π/3, 4π/3
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Q. What are the solutions of the equation cos(x) = -1/2?
A.
2π/3
B.
4π/3
C.
π/3
D.
5π/3
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Solution
The solutions are x = 2π/3 and x = 4π/3.
Correct Answer: A — 2π/3
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Q. What are the solutions of the equation cos^2(x) - 1/2 = 0?
A.
x = π/4
B.
x = 3π/4
C.
x = 5π/4
D.
x = 7π/4
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Solution
The solutions are x = π/4, 3π/4, 5π/4, and 7π/4.
Correct Answer: A — x = π/4
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Q. What are the solutions of the equation sin(2x) = 0 in the interval [0, 2π]?
A.
0, π, 2π
B.
0, π/2, π
C.
0, π/4, π/2
D.
0, 3π/2
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Solution
The solutions are x = 0, π, and 2π.
Correct Answer: A — 0, π, 2π
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Q. What are the solutions of the equation sin(2x) = 0?
A.
x = nπ/2
B.
x = nπ
C.
x = nπ + π/2
D.
x = nπ + π
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Solution
sin(2x) = 0 implies 2x = nπ, thus x = nπ/2 for n ∈ Z.
Correct Answer: A — x = nπ/2
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Q. What are the solutions of the equation sin(x) = sin(π/3)?
A.
x = π/3
B.
x = 2π/3
C.
x = 4π/3
D.
x = 5π/3
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Solution
The solutions are x = π/3 + 2nπ and x = 2π/3 + 2nπ.
Correct Answer: A — x = π/3
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Q. What are the solutions of the equation sin^2(x) - sin(x) = 0?
A.
x = nπ
B.
x = nπ + π/2
C.
x = nπ + 2π
D.
x = nπ + π
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Solution
Factoring gives sin(x)(sin(x) - 1) = 0, so sin(x) = 0 or sin(x) = 1. Thus, x = nπ or x = π/2 + 2nπ.
Correct Answer: A — x = nπ
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Q. What can be concluded about the author's perspective on the topic?
A.
The author is indifferent to the topic.
B.
The author has a strong personal connection to the topic.
C.
The author presents a balanced view of the topic.
D.
The author is biased towards one side of the argument.
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Solution
The author presents a balanced view, considering multiple perspectives and providing a fair analysis of the topic.
Correct Answer: C — The author presents a balanced view of the topic.
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Q. What can be concluded about the author's tone in the passage?
A.
Optimistic and hopeful
B.
Skeptical and critical
C.
Neutral and objective
D.
Emotional and passionate
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Solution
The author expresses optimism about the implications of the discovery, indicating a hopeful tone.
Correct Answer: A — Optimistic and hopeful
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Q. What can be concluded about the author's view on education and technology?
A.
Education should remain unchanged despite technological advances.
B.
Technology should be integrated into education to enhance learning.
C.
Technology is a hindrance to effective education.
D.
Education and technology are unrelated fields.
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Solution
The passage suggests that integrating technology into education can enhance learning experiences.
Correct Answer: B — Technology should be integrated into education to enhance learning.
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Q. What can be concluded about the customer satisfaction ratings from the mixed graph?
A.
Customer satisfaction has improved steadily over the years.
B.
There was a sharp decline in customer satisfaction in the last year.
C.
Customer satisfaction ratings have fluctuated without a clear trend.
D.
Customer satisfaction ratings are irrelevant to sales performance.
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Solution
The graph illustrates fluctuations in customer satisfaction ratings, indicating no clear upward or downward trend.
Correct Answer: C — Customer satisfaction ratings have fluctuated without a clear trend.
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Q. What can be concluded about the impact of variable D on variable E from the mixed graph? (2023)
A.
D has a positive impact on E.
B.
D negatively affects E.
C.
D does not influence E.
D.
The impact of D on E is inconclusive.
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Solution
The graph does not provide sufficient evidence to determine a clear impact of D on E, making the relationship inconclusive.
Correct Answer: D — The impact of D on E is inconclusive.
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