Q. The magnetic field due to a straight current-carrying conductor at a distance r from the wire is given by which formula? (2019)
A.
B = μ₀I/(2πr)
B.
B = μ₀I/(4πr²)
C.
B = μ₀I/(2r)
D.
B = μ₀I/(πr)
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Solution
The magnetic field (B) due to a straight current-carrying conductor at a distance r is given by B = μ₀I/(2πr).
Correct Answer: A — B = μ₀I/(2πr)
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Q. The magnetic field due to a straight current-carrying conductor at a distance r is given by which formula? (2022)
A.
B = μ₀I/2πr
B.
B = μ₀I/r
C.
B = μ₀I/4πr²
D.
B = μ₀I/2r
Show solution
Solution
The magnetic field (B) at a distance r from a straight current-carrying conductor is given by B = μ₀I/2πr.
Correct Answer: A — B = μ₀I/2πr
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Q. The magnetic field inside a long solenoid is given by which of the following expressions? (2020)
A.
μ₀nI
B.
μ₀I/n
C.
nI/μ₀
D.
I/μ₀n
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Solution
The magnetic field (B) inside a long solenoid is given by B = μ₀nI, where n is the number of turns per unit length and I is the current.
Correct Answer: A — μ₀nI
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Q. The magnetic field lines around a straight current-carrying conductor are in which shape? (2022)
A.
Straight lines
B.
Concentric circles
C.
Ellipses
D.
Spirals
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Solution
The magnetic field lines around a straight current-carrying conductor form concentric circles centered around the wire.
Correct Answer: B — Concentric circles
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Q. The magnetic field lines around a straight current-carrying conductor are: (2022)
A.
Straight lines
B.
Concentric circles
C.
Elliptical
D.
Random
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Solution
The magnetic field lines around a straight current-carrying conductor form concentric circles centered around the wire.
Correct Answer: B — Concentric circles
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Q. The magnetic field lines inside a bar magnet are directed from: (2019)
A.
North to South
B.
South to North
C.
East to West
D.
West to East
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Solution
The magnetic field lines inside a bar magnet are directed from the North pole to the South pole.
Correct Answer: A — North to South
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Q. The maximum displacement from the mean position in simple harmonic motion is called: (2019)
A.
Amplitude
B.
Frequency
C.
Wavelength
D.
Period
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Solution
The maximum displacement is defined as the amplitude.
Correct Answer: A — Amplitude
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Q. The maximum displacement of a wave from its rest position is called what? (2022)
A.
Amplitude
B.
Wavelength
C.
Frequency
D.
Period
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Solution
The maximum displacement from the rest position is defined as the amplitude of the wave.
Correct Answer: A — Amplitude
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Q. The part of the flower that receives pollen is called the: (2022)
A.
Ovary
B.
Stigma
C.
Style
D.
Anther
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Solution
The stigma is the part of the pistil that receives pollen during fertilization.
Correct Answer: B — Stigma
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Q. The phenomenon of electromagnetic induction was discovered by which scientist? (2022)
A.
Michael Faraday
B.
James Clerk Maxwell
C.
Nikola Tesla
D.
Albert Einstein
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Solution
Electromagnetic induction was discovered by Michael Faraday.
Correct Answer: A — Michael Faraday
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Q. The potential energy stored in a capacitor is given by which of the following formulas? (2020)
A.
1/2 CV^2
B.
CV
C.
Q^2/2C
D.
1/2 QV
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Solution
The potential energy (U) stored in a capacitor is given by U = 1/2 CV^2.
Correct Answer: A — 1/2 CV^2
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Q. The pressure of a gas is inversely proportional to its volume at constant temperature is known as: (2022)
A.
Charles's Law
B.
Boyle's Law
C.
Avogadro's Law
D.
Ideal Gas Law
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Solution
Boyle's Law states that the pressure of a gas is inversely proportional to its volume at constant temperature.
Correct Answer: B — Boyle's Law
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Q. The pressure of an ideal gas is directly proportional to its temperature when: (2022)
A.
Volume is constant
B.
Number of moles is constant
C.
Both volume and number of moles are constant
D.
None of the above
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Solution
According to Gay-Lussac's law, the pressure of an ideal gas is directly proportional to its temperature when the volume is held constant.
Correct Answer: A — Volume is constant
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Q. The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)
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Solution
The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.
Correct Answer: B — 1
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Q. The rate constant of a reaction is affected by which of the following? (2023)
A.
Nature of the reactants
B.
Temperature
C.
Catalysts
D.
All of the above
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Solution
The rate constant of a reaction is affected by the nature of the reactants, temperature, and the presence of catalysts.
Correct Answer: D — All of the above
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Q. The rate of a reaction is directly proportional to the concentration of one reactant raised to the power of 2. What is the order of the reaction? (2022)
A.
Zero order
B.
First order
C.
Second order
D.
Third order
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Solution
If the rate is proportional to the concentration of one reactant raised to the power of 2, the reaction is second order.
Correct Answer: C — Second order
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Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This statement defines:
A.
Rate law
B.
Equilibrium constant
C.
Reaction quotient
D.
Catalytic efficiency
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Solution
This statement defines the rate law of a reaction.
Correct Answer: A — Rate law
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Q. The rate of a reaction is given by the equation rate = k[A]^2[B]. What is the overall order of the reaction? (2020)
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Solution
The overall order of the reaction is 2 (from [A]^2) + 1 (from [B]) = 3.
Correct Answer: C — 3
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Q. The resonant frequency of an RLC circuit is given by which formula? (2022)
A.
f = 1/(2π√(LC))
B.
f = 2π√(LC)
C.
f = LC
D.
f = R/(2πL)
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Solution
The resonant frequency f of an RLC circuit is given by f = 1/(2π√(LC)).
Correct Answer: A — f = 1/(2π√(LC))
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Q. The restoring force in a simple harmonic oscillator is directly proportional to what? (2022)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
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Solution
The restoring force (F) is directly proportional to the displacement (x) and acts in the opposite direction, F = -kx.
Correct Answer: A — Displacement
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Q. The restoring force in simple harmonic motion is directly proportional to what? (2022)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
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Solution
The restoring force (F) is directly proportional to the displacement (x) and acts in the opposite direction, F = -kx.
Correct Answer: A — Displacement
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Q. The restoring force in simple harmonic motion is directly proportional to: (2023)
A.
Displacement
B.
Velocity
C.
Acceleration
D.
Mass
Show solution
Solution
Restoring force (F) is proportional to displacement (x), F = -kx.
Correct Answer: A — Displacement
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Q. The roots of the equation x² + 2x + k = 0 are real and distinct if k is: (2020)
A.
< 1
B.
≥ 1
C.
≤ 1
D.
> 1
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Solution
For real and distinct roots, the discriminant must be positive: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer: A — < 1
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Q. The roots of the equation x² + 4x + 4 = 0 are: (2020)
A.
-2 and -2
B.
2 and 2
C.
0 and 4
D.
1 and 3
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Solution
The equation can be factored as (x + 2)² = 0, giving the double root x = -2.
Correct Answer: A — -2 and -2
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Q. The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)
A.
-12
B.
-8
C.
-10
D.
-14
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Solution
Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.
Correct Answer: B — -8
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Q. The roots of the equation x² - 8x + k = 0 are 4 and 4. Find k. (2021)
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Solution
Using the product of roots: k = 4 * 4 = 16.
Correct Answer: A — 16
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Q. The scientific study of classification is known as: (2022)
A.
Taxonomy
B.
Morphology
C.
Anatomy
D.
Ecology
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Solution
Taxonomy is the scientific study of classification of organisms.
Correct Answer: A — Taxonomy
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Q. The self-inductance of a coil depends on which of the following factors? (2021)
A.
Number of turns
B.
Area of cross-section
C.
Length of the coil
D.
All of the above
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Solution
The self-inductance of a coil depends on the number of turns, area of cross-section, and length of the coil.
Correct Answer: D — All of the above
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Q. The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of: (2023)
A.
1 kg of the substance by 1°C
B.
1 g of the substance by 1°C
C.
1 L of the substance by 1°C
D.
1 mole of the substance by 1°C
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Solution
The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1°C.
Correct Answer: A — 1 kg of the substance by 1°C
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Q. The specific heat capacity of a substance is defined as: (2023)
A.
The amount of heat required to raise the temperature by 1 degree Celsius
B.
The amount of heat required to change the phase of a substance
C.
The heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius
D.
The heat required to raise the temperature of 1 mole of the substance by 1 degree Celsius
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Solution
The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius.
Correct Answer: C — The heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius
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