Q. The force experienced by a charged particle moving in a magnetic field is maximum when the angle between the velocity and magnetic field is: (2020)
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
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Solution
The force (F) on a charged particle in a magnetic field is given by F = qvB sin(θ). The force is maximum when θ = 90 degrees, as sin(90) = 1.
Correct Answer: B — 90 degrees
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Q. The force on a charged particle in a magnetic field is maximum when the angle between the velocity and the magnetic field is: (2021)
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
The force on a charged particle in a magnetic field is maximum when the angle between the velocity and the magnetic field is 90 degrees.
Correct Answer: B — 90 degrees
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Q. The force on a charged particle moving in a magnetic field is given by which law? (2021)
A.
Coulomb's Law
B.
Lorentz Force Law
C.
Faraday's Law
D.
Ampere's Law
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Solution
The force (F) on a charged particle moving in a magnetic field is described by the Lorentz Force Law, F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field.
Correct Answer: B — Lorentz Force Law
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Q. The force on a charged particle moving in a magnetic field is maximum when the angle between the velocity and magnetic field is: (2021)
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
The force on a charged particle in a magnetic field is given by F = qvB sin(θ). The force is maximum when sin(θ) = 1, which occurs at θ = 90 degrees.
Correct Answer: B — 90 degrees
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Q. The force on a charged particle moving in a magnetic field is maximum when the angle between the velocity and the magnetic field is: (2021)
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
The force on a charged particle moving in a magnetic field is maximum when the angle between the velocity and the magnetic field is 90 degrees.
Correct Answer: B — 90 degrees
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Q. The force on a charged particle moving in a magnetic field is maximum when: (2021)
A.
The particle moves parallel to the field
B.
The particle moves perpendicular to the field
C.
The particle is at rest
D.
The particle moves in a circular path
Show solution
Solution
The force on a charged particle moving in a magnetic field is maximum when the particle moves perpendicular to the field.
Correct Answer: B — The particle moves perpendicular to the field
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Q. The force that opposes the motion of an object through a fluid is called _____. (2020)
A.
Friction
B.
Drag
C.
Lift
D.
Thrust
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Solution
Drag is the force that opposes the motion of an object through a fluid, such as air or water.
Correct Answer: B — Drag
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Q. The forward bias condition in a diode occurs when: (2020)
A.
Anode is at a higher potential than cathode
B.
Cathode is at a higher potential than anode
C.
Both terminals are at the same potential
D.
None of the above
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Solution
In forward bias, the anode is connected to a higher potential than the cathode, allowing current to flow.
Correct Answer: A — Anode is at a higher potential than cathode
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Q. The frequency of a simple harmonic oscillator is 5 Hz. What is its angular frequency? (2020)
A.
10 rad/s
B.
5 rad/s
C.
15 rad/s
D.
20 rad/s
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Solution
Angular frequency (ω) = 2πf = 2π × 5 = 10 rad/s
Correct Answer: A — 10 rad/s
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Q. The frequency of a tuning fork is 440 Hz. What is the time period of the fork? (2019)
A.
0.00227 s
B.
0.0045 s
C.
0.01 s
D.
0.005 s
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Solution
Time period (T) = 1 / frequency (f) = 1 / 440 Hz ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. The frequency of a tuning fork is 440 Hz. What is the time period of the sound wave produced? (2022)
A.
0.00227 s
B.
0.0045 s
C.
0.01 s
D.
0.005 s
Show solution
Solution
Time period (T) = 1 / frequency (f) = 1 / 440 Hz ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. The frequency of a wave is 10 Hz. What is the frequency of its second harmonic? (2021)
A.
5 Hz
B.
10 Hz
C.
20 Hz
D.
30 Hz
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Solution
The frequency of the second harmonic is twice the fundamental frequency. Therefore, if the fundamental frequency is 10 Hz, the second harmonic frequency is 2 * 10 Hz = 20 Hz.
Correct Answer: C — 20 Hz
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Q. The frequency of a wave is doubled. How does this affect its wavelength if the speed of the wave remains constant? (2022)
A.
Wavelength doubles
B.
Wavelength halves
C.
Wavelength remains the same
D.
Wavelength quadruples
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Solution
According to the wave equation v = fλ, if frequency (f) is doubled and speed (v) remains constant, wavelength (λ) must halve.
Correct Answer: B — Wavelength halves
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Q. The frescoes of the Sistine Chapel, painted by Michelangelo, primarily depict which biblical event?
A.
The Creation of Adam
B.
The Last Supper
C.
The Crucifixion
D.
The Nativity
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Solution
The Creation of Adam is one of the most famous frescoes in the Sistine Chapel, illustrating the biblical story of God giving life to Adam.
Correct Answer: A — The Creation of Adam
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Q. The Freundlich adsorption isotherm is applicable to which type of adsorption?
A.
Physisorption only
B.
Chemisorption only
C.
Both physisorption and chemisorption
D.
None of the above
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Solution
The Freundlich isotherm can describe both physisorption and chemisorption processes.
Correct Answer: C — Both physisorption and chemisorption
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Q. The Freundlich adsorption isotherm is best described by which equation? (2023)
A.
x/m = kP
B.
x/m = kP^(1/n)
C.
P = k(x/m)
D.
P = k(x/m)^(1/n)
Show solution
Solution
The Freundlich isotherm is represented by the equation x/m = kP^(1/n), where x is the amount adsorbed, m is the mass of the adsorbent, and P is the pressure.
Correct Answer: B — x/m = kP^(1/n)
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Q. The function f(x) = 1/(x-1) is continuous on which of the following intervals?
A.
(-∞, 1)
B.
(1, ∞)
C.
(-∞, ∞)
D.
(-∞, 0)
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Solution
The function f(x) = 1/(x-1) is discontinuous at x = 1, hence it is continuous on (1, ∞).
Correct Answer: B — (1, ∞)
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Q. The function f(x) = e^x is differentiable at all points?
A.
True
B.
False
C.
Only at x = 0
D.
Only at x = 1
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Solution
f(x) = e^x is differentiable everywhere as it is an exponential function.
Correct Answer: A — True
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Q. The function f(x) = ln(x) + x has a minimum at:
A.
x = 1
B.
x = 0
C.
x = e
D.
x = 2
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Solution
Finding f'(x) = 1/x + 1. Setting f'(x) = 0 gives x = 1 as the minimum point.
Correct Answer: A — x = 1
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Q. The function f(x) = ln(x) is differentiable at x = 1?
A.
Yes
B.
No
C.
Only for x > 1
D.
Only for x < 1
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Solution
f'(x) = 1/x; f'(1) = 1/1 = 1, hence it is differentiable at x = 1.
Correct Answer: A — Yes
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Q. The function f(x) = sqrt(x) is differentiable at x = 0?
A.
Yes
B.
No
C.
Only from the right
D.
Only from the left
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Solution
f(x) = sqrt(x) is not differentiable at x = 0 because the left-hand derivative does not exist.
Correct Answer: B — No
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Q. The function f(x) = x^2 + 2x + 1 is differentiable everywhere?
A.
True
B.
False
C.
Only at x = 0
D.
Only for x > 0
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Solution
f(x) is a polynomial function, which is differentiable everywhere.
Correct Answer: A — True
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Q. The function f(x) = x^2 - 2x + 1 is differentiable at all points?
A.
True
B.
False
C.
Only at x = 0
D.
Only for x > 0
Show solution
Solution
f(x) is a polynomial function, which is differentiable everywhere.
Correct Answer: A — True
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Q. The function f(x) = x^2 - 2x + 1 is differentiable at x = 2?
A.
Yes
B.
No
C.
Only left
D.
Only right
Show solution
Solution
f(x) is a polynomial function, hence it is differentiable everywhere including at x = 2.
Correct Answer: A — Yes
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Q. The function f(x) = x^2 - 4 is:
A.
Always increasing
B.
Always decreasing
C.
Neither increasing nor decreasing
D.
Both increasing and decreasing
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Solution
The function has a minimum at x = 0, hence it is neither always increasing nor decreasing.
Correct Answer: C — Neither increasing nor decreasing
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Q. The function f(x) = x^2 - 4x + 4 can be expressed in which form?
A.
(x - 2)^2
B.
(x + 2)^2
C.
(x - 4)^2
D.
(x + 4)^2
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Solution
f(x) = (x - 2)^2 is the completed square form.
Correct Answer: A — (x - 2)^2
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Q. The function f(x) = x^2 - 4x + 4 is differentiable at x = 2?
A.
Yes
B.
No
C.
Only left
D.
Only right
Show solution
Solution
f(x) is a polynomial function, hence differentiable everywhere including at x = 2.
Correct Answer: A — Yes
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Q. The function f(x) = x^2 - 4x + 4 is differentiable everywhere?
A.
True
B.
False
C.
Only at x = 0
D.
Only at x = 2
Show solution
Solution
f(x) is a polynomial function, hence it is differentiable everywhere.
Correct Answer: A — True
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Q. The function f(x) = x^2 for x < 1 and f(x) = 2x - 1 for x ≥ 1 is differentiable at x = 1?
A.
Yes
B.
No
C.
Only continuous
D.
Only from the left
Show solution
Solution
f'(1) from left = 2 and from right = 2; hence, f is continuous but not differentiable at x = 1.
Correct Answer: B — No
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Q. The function f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0 is differentiable at x = 0. True or False?
A.
True
B.
False
C.
Depends on x
D.
Not enough information
Show solution
Solution
True, as the limit of f'(x) as x approaches 0 exists and equals 0.
Correct Answer: A — True
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