Q. In simple harmonic motion, the maximum displacement from the mean position is called what?
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A.
Amplitude
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B.
Frequency
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C.
Period
-
D.
Wavelength
Solution
The maximum displacement from the mean position in simple harmonic motion is called amplitude.
Correct Answer: A — Amplitude
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Q. In simple harmonic motion, the maximum speed occurs at which point?
-
A.
At the mean position
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B.
At the amplitude
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C.
At one-fourth of the amplitude
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D.
At three-fourths of the amplitude
Solution
The maximum speed in SHM occurs at the mean position where the displacement is zero.
Correct Answer: A — At the mean position
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Q. In simple harmonic motion, the restoring force is directly proportional to which of the following?
-
A.
Displacement
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B.
Velocity
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C.
Acceleration
-
D.
Mass
Solution
The restoring force is directly proportional to the displacement from the mean position.
Correct Answer: A — Displacement
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Q. In simple harmonic motion, the total mechanical energy is conserved. What forms of energy are involved?
-
A.
Kinetic and Potential Energy
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B.
Kinetic and Thermal Energy
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C.
Potential and Thermal Energy
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D.
Only Kinetic Energy
Solution
In SHM, the total mechanical energy is the sum of kinetic and potential energy, which remains constant.
Correct Answer: A — Kinetic and Potential Energy
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Q. In simple harmonic motion, the velocity of the particle is maximum when it is at which position?
-
A.
Mean position
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B.
Maximum displacement
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C.
Equilibrium position
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D.
None of the above
Solution
In simple harmonic motion, the velocity is maximum at the mean position where the displacement is zero.
Correct Answer: A — Mean position
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Q. In the Biot-Savart Law, what does the term 'dl' represent?
-
A.
The length of the wire segment
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B.
The distance from the wire to the point of interest
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C.
The current flowing through the wire
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D.
The angle between the wire and the point
Solution
'dl' represents the infinitesimal length of the wire segment that contributes to the magnetic field at a point.
Correct Answer: A — The length of the wire segment
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Q. In the Bohr model of the hydrogen atom, what is the energy of the electron in the n=2 level?
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A.
-13.6 eV
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B.
-3.4 eV
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C.
-1.51 eV
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D.
0 eV
Solution
The energy of an electron in the nth level of hydrogen is given by E_n = -13.6 eV/n². For n=2, E_2 = -13.6 eV/2² = -3.4 eV.
Correct Answer: B — -3.4 eV
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Q. In the Bohr model of the hydrogen atom, what is the radius of the first orbit?
-
A.
0.0529 nm
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B.
0.1 nm
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C.
0.529 nm
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D.
0.529 pm
Solution
The radius of the first orbit in the Bohr model is 0.529 Å or 0.0529 nm.
Correct Answer: C — 0.529 nm
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Q. In the calculation 12.11 + 0.3 + 1.234, how many significant figures should the answer have?
Solution
The answer should have 2 decimal places, as 0.3 has the least precision.
Correct Answer: C — 4
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Q. In the complex [Ni(CO)4], what is the hybridization of the nickel atom?
-
A.
sp
-
B.
sp2
-
C.
sp3
-
D.
d2sp3
Solution
Nickel in [Ni(CO)4] undergoes sp3 hybridization as it forms four sigma bonds with CO ligands.
Correct Answer: C — sp3
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Q. In the context of adsorption, what does the term 'saturation' refer to?
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A.
Complete coverage of the adsorbent surface
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B.
Maximum temperature for adsorption
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C.
Equilibrium state of adsorption and desorption
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D.
None of the above
Solution
Saturation refers to the complete coverage of the adsorbent surface by the adsorbate.
Correct Answer: A — Complete coverage of the adsorbent surface
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Q. In the context of diffraction, what does the term 'angular width' refer to?
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A.
The angle between the first and second minima
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B.
The angle of incidence
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C.
The angle of reflection
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D.
The angle of diffraction
Solution
Angular width refers to the angle between the first and second minima in a diffraction pattern.
Correct Answer: A — The angle between the first and second minima
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Q. In the context of diffraction, what does the term 'coherence' refer to?
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A.
The ability of waves to interfere
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B.
The speed of light
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C.
The intensity of light
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D.
The wavelength of light
Solution
Coherence refers to the ability of waves to maintain a constant phase relationship, which is essential for producing clear interference patterns.
Correct Answer: A — The ability of waves to interfere
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Q. In the context of diffraction, what does the term 'resolution' refer to?
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A.
The ability to distinguish between two closely spaced objects
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B.
The intensity of the diffracted light
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C.
The wavelength of the light used
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D.
The width of the slit
Solution
Resolution refers to the ability to distinguish between two closely spaced objects, which is affected by diffraction.
Correct Answer: A — The ability to distinguish between two closely spaced objects
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Q. In the context of measurement, what does the term 'accuracy' refer to?
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A.
The closeness of a measured value to the true value
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B.
The repeatability of measurements
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C.
The range of values within which the true value lies
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D.
The number of significant figures in a measurement
Solution
Accuracy refers to how close a measured value is to the true or accepted value.
Correct Answer: A — The closeness of a measured value to the true value
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Q. In the context of measurement, what does the term 'precision' refer to?
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A.
The closeness of a measurement to the true value
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B.
The reproducibility of measurements
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C.
The range of values
-
D.
The average of measurements
Solution
Precision refers to the reproducibility of measurements, indicating how consistent the results are when repeated.
Correct Answer: B — The reproducibility of measurements
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Q. In the context of the Biot-Savart Law, what does the symbol μ₀ represent?
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A.
Electric permittivity
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B.
Magnetic permeability of free space
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C.
Magnetic field strength
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D.
Electric field strength
Solution
The symbol μ₀ represents the magnetic permeability of free space, which is a constant used in the Biot-Savart Law.
Correct Answer: B — Magnetic permeability of free space
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Q. In the context of the Biot-Savart Law, what does the term 'current element' refer to?
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A.
A small segment of wire carrying current
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B.
The total current in the wire
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C.
The direction of current flow
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D.
The magnetic field produced by the current
Solution
A 'current element' refers to a small segment of wire carrying current, which contributes to the overall magnetic field.
Correct Answer: A — A small segment of wire carrying current
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Q. In the equilibrium constant expression Kc, what is the unit for Kc if the reaction is A(g) + B(g) ⇌ C(g)?
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A.
mol/L
-
B.
L/mol
-
C.
dimensionless
-
D.
mol^2/L^2
Solution
The equilibrium constant Kc is dimensionless because it is a ratio of concentrations raised to their stoichiometric coefficients.
Correct Answer: C — dimensionless
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Q. In the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), if SO2 is added, what will be the effect on the equilibrium?
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A.
Shift to the right
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B.
Shift to the left
-
C.
No change
-
D.
Increase in pressure
Solution
Adding SO2 will shift the equilibrium to the right to produce more SO3, according to Le Chatelier's principle.
Correct Answer: A — Shift to the right
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Q. In the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), what happens if SO3 is removed?
-
A.
Shift to the right
-
B.
Shift to the left
-
C.
No change
-
D.
Increase in pressure
Solution
Removing SO3 will shift the equilibrium to the right to produce more SO3.
Correct Answer: A — Shift to the right
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Q. In the expansion of (1 + x)^10, what is the coefficient of x^5?
-
A.
252
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B.
210
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C.
120
-
D.
300
Solution
The coefficient of x^5 is C(10,5) = 10! / (5!5!) = 252.
Correct Answer: A — 252
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x?
Solution
The coefficient of x is C(4,1) * 2^3 * 3 = 4 * 8 * 3 = 96.
Correct Answer: A — 12
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x^2?
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: B — 54
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^1?
Solution
The coefficient of x^1 is C(4,1) * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.
Correct Answer: B — 48
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^2?
-
A.
108
-
B.
72
-
C.
36
-
D.
144
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: B — 72
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Q. In the expansion of (2x + 3)^6, what is the coefficient of x^4?
-
A.
540
-
B.
720
-
C.
810
-
D.
900
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (3)^2 = 15 * 16 * 9 = 2160.
Correct Answer: B — 720
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Q. In the expansion of (2x + 3y)^4, what is the coefficient of x^2y^2?
-
A.
108
-
B.
72
-
C.
36
-
D.
144
Solution
The coefficient is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: A — 108
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Q. In the expansion of (2x + 5)^4, what is the coefficient of x^2?
-
A.
300
-
B.
600
-
C.
450
-
D.
500
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer: A — 300
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Q. In the expansion of (2x - 3)^3, what is the coefficient of x?
-
A.
-9
-
B.
-18
-
C.
-27
-
D.
-6
Solution
The coefficient of x is C(3,1) * (2)^1 * (-3)^2 = 3 * 2 * 9 = -54.
Correct Answer: B — -18
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