Q. If the following numbers are given: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, what is the median? (2019)
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Solution
The numbers are already in order. The median is the average of the 5th and 6th numbers: (5 + 6) / 2 = 5.5.
Correct Answer:
B
— 6
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Q. If the forward reaction is exothermic, what effect does increasing the temperature have on the equilibrium position?
A.
Shifts to the right
B.
Shifts to the left
C.
No effect
D.
Increases the rate of reaction
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Solution
According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium position to the left, favoring the reactants.
Correct Answer:
B
— Shifts to the left
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Q. If the freezing point of a solution is -5°C, what is the molality of the solution if the freezing point depression constant (Kf) is 1.86°C kg/mol? (2022)
A.
1.34 m
B.
2.68 m
C.
0.5 m
D.
3.72 m
Show solution
Solution
ΔTf = Kf * m; -5 = -1.86 * m; m = 5 / 1.86 = 2.68 m.
Correct Answer:
B
— 2.68 m
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Q. If the freezing point of pure water is 0 °C, what will be the freezing point of a solution containing 1 mole of NaCl in 1 kg of water? (2023)
A.
-1.86 °C
B.
-3.72 °C
C.
-2.26 °C
D.
-0.93 °C
Show solution
Solution
Freezing point depression = i * Kf * m = 2 * 1.86 °C kg/mol * 1 mol/kg = 3.72 °C. Thus, freezing point = 0 - 3.72 = -3.72 °C.
Correct Answer:
B
— -3.72 °C
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Q. If the freezing point of pure water is 0°C, what will be the freezing point of a 1 molal solution of NaCl? (2022)
A.
-1.86°C
B.
-3.72°C
C.
-2.52°C
D.
-0.52°C
Show solution
Solution
Freezing point depression = i * Kf * m = 2 * 1.86 * 1 = 3.72°C. Therefore, freezing point = 0 - 3.72 = -1.86°C.
Correct Answer:
A
— -1.86°C
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Q. If the frequency of a simple harmonic motion is doubled, what happens to the time period?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The time period T is inversely proportional to the frequency f. If the frequency is doubled, the time period halves.
Correct Answer:
B
— It halves
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Q. If the frequency of a simple harmonic oscillator is doubled, what happens to its period? (2021)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The period T is inversely proportional to frequency f. If f is doubled, T is halved.
Correct Answer:
B
— It halves
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Q. If the frequency of a simple harmonic oscillator is halved, what happens to the period?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Period T = 1/f, if frequency is halved, period doubles.
Correct Answer:
A
— It doubles
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Q. If the frequency of a sound wave is doubled, what happens to its wavelength in a given medium?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases by a factor of four
Show solution
Solution
Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength is halved.
Correct Answer:
B
— Halves
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Q. If the frequency of a sound wave is doubled, what happens to its wavelength?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength halves.
Correct Answer:
B
— It halves
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Q. If the frequency of a vibrating tuning fork is 440 Hz, what is the time period of the vibration? (2023)
A.
0.00227 s
B.
0.005 s
C.
0.01 s
D.
0.0227 s
Show solution
Solution
The time period T is the reciprocal of frequency f, T = 1/f. Therefore, T = 1/440 ≈ 0.00227 s.
Correct Answer:
A
— 0.00227 s
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Q. If the frequency of a wave is doubled, what happens to its wavelength, assuming the speed of the wave remains constant?
A.
Wavelength doubles
B.
Wavelength halves
C.
Wavelength remains the same
D.
Wavelength quadruples
Show solution
Solution
According to the wave equation v = fλ, if frequency (f) is doubled and speed (v) remains constant, the wavelength (λ) must halve.
Correct Answer:
B
— Wavelength halves
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Q. If the frequency of a wave is doubled, what happens to its wavelength, assuming the speed remains constant? (2021)
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
Show solution
Solution
Wavelength (λ) is inversely proportional to frequency (f) when speed (v) is constant: λ = v/f. If f is doubled, λ is halved.
Correct Answer:
B
— Halves
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Q. If the frequency of a wave is doubled, what happens to its wavelength?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The speed of a wave is given by the product of its frequency and wavelength (v = fλ). If the frequency is doubled, the wavelength must be halved to keep the speed constant.
Correct Answer:
B
— It halves
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Q. If the frequency of a wave is halved, what happens to its wavelength? (2015)
A.
Halves
B.
Doubles
C.
Remains the same
D.
Increases by four times
Show solution
Solution
Wavelength is inversely proportional to frequency. If frequency is halved, wavelength doubles.
Correct Answer:
B
— Doubles
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Q. If the frequency of an AC circuit is doubled, what happens to the inductive reactance?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Inductive reactance (X_L) is given by X_L = 2πfL. If the frequency (f) is doubled, the inductive reactance also doubles.
Correct Answer:
A
— It doubles
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Q. If the frequency of an AC signal is doubled, what happens to its period?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The period T is the reciprocal of frequency f (T = 1/f). If frequency is doubled, the period halves.
Correct Answer:
B
— It halves
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Q. If the frequency of an AC source is 50 Hz, what is the time period of the AC signal? (2019)
A.
0.02 s
B.
0.01 s
C.
0.5 s
D.
1 s
Show solution
Solution
The time period (T) is the reciprocal of frequency (f). Therefore, T = 1/f = 1/50 Hz = 0.02 s.
Correct Answer:
A
— 0.02 s
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Q. If the frequency of an AC source is 60 Hz, what is the time period of the AC signal?
A.
0.0167 s
B.
0.0333 s
C.
0.05 s
D.
0.1 s
Show solution
Solution
The time period (T) is the reciprocal of frequency (f). T = 1/f = 1/60 Hz = 0.0167 s.
Correct Answer:
B
— 0.0333 s
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Q. If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
Show solution
Solution
Xl = 2πfL; if f is doubled, Xl also doubles.
Correct Answer:
B
— Halves
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Q. If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.
Correct Answer:
B
— It halves
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Q. If the frequency of an AC source is doubled, what happens to the inductive reactance of an inductor? (2021)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Inductive reactance Xl = ωL, so if frequency is doubled, Xl halves.
Correct Answer:
B
— It halves
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Q. If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.
Correct Answer:
B
— It halves
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Q. If the frequency of an AC source is doubled, what happens to the reactance of an inductor? (2023)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The reactance of an inductor is given by XL = ωL. If frequency is doubled, reactance also doubles.
Correct Answer:
A
— It doubles
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Q. If the frequency of an AC source is increased, what happens to the capacitive reactance?
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes infinite
Show solution
Solution
Capacitive reactance X_C = 1/(ωC) decreases as frequency increases.
Correct Answer:
B
— It decreases
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Q. If the frequency of an AC source is increased, what happens to the inductive reactance? (2019)
A.
Increases
B.
Decreases
C.
Remains constant
D.
Becomes zero
Show solution
Solution
Inductive reactance (X_L) is directly proportional to frequency (f). Therefore, if frequency increases, X_L decreases.
Correct Answer:
B
— Decreases
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Q. If the frequency of incident light is doubled, what happens to the kinetic energy of the emitted electrons?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It decreases
Show solution
Solution
The kinetic energy of the emitted electrons is given by KE = hf - φ. If the frequency is doubled, the kinetic energy increases as it is directly proportional to frequency.
Correct Answer:
B
— It doubles
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Q. If the function f(x) = e^x + x^2 has a minimum at x = 0, then f(0) is:
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Solution
Evaluating f(0) = e^0 + 0^2 = 1 + 0 = 1.
Correct Answer:
A
— 1
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Q. If the function f(x) = x^2 - 4x + 3 has a minimum value, what is it?
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Solution
The vertex form gives the minimum value at x = 2, f(2) = 1.
Correct Answer:
A
— -1
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Q. If the function f(x) = x^3 - 3x + 2 has a local maximum, what is the value of x?
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Solution
Setting f'(x) = 0 gives x = 1 as a local maximum.
Correct Answer:
C
— 1
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