Q. If the first three terms of a harmonic progression are 1, 1/2, and 1/3, what is the fourth term?
A.
1/4
B.
1/5
C.
1/6
D.
1/7
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Solution
The reciprocals are 1, 2, and 3, which are in arithmetic progression. The next term in the sequence of reciprocals is 4, so the fourth term is 1/4.
Correct Answer: C — 1/6
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Q. If the first three terms of a harmonic progression are 1/2, 1/3, and 1/x, what is the value of x?
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Solution
The reciprocals of the terms form an arithmetic progression: 2, 3, and x. The common difference is 1. Therefore, x = 6.
Correct Answer: B — 6
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Q. If the first three terms of a harmonic progression are a, b, and c, which of the following equations holds true?
A.
1/a + 1/b = 1/c
B.
1/a + 1/c = 1/b
C.
1/b + 1/c = 1/a
D.
1/a + 1/b + 1/c = 0
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Solution
In a harmonic progression, the reciprocals of the terms form an arithmetic progression, hence 1/a + 1/b = 1/c.
Correct Answer: A — 1/a + 1/b = 1/c
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Q. If the first three terms of a harmonic progression are a, b, c, which of the following is true?
A.
1/a, 1/b, 1/c are in AP
B.
a, b, c are in AP
C.
1/a, 1/b, 1/c are in GP
D.
b = (a+c)/2
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Solution
In a harmonic progression, the reciprocals of the terms are in arithmetic progression, hence 1/a, 1/b, 1/c are in AP.
Correct Answer: A — 1/a, 1/b, 1/c are in AP
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Q. If the first two statements are true, is the final statement true? 1. All cats are animals. 2. Some animals are not dogs. 3. Therefore, some cats are not dogs.
A.
True
B.
False
C.
Cannot be determined
D.
None of the above
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Solution
The conclusion cannot be definitively drawn from the premises provided.
Correct Answer: C — Cannot be determined
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Q. If the focal length of a concave lens is -10 cm, what is the nature of the image formed when an object is placed at 15 cm?
A.
Real and inverted
B.
Virtual and erect
C.
Real and erect
D.
Virtual and inverted
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Solution
Concave lenses always produce virtual and erect images regardless of the object distance.
Correct Answer: B — Virtual and erect
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Q. If the focal length of a concave mirror is 10 cm, what is the radius of curvature?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 10 cm = 20 cm.
Correct Answer: B — 10 cm
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Q. If the focal length of a concave mirror is 20 cm, what is the radius of curvature?
A.
10 cm
B.
20 cm
C.
30 cm
D.
40 cm
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Solution
The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 20 cm = 40 cm.
Correct Answer: B — 20 cm
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Q. If the focal length of a lens is -10 cm, what type of lens is it?
A.
Convex lens
B.
Concave lens
C.
Bifocal lens
D.
Cylindrical lens
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Solution
A negative focal length indicates that the lens is a concave lens.
Correct Answer: B — Concave lens
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Q. If the focal length of a lens is 20 cm, what is the power of the lens?
A.
+5 D
B.
+10 D
C.
-5 D
D.
-10 D
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Solution
Power (P) = 1/f (in meters). Here, f = 0.2 m, so P = 1/0.2 = +5 D.
Correct Answer: B — +10 D
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Q. If the focal length of a lens is 25 cm, what is the power of the lens?
A.
+2 D
B.
+4 D
C.
+5 D
D.
+10 D
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Solution
Power (P) is given by P = 1/f (in meters). Thus, P = 1/0.25 m = +4 D.
Correct Answer: C — +5 D
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Q. If the focal length of a lens is doubled, how does the power of the lens change?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Power is inversely proportional to focal length. If f is doubled, P = 1/f will halve.
Correct Answer: B — Halves
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Q. If the focus of a parabola is at (0, 2) and the directrix is y = -2, what is the equation of the parabola?
A.
x^2 = 8y
B.
x^2 = 4y
C.
y^2 = 8x
D.
y^2 = 4x
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Solution
The distance from the focus to the directrix is 4, so the equation is x^2 = 8y.
Correct Answer: A — x^2 = 8y
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Q. If the following numbers are arranged in ascending order: 3, 7, 8, 12, 14, what is the range?
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Solution
Range = Maximum - Minimum = 14 - 3 = 11
Correct Answer: A — 11
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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