Major Competitive Exams
Q. What is the midpoint of the line segment joining the points (2, 3) and (4, 7)?
A.
(3, 5)
B.
(2, 5)
C.
(4, 3)
D.
(5, 7)
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Solution
Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).
Correct Answer: A — (3, 5)
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Q. What is the minimum age for contesting elections to the Lok Sabha?
A.
25 years
B.
30 years
C.
21 years
D.
18 years
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Solution
The minimum age for contesting elections to the Lok Sabha is 25 years.
Correct Answer: A — 25 years
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Q. What is the minimum age required to be a member of the State Legislative Assembly in India? (1950)
A.
25 years
B.
30 years
C.
21 years
D.
18 years
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Solution
A candidate must be at least 25 years old to be eligible for election to the State Legislative Assembly as per Article 173 of the Constitution.
Correct Answer: A — 25 years
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Q. What is the minimum age required to become a member of the Rajya Sabha? (2020)
A.
25 years
B.
30 years
C.
35 years
D.
40 years
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Solution
A candidate must be at least 30 years old to be eligible for membership in the Rajya Sabha as per Article 80 of the Constitution.
Correct Answer: B — 30 years
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Q. What is the minimum age to be eligible for election as a member of the Lok Sabha in India?
A.
25 years
B.
30 years
C.
21 years
D.
18 years
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Solution
According to Article 84 of the Indian Constitution, the minimum age to be a member of the Lok Sabha is 25 years.
Correct Answer: A — 25 years
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Q. What is the minimum age to become a member of the Rajya Sabha? (2023)
A.
25 years
B.
30 years
C.
35 years
D.
40 years
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Solution
The minimum age to become a member of the Rajya Sabha is 30 years as per Article 80 of the Constitution.
Correct Answer: B — 30 years
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Q. What is the minimum age to contest for the Lok Sabha elections in India? (2023)
A.
25 years
B.
30 years
C.
21 years
D.
18 years
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Solution
The minimum age to contest for the Lok Sabha elections in India is 25 years as per Article 84 of the Constitution.
Correct Answer: A — 25 years
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Q. What is the minimum distance from the point (3, 4) to the line 2x + 3y - 6 = 0? (2023)
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Solution
Using the distance formula from a point to a line, the minimum distance is calculated to be 2 units.
Correct Answer: A — 2
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Q. What is the minimum energy required to remove an electron from the surface of a metal called?
A.
Work function
B.
Ionization energy
C.
Binding energy
D.
Threshold energy
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Solution
The minimum energy required to remove an electron from the surface of a metal is known as the work function.
Correct Answer: A — Work function
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Q. What is the minimum frequency of light required to eject electrons from a metal surface in the photoelectric effect?
A.
It depends on the intensity of light
B.
It is constant for all metals
C.
It depends on the work function of the metal
D.
It is equal to the energy of the incident photons
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Solution
The minimum frequency required to eject electrons is determined by the work function of the metal, given by the equation E = hf, where E is the work function, h is Planck's constant, and f is the frequency.
Correct Answer: C — It depends on the work function of the metal
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Q. What is the minimum number of sides a polygon can have?
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Solution
The minimum number of sides a polygon can have is 3, which is a triangle.
Correct Answer: B — 3
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Q. What is the minimum speed required for a satellite to achieve a low Earth orbit?
A.
7.9 km/s
B.
11.2 km/s
C.
5.0 km/s
D.
9.8 km/s
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Solution
The minimum speed required for a satellite to achieve a low Earth orbit is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. What is the minimum speed required for a satellite to maintain a low Earth orbit?
A.
7.9 km/s
B.
11.2 km/s
C.
5.0 km/s
D.
9.8 km/s
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Solution
The minimum speed required for a satellite in low Earth orbit is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. What is the minimum thickness of a soap bubble for which the first order of bright fringe appears for light of wavelength 550 nm?
A.
275 nm
B.
550 nm
C.
1100 nm
D.
2200 nm
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Solution
For the first order bright fringe, thickness t = λ/2 = 550 nm / 2 = 275 nm.
Correct Answer: A — 275 nm
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Q. What is the minimum thickness of a soap bubble for which the first order of constructive interference occurs for light of wavelength 600 nm?
A.
100 nm
B.
200 nm
C.
300 nm
D.
400 nm
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Solution
For constructive interference in a soap bubble, the minimum thickness t = λ/2 = 600 nm / 2 = 300 nm.
Correct Answer: B — 200 nm
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Q. What is the minimum thickness of a soap bubble for which the first order of constructive interference occurs for light of wavelength 550 nm?
A.
275 nm
B.
550 nm
C.
1100 nm
D.
825 nm
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Solution
For constructive interference, the minimum thickness t = λ/2 = 550 nm / 2 = 275 nm.
Correct Answer: A — 275 nm
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Q. What is the minimum thickness of a soap bubble that appears black in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black in reflected light when the thickness is λ/4, leading to destructive interference.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap bubble that will appear black in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black in reflected light when the thickness is λ/4, leading to destructive interference.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap bubble that will appear black when viewed in white light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black when the thickness is λ/4 due to destructive interference of light reflected from the top and bottom surfaces.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap film that appears dark in reflected light for a wavelength of 600 nm?
A.
150 nm
B.
300 nm
C.
600 nm
D.
1200 nm
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Solution
For destructive interference in reflected light, the minimum thickness t = λ/2n, where n is the refractive index (approximately 1.5 for soap). Thus, t = 600 nm / (2 * 1.5) = 200 nm.
Correct Answer: B — 300 nm
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Q. What is the minimum thickness of a soap film that appears dark when illuminated by white light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
For destructive interference in a soap film, the minimum thickness should be λ/2, considering the phase change upon reflection.
Correct Answer: B — λ/2
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Q. What is the minimum thickness of a soap film that appears dark when viewed in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
For destructive interference in reflected light, the minimum thickness of the film must be λ/2.
Correct Answer: B — λ/2
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Q. What is the minimum value of f(x) = 3x^2 - 12x + 9? (2022)
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Solution
The vertex occurs at x = 2. f(2) = 3(2^2) - 12(2) + 9 = 0.
Correct Answer: B — 1
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Q. What is the minimum value of f(x) = x^2 - 4x + 5? (2020)
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2.
Correct Answer: A — 1
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Q. What is the minimum value of f(x) = x^2 - 4x + 6? (2022)
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Solution
The vertex occurs at x = 2. f(2) = 2.
Correct Answer: B — 3
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Q. What is the minimum value of f(x) = x^2 - 6x + 10? (2020)
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Solution
The vertex form gives the minimum at x = 3. f(3) = 3^2 - 6(3) + 10 = 1.
Correct Answer: A — 4
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Q. What is the minimum value of the function f(x) = 2x^2 - 8x + 10?
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.
Correct Answer: B — 4
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Q. What is the minimum value of the function f(x) = 4x^2 - 16x + 20? (2021) 2021
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Solution
The vertex occurs at x = 2. f(2) = 4(2^2) - 16(2) + 20 = 4.
Correct Answer: B — 5
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Q. What is the minimum value of the function f(x) = x^2 - 4x + 5?
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4(2) + 5 = 1.
Correct Answer: A — 1
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Q. What is the minimum value of the function f(x) = x^4 - 8x^2 + 16?
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Solution
f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x(x^2 - 4) = 0, so x = 0, 2, -2. f(0) = 16, f(2) = 0, f(-2) = 0. Minimum value is 0.
Correct Answer: A — 0
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