Major Competitive Exams
Q. In a diode, what is the region called where no current flows?
A.
Forward bias
B.
Reverse bias
C.
Depletion region
D.
Conduction region
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Solution
The depletion region is the area in a diode where no current flows under reverse bias.
Correct Answer: C — Depletion region
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Q. In a double convex lens, if the radii of curvature are 10 cm and 15 cm, what is the focal length using the lens maker's formula?
A.
6 cm
B.
10 cm
C.
12 cm
D.
8 cm
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Solution
Using the lens maker's formula, f = (R1 * R2) / (n - 1) * (1/R1 - 1/R2), we find f = 12 cm.
Correct Answer: C — 12 cm
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Q. In a double-slit experiment, if the distance between the screen and the slits is increased, what happens to the fringe separation?
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
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Solution
Fringe separation is directly proportional to the distance from the slits to the screen; increasing this distance increases fringe separation.
Correct Answer: A — It increases
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Q. In a double-slit experiment, if the distance between the slits is 0.2 mm and the distance to the screen is 1 m, what is the fringe width for light of wavelength 600 nm?
A.
0.3 mm
B.
0.6 mm
C.
0.9 mm
D.
1.2 mm
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Solution
Fringe width β = λD/d = (600 x 10^-9 m)(1 m)/(0.2 x 10^-3 m) = 0.003 m = 0.6 mm.
Correct Answer: B — 0.6 mm
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Q. In a double-slit experiment, if the distance between the slits is 0.5 mm and the wavelength of light is 400 nm, what is the distance between the first and second bright fringes?
A.
0.4 m
B.
0.8 m
C.
1.2 m
D.
1.6 m
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Solution
Distance between fringes = β = λD/d. For first and second bright fringes, the distance is 2β.
Correct Answer: B — 0.8 m
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Q. In a double-slit experiment, if the distance between the slits is 0.5 mm and the distance to the screen is 2 m, what is the distance between the first and second bright fringes if the wavelength of light used is 500 nm?
A.
0.5 cm
B.
1 cm
C.
1.5 cm
D.
2 cm
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Solution
Using the formula for fringe separation, y = (λD)/d, we find y = (500 x 10^-9 m * 2 m) / (0.5 x 10^-3 m) = 2 cm.
Correct Answer: B — 1 cm
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Q. In a double-slit experiment, if the distance between the slits is doubled while keeping the wavelength constant, what happens to the fringe width?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Fringe width (β) is given by β = λD/d, where d is the distance between the slits. If d is doubled, β is halved.
Correct Answer: B — Halves
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Q. In a double-slit experiment, if the distance between the slits is doubled, how does the fringe width change?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Fringe width (β) is inversely proportional to the distance between the slits (d). If d is doubled, β is halved.
Correct Answer: B — Halves
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Q. In a double-slit experiment, if the distance between the slits is doubled, what happens to the fringe width?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Fringe width (β) is given by β = λD/d, where d is the distance between the slits. If d is doubled, β becomes β/2, hence the fringe width halves.
Correct Answer: B — Halves
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Q. In a double-slit experiment, if the distance between the slits is doubled, what happens to the fringe separation on the screen?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The fringe separation is inversely proportional to the distance between the slits; thus, if the distance is doubled, the fringe separation halves.
Correct Answer: B — It halves
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Q. In a double-slit experiment, if the distance between the slits is halved, what happens to the fringe separation on the screen?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The fringe separation is inversely proportional to the distance between the slits; halving the distance doubles the fringe separation.
Correct Answer: A — It doubles
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Q. In a double-slit experiment, if the distance between the slits is increased, what happens to the interference pattern?
A.
Fringes become wider
B.
Fringes become narrower
C.
Fringes disappear
D.
Fringes remain unchanged
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Solution
Increasing the distance between the slits (d) causes the fringe width (β) to decrease, making the fringes narrower.
Correct Answer: B — Fringes become narrower
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Q. In a double-slit experiment, if the distance between the slits is increased, what happens to the number of visible fringes on the screen?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Increasing the distance between the slits decreases the fringe width, which can lead to more visible fringes within a given distance on the screen.
Correct Answer: B — Decreases
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Q. In a double-slit experiment, if the distance to the screen is increased, what happens to the fringe pattern?
A.
Fringe width decreases
B.
Fringe width increases
C.
Fringe pattern disappears
D.
Fringe pattern becomes sharper
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Solution
Increasing the distance to the screen increases the fringe width, as fringe width is proportional to the distance from the slits.
Correct Answer: B — Fringe width increases
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Q. In a double-slit experiment, if the distance to the screen is increased, what happens to the fringe separation?
A.
Fringe separation decreases
B.
Fringe separation increases
C.
Fringe separation remains the same
D.
Fringe separation becomes zero
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Solution
Fringe separation is directly proportional to the distance from the slits to the screen (D), so increasing D increases the fringe separation.
Correct Answer: B — Fringe separation increases
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Q. In a double-slit experiment, if the distance to the screen is increased, what happens to the interference pattern?
A.
Fringe width decreases
B.
Fringe width increases
C.
Fringe pattern disappears
D.
Fringe spacing remains unchanged
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Solution
Increasing the distance to the screen increases the fringe width, as fringe width is proportional to the distance from the slits.
Correct Answer: B — Fringe width increases
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Q. In a double-slit experiment, if the intensity of light at the center of the fringe pattern is I0, what is the intensity at the first minimum?
A.
0
B.
I0
C.
I0/2
D.
I0/4
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Solution
At the first minimum, the intensity is 0 due to destructive interference.
Correct Answer: A — 0
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Q. In a double-slit experiment, if the screen distance is increased, what happens to the fringe separation?
A.
Fringe separation increases
B.
Fringe separation decreases
C.
Fringe separation remains the same
D.
Fringe separation becomes zero
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Solution
Fringe separation is directly proportional to the distance from the slits to the screen (D), hence it increases.
Correct Answer: A — Fringe separation increases
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Q. In a double-slit experiment, if the screen is moved further away from the slits, what happens to the fringe pattern?
A.
Fringes become wider
B.
Fringes become narrower
C.
Fringe intensity increases
D.
Fringe intensity decreases
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Solution
Moving the screen further away increases the distance (D) in the fringe width formula, causing the fringes to become wider.
Correct Answer: A — Fringes become wider
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Q. In a double-slit experiment, if the screen is moved further away from the slits, what effect does this have on the fringe spacing?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Moving the screen further away increases the fringe spacing, as fringe width is directly proportional to the distance from the slits.
Correct Answer: A — Increases
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Q. In a double-slit experiment, if the wavelength of light is 600 nm and the distance between the slits is 0.5 mm, what is the fringe width if the screen is 1 m away?
A.
0.12 mm
B.
0.3 mm
C.
0.6 mm
D.
0.5 mm
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Solution
Fringe width β = λD/d = (600 x 10^-9 m)(1 m)/(0.5 x 10^-3 m) = 0.12 mm.
Correct Answer: A — 0.12 mm
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Q. In a double-slit experiment, if the wavelength of light is increased, what happens to the distance between the fringes?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
The distance between the fringes increases with an increase in wavelength, as fringe separation is directly proportional to wavelength.
Correct Answer: A — Increases
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Q. In a double-slit experiment, what happens to the interference pattern if the distance between the slits is increased?
A.
Pattern becomes wider
B.
Pattern becomes narrower
C.
No change
D.
Pattern disappears
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Solution
Increasing the distance between the slits decreases the fringe width, making the pattern narrower.
Correct Answer: B — Pattern becomes narrower
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Q. In a double-slit experiment, what is the effect of increasing the distance between the slits on the fringe width?
A.
Fringe width increases
B.
Fringe width decreases
C.
Fringe width remains constant
D.
Fringe width becomes zero
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Solution
Increasing the distance between the slits increases the fringe width because the angle of diffraction increases.
Correct Answer: A — Fringe width increases
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Q. In a dynamic equilibrium, which of the following statements is true?
A.
The rates of the forward and reverse reactions are equal
B.
The concentrations of reactants and products are equal
C.
The reaction has stopped
D.
The system is at rest
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Solution
In a dynamic equilibrium, the rates of the forward and reverse reactions are equal, but the concentrations of reactants and products may not be equal.
Correct Answer: A — The rates of the forward and reverse reactions are equal
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Q. In a family of 4 children, what is the probability that at least one is a girl given that there are at least 2 boys?
A.
1/2
B.
3/4
C.
1/4
D.
2/3
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Solution
If there are at least 2 boys, the possible combinations are (2B, 2G), (3B, 1G), (4B). Thus, the probability of having at least one girl is 3/4.
Correct Answer: B — 3/4
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Q. In a family with 3 children, what is the probability that at least one child is a girl given that at least one child is a boy?
A.
0.75
B.
0.5
C.
0.25
D.
0.6
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Solution
The total outcomes for 3 children are 8. The outcomes with at least one boy are 7. The outcomes with at least one girl and one boy are 6. Thus, P(Girl|Boy) = 6/7 ≈ 0.857.
Correct Answer: A — 0.75
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Q. In a first-order reaction, if the concentration of reactant decreases from 0.8 M to 0.2 M in 20 minutes, what is the rate constant? (2022)
A.
0.0347 min⁻¹
B.
0.0693 min⁻¹
C.
0.1 min⁻¹
D.
0.2 min⁻¹
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Solution
Using the first-order rate equation, k = (ln[A₀] - ln[A]) / t. Here, k = (ln(0.8) - ln(0.2)) / 20 = 0.0347 min⁻¹.
Correct Answer: A — 0.0347 min⁻¹
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Q. In a first-order reaction, if the concentration of the reactant is halved, what happens to the half-life?
A.
It doubles
B.
It remains the same
C.
It is halved
D.
It becomes zero
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Solution
In a first-order reaction, the half-life is independent of the concentration of the reactant, so it remains the same.
Correct Answer: B — It remains the same
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Q. In a first-order reaction, if the rate constant k is 0.03 min⁻¹, what is the time required for the concentration to decrease to half? (2020)
A.
23.1 min
B.
10.0 min
C.
20.0 min
D.
15.0 min
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Solution
t₁/₂ = 0.693 / k = 0.693 / 0.03 = 23.1 min.
Correct Answer: A — 23.1 min
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