Q. In a deck of 52 cards, what is the probability of drawing a heart given that the card drawn is a red card?
A.
1/2
B.
1/4
C.
1/3
D.
1/5
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Solution
There are 26 red cards (hearts and diamonds). The number of hearts is 13. Thus, P(Heart | Red) = 13/26 = 1/2.
Correct Answer:
A
— 1/2
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Q. In a deck of cards, what is the probability of drawing a heart given that the card drawn is a red card?
A.
1/2
B.
1/4
C.
1/3
D.
1/5
Show solution
Solution
There are 26 red cards (hearts and diamonds). The number of hearts is 13. Thus, P(Heart | Red) = 13/26 = 1/2.
Correct Answer:
A
— 1/2
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Q. In a diffraction grating, if the number of slits is increased, what happens to the angular width of the principal maxima?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
Show solution
Solution
Increasing the number of slits increases the sharpness of the maxima, thus decreasing the angular width.
Correct Answer:
B
— Decreases
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Q. In a diffraction grating, if the number of slits is increased, what happens to the intensity of the maxima?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
Show solution
Solution
Increasing the number of slits increases the intensity of the maxima due to constructive interference.
Correct Answer:
A
— Increases
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Q. In a diffraction grating, if the number of slits is increased, what happens to the sharpness of the maxima?
A.
Sharpness increases
B.
Sharpness decreases
C.
No effect
D.
Maxima disappear
Show solution
Solution
Increasing the number of slits in a diffraction grating increases the sharpness of the maxima due to constructive interference.
Correct Answer:
A
— Sharpness increases
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Q. In a diffraction grating, what is the relationship between the angle of diffraction and the order of the maximum?
A.
Directly proportional
B.
Inversely proportional
C.
Independent
D.
Exponential
Show solution
Solution
The angle of diffraction is directly proportional to the order of the maximum in a diffraction grating.
Correct Answer:
A
— Directly proportional
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Q. In a diffraction pattern produced by a single slit, what happens to the central maximum when the slit width is decreased? (2022)
A.
It becomes narrower
B.
It becomes wider
C.
It disappears
D.
It remains the same
Show solution
Solution
Decreasing the slit width increases the diffraction angle, causing the central maximum to become wider.
Correct Answer:
B
— It becomes wider
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Q. In a diffraction pattern, how does the intensity of the maxima compare to the minima?
A.
Maxima are always brighter than minima
B.
Minima have the same intensity as maxima
C.
Minima are always darker than maxima
D.
Intensity is uniform throughout
Show solution
Solution
In a diffraction pattern, the minima are always darker than the maxima, which have higher intensity.
Correct Answer:
C
— Minima are always darker than maxima
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Q. In a diffraction pattern, if the distance between the slits is decreased, what happens to the central maximum? (2022)
A.
It becomes wider
B.
It becomes narrower
C.
It disappears
D.
It remains unchanged
Show solution
Solution
Decreasing the distance between the slits increases the diffraction effect, causing the central maximum to become wider.
Correct Answer:
A
— It becomes wider
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Q. In a diffraction pattern, if the first minimum occurs at an angle of 30°, what is the ratio of the slit width to the wavelength?
A.
1:2
B.
1:√3
C.
√3:1
D.
2:1
Show solution
Solution
Using the condition for the first minimum a sin(30°) = λ, we find the ratio a/λ = 1/√3.
Correct Answer:
B
— 1:√3
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Q. In a diffraction pattern, the central maximum is observed to be the brightest. What is the reason for this? (2022)
A.
It has the least path difference
B.
It has the maximum path difference
C.
It has the maximum intensity
D.
It has the minimum intensity
Show solution
Solution
The central maximum has the maximum intensity because all light waves arrive in phase at this point, leading to constructive interference.
Correct Answer:
C
— It has the maximum intensity
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Q. In a diffraction pattern, the intensity of the central maximum is how many times that of the first minimum?
A.
Zero
B.
One
C.
Infinity
D.
Two
Show solution
Solution
The intensity of the central maximum is theoretically infinite compared to the first minimum, which has zero intensity.
Correct Answer:
C
— Infinity
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Q. In a diffraction pattern, the intensity of the central maximum is typically:
A.
Zero
B.
Minimum
C.
Maximum
D.
Constant
Show solution
Solution
The intensity of the central maximum in a diffraction pattern is at its maximum compared to other maxima.
Correct Answer:
C
— Maximum
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Q. In a diffraction pattern, what does the intensity of the central maximum depend on?
A.
Wavelength only
B.
Slit width only
C.
Both wavelength and slit width
D.
Distance from the slit
Show solution
Solution
The intensity of the central maximum in a diffraction pattern depends on both the wavelength of light and the slit width.
Correct Answer:
C
— Both wavelength and slit width
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Q. In a diffraction pattern, what does the term 'fringe separation' refer to?
A.
Distance between two minima
B.
Distance between two maxima
C.
Distance between a maximum and a minimum
D.
None of the above
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Solution
Fringe separation refers to the distance between two consecutive maxima in a diffraction pattern.
Correct Answer:
B
— Distance between two maxima
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Q. In a diffraction pattern, what does the term 'order of diffraction' refer to?
A.
The number of slits used
B.
The number of maxima observed
C.
The wavelength of light used
D.
The distance to the screen
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Solution
The order of diffraction refers to the number of maxima observed in the diffraction pattern, with the central maximum being the zeroth order.
Correct Answer:
B
— The number of maxima observed
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Q. In a diffraction pattern, what is the effect of increasing the slit width?
A.
Wider central maximum
B.
Narrower central maximum
C.
No effect
D.
Increased number of fringes
Show solution
Solution
Increasing the slit width results in a wider central maximum due to the decrease in diffraction effects.
Correct Answer:
A
— Wider central maximum
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Q. In a diffraction pattern, what is the ratio of the intensity of the central maximum to that of the first minimum?
A.
1:0
B.
1:1
C.
1:2
D.
1:4
Show solution
Solution
The intensity of the central maximum is typically much greater than that of the first minimum, often approximated as 1:4.
Correct Answer:
D
— 1:4
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Q. In a digital communication system, what does the term 'bit rate' refer to?
A.
The number of bits transmitted per second
B.
The number of bits stored in a device
C.
The frequency of the carrier wave
D.
The duration of each bit
Show solution
Solution
Bit rate refers to the number of bits transmitted per second in a digital communication system.
Correct Answer:
A
— The number of bits transmitted per second
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Q. In a dihybrid cross between two heterozygous parents (AaBb x AaBb), what fraction of the offspring will be homozygous recessive for both traits?
A.
1/16
B.
3/16
C.
1/4
D.
9/16
Show solution
Solution
The probability of being homozygous recessive for both traits (aabb) in a dihybrid cross is 1/16.
Correct Answer:
A
— 1/16
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Q. In a dihybrid cross between two pea plants, one with genotype AaBb and the other with genotype Aabb, what fraction of the offspring will be homozygous recessive for both traits?
A.
1/16
B.
1/8
C.
1/4
D.
1/2
Show solution
Solution
The cross AaBb x Aabb results in 1/8 of the offspring being aabb (homozygous recessive for both traits).
Correct Answer:
B
— 1/8
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Q. In a dihybrid cross between two plants, one with genotype AaBb and the other with genotype Aabb, what fraction of the offspring will be expected to show the dominant phenotype for both traits?
A.
1/4
B.
1/2
C.
3/4
D.
1/8
Show solution
Solution
The cross AaBb x Aabb results in 1/4 AABB, 1/4 AABb, 1/4 AaBb, and 1/4 Aabb. Only AABB, AABb, and AaBb show the dominant phenotype for both traits, which is 3 out of 8, hence 3/8.
Correct Answer:
B
— 1/2
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Q. In a dihybrid cross, what is the expected phenotypic ratio? (2023)
A.
1:1
B.
3:1
C.
9:3:3:1
D.
1:2:1
Show solution
Solution
The expected phenotypic ratio in a dihybrid cross is 9:3:3:1.
Correct Answer:
C
— 9:3:3:1
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Q. In a diode, what is the region called where no charge carriers are present?
A.
Conduction band
B.
Valence band
C.
Depletion region
D.
N-type region
Show solution
Solution
The depletion region in a diode is the area where no charge carriers are present.
Correct Answer:
C
— Depletion region
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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
Show solution
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 disaster management drill, 25% of the participants were volunteers. If there were 200 participants, how many were volunteers?
Show solution
Solution
25% of 200 = 0.25 * 200 = 50 volunteers.
Correct Answer:
B
— 50
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Q. In a distribution problem, if the total number of items is 50 and the constraints require that at least 10 items go to group A, how many items can go to group B at most?
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Solution
If at least 10 items go to group A, then at most 50 - 10 = 40 items can go to group B.
Correct Answer:
A
— 40
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Q. In a distribution puzzle, if A is taller than B and C is shorter than D, who is the tallest among A, B, C, and D? (2021)
Show solution
Solution
Since A is taller than B and C is shorter than D, A must be the tallest.
Correct Answer:
A
— A
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Q. In a double convex lens, if the focal length is 15 cm, what is the power of the lens? (2022)
A.
+6.67 D
B.
+7.5 D
C.
+10 D
D.
+15 D
Show solution
Solution
Power (P) of a lens is given by P = 1/f (in meters). Here, f = 15 cm = 0.15 m, so P = 1/0.15 = +6.67 D.
Correct Answer:
B
— +7.5 D
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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
Show solution
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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