Q. If two angles are supplementary and one angle measures 120 degrees, what is the measure of the other angle? (2022)
A.
60 degrees
B.
90 degrees
C.
120 degrees
D.
180 degrees
Show solution
Solution
Supplementary angles sum up to 180 degrees. Therefore, the other angle = 180 - 120 = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. If two angles are supplementary and one angle measures 3 times the other, what is the measure of the smaller angle? (2023)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
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Solution
Let the smaller angle be x. Then the larger angle is 3x. Since they are supplementary, x + 3x = 180. Solving gives x = 45 degrees.
Correct Answer:
A
— 30 degrees
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Q. If two angles are supplementary and one angle measures 75 degrees, what is the measure of the other angle?
A.
85 degrees
B.
90 degrees
C.
95 degrees
D.
105 degrees
Show solution
Solution
Supplementary angles sum up to 180 degrees. Therefore, the other angle = 180 - 75 = 105 degrees.
Correct Answer:
D
— 105 degrees
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Q. If two capacitors of capacitance C1 and C2 are connected in series, what is the equivalent capacitance?
A.
C1 + C2
B.
1 / (1/C1 + 1/C2)
C.
C1 * C2 / (C1 + C2)
D.
C1 - C2
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Solution
The equivalent capacitance C_eq of capacitors in series is given by 1 / C_eq = 1 / C1 + 1 / C2.
Correct Answer:
B
— 1 / (1/C1 + 1/C2)
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Q. If two cars are moving in opposite directions at speeds of 40 km/h and 60 km/h, what is their relative speed?
A.
100 km/h
B.
20 km/h
C.
40 km/h
D.
60 km/h
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Solution
Relative speed = Speed of car 1 + Speed of car 2 = 40 km/h + 60 km/h = 100 km/h.
Correct Answer:
A
— 100 km/h
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Q. If two cars are moving in the same direction at speeds of 60 km/h and 80 km/h, how long will it take for the faster car to overtake the slower car if they start 100 km apart?
A.
1 hour
B.
1.5 hours
C.
2 hours
D.
2.5 hours
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Solution
Relative speed = 80 km/h - 60 km/h = 20 km/h. Time = Distance / Speed = 100 km / 20 km/h = 5 hours.
Correct Answer:
B
— 1.5 hours
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Q. If two cars are moving towards each other at speeds of 40 km/h and 60 km/h, how long will it take for them to meet if they are 200 km apart?
A.
1 hour
B.
2 hours
C.
3 hours
D.
4 hours
Show solution
Solution
Relative speed = 40 km/h + 60 km/h = 100 km/h. Time = Distance / Relative Speed = 200 km / 100 km/h = 2 hours.
Correct Answer:
B
— 2 hours
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Q. If two charges +Q and -Q are placed at a distance 'd' apart, what is the electric field at the midpoint? (2020)
A.
0
B.
kQ/d^2
C.
kQ/(2d^2)
D.
kQ/d
Show solution
Solution
At the midpoint, the electric fields due to +Q and -Q cancel each other out, resulting in a net electric field of 0.
Correct Answer:
A
— 0
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Q. If two charges of +2 µC and -2 µC are placed 1 m apart, what is the net electric field at the midpoint? (2023)
A.
0 N/C
B.
4 N/C
C.
2 N/C
D.
8 N/C
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Solution
The electric fields due to both charges at the midpoint cancel each other out, resulting in a net electric field of 0 N/C.
Correct Answer:
A
— 0 N/C
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Q. If two charges of +3μC and +5μC are placed 0.3m apart, what is the magnitude of the force between them?
A.
0.15 N
B.
0.25 N
C.
0.45 N
D.
0.75 N
Show solution
Solution
Using Coulomb's law, F = k * |q1 * q2| / r² = (9 × 10^9 N m²/C²) * |(3 × 10^-6 C) * (5 × 10^-6 C)| / (0.3 m)² = 0.45 N.
Correct Answer:
C
— 0.45 N
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Q. If two charges of +3μC and -3μC are placed 0.1m apart, what is the net electric field at the midpoint?
A.
0 N/C
B.
54000 N/C
C.
27000 N/C
D.
81000 N/C
Show solution
Solution
The electric fields due to both charges at the midpoint cancel each other out, resulting in a net electric field of 0 N/C.
Correct Answer:
A
— 0 N/C
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Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3, EB = 5, CE = 4, what is the length of ED?
Show solution
Solution
Using the intersecting chords theorem: AE * EB = CE * ED. Thus, 3 * 5 = 4 * ED, so 15 = 4 * ED, giving ED = 15/4 = 3.75.
Correct Answer:
A
— 2
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Q. If two chords intersect inside a circle, and the lengths of the segments of one chord are 4 cm and 6 cm, what is the length of the other chord if its segments are x cm and y cm?
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Solution
Using the intersecting chords theorem: 4 * 6 = x * y. If x + y = 10, then x = 4 and y = 6.
Correct Answer:
C
— 14
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Q. If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
The maximum radius of each circle can be half the distance between the centers, which is 10 cm.
Correct Answer:
B
— 10 cm
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Q. If two circles intersect at two points, what can be said about their centers?
A.
They are the same.
B.
They are equidistant from the intersection points.
C.
They lie on the same line.
D.
They are at a fixed distance apart.
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Solution
The centers of two intersecting circles are equidistant from the points of intersection.
Correct Answer:
B
— They are equidistant from the intersection points.
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Q. If two circles intersect at two points, what can be said about their relationship?
A.
They are concentric.
B.
They are tangent to each other.
C.
They are secant to each other.
D.
They do not intersect.
Show solution
Solution
Circles that intersect at two points are said to be secant to each other.
Correct Answer:
C
— They are secant to each other.
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Q. If two circles intersect at two points, which of the following statements is true? (2021)
A.
The centers of the circles are equidistant from the intersection points.
B.
The line joining the centers of the circles passes through the intersection points.
C.
The circles are tangent to each other.
D.
The area of intersection is always a triangle.
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Solution
The centers of the circles are equidistant from the intersection points, making option 0 true.
Correct Answer:
A
— The centers of the circles are equidistant from the intersection points.
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Q. If two coherent sources of light are in phase, what type of interference pattern will be observed?
A.
No interference pattern
B.
Destructive interference
C.
Constructive interference
D.
Random interference
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Solution
When two coherent sources are in phase, they produce constructive interference, resulting in bright fringes.
Correct Answer:
C
— Constructive interference
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Q. If two coherent sources of light are in phase, what type of interference will occur?
A.
Destructive interference
B.
Constructive interference
C.
No interference
D.
Random interference
Show solution
Solution
When two coherent sources are in phase, they produce constructive interference, resulting in bright fringes.
Correct Answer:
B
— Constructive interference
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Q. If two coherent sources of light are in phase, what will be the phase difference at a point where the path difference is λ/4?
A.
0 radians
B.
π/2 radians
C.
π radians
D.
3π/2 radians
Show solution
Solution
The phase difference (Δφ) is given by (2π/λ) * path difference. For a path difference of λ/4, Δφ = (2π/λ) * (λ/4) = π/2 radians.
Correct Answer:
B
— π/2 radians
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Q. If two coherent sources of light are in phase, what will be the phase difference at a point where the path difference is λ/2?
A.
0 radians
B.
π/2 radians
C.
π radians
D.
2π radians
Show solution
Solution
A path difference of λ/2 corresponds to a phase difference of π radians, leading to destructive interference.
Correct Answer:
C
— π radians
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Q. If two coherent sources of light are in phase, what will be the result at a point where the path difference is λ/2?
A.
Constructive interference
B.
Destructive interference
C.
No interference
D.
Partial interference
Show solution
Solution
A path difference of λ/2 results in destructive interference, as the waves will be out of phase.
Correct Answer:
B
— Destructive interference
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Q. If two coins are tossed, what is the probability of getting at least one head?
A.
1/4
B.
1/2
C.
3/4
D.
1
Show solution
Solution
Total outcomes = 4 (HH, HT, TH, TT). At least one head = 3 outcomes. Probability = 3/4.
Correct Answer:
C
— 3/4
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Q. If two coins are tossed, what is the probability of getting at least one tail? (2023)
A.
1/4
B.
1/2
C.
3/4
D.
1/3
Show solution
Solution
The possible outcomes are HH, HT, TH, TT. The outcomes with at least one tail are HT, TH, TT (3 outcomes). So, the probability is 3/4.
Correct Answer:
C
— 3/4
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Q. If two dice are rolled, what is the probability of getting a sum of 7?
A.
1/6
B.
1/12
C.
1/36
D.
1/18
Show solution
Solution
Possible combinations for sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.
Correct Answer:
A
— 1/6
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Q. If two dice are rolled, what is the probability that the sum is 7?
A.
1/6
B.
1/12
C.
1/36
D.
5/36
Show solution
Solution
Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.
Correct Answer:
D
— 5/36
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Q. If two dice are rolled, what is the probability that the sum is greater than 10?
A.
1/12
B.
1/6
C.
1/8
D.
1/4
Show solution
Solution
The combinations for a sum greater than 10 are (5,6), (6,5), (6,6), giving a probability of 3/36 = 1/12.
Correct Answer:
B
— 1/6
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Q. If two dice are rolled, what is the probability that the sum of the numbers on the dice is 7?
A.
1/6
B.
1/12
C.
1/36
D.
5/36
Show solution
Solution
The combinations that give a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), totaling 6 combinations. The total outcomes are 36, so the probability is 6/36 = 1/6.
Correct Answer:
A
— 1/6
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Q. If two equal and opposite forces are applied at the ends of a lever arm of length 1 m, what is the net torque about the center?
A.
0 Nm
B.
1 Nm
C.
2 Nm
D.
4 Nm
Show solution
Solution
The net torque is zero because the forces are equal and opposite, producing no rotational effect.
Correct Answer:
A
— 0 Nm
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Q. If two equal and opposite forces are applied at the ends of a lever arm of length 4 m, what is the net torque about the center?
A.
0 Nm
B.
8 Nm
C.
4 Nm
D.
16 Nm
Show solution
Solution
The net torque is zero because the forces are equal and opposite, resulting in no rotational effect.
Correct Answer:
A
— 0 Nm
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