Q. A train travels at a speed of 72 km/h. How long will it take to cover a distance of 180 km?
A.
2 hours
B.
2.5 hours
C.
3 hours
D.
3.5 hours
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Solution
Time = distance / speed. Convert speed to m/s: 72 km/h = 20 m/s. Time = 180 km / 72 km/h = 2.5 hours.
Correct Answer: C — 3 hours
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Q. A train travels at a speed of 80 km/h. How far will it travel in 2.5 hours?
A.
200 km
B.
180 km
C.
220 km
D.
240 km
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Solution
Distance = speed × time. Therefore, distance = 80 km/h × 2.5 h = 200 km.
Correct Answer: A — 200 km
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Q. A train travels at a speed of 90 km/h and a car at 60 km/h. If they start from the same point and travel in the same direction, how far apart will they be after 1 hour?
A.
30 km
B.
20 km
C.
10 km
D.
40 km
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Solution
Relative speed = 90 - 60 = 30 km/h. Distance apart after 1 hour = 30 km.
Correct Answer: A — 30 km
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Q. A train travels at a speed of 90 km/h. How far will it travel in 2.5 hours? (2019)
A.
200 km
B.
225 km
C.
250 km
D.
300 km
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Solution
Distance = Speed * Time = 90 km/h * 2.5 h = 225 km.
Correct Answer: B — 225 km
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Q. A train travels at a speed of 90 km/h. How long will it take to cover 270 km? (2020)
A.
2 hours
B.
3 hours
C.
4 hours
D.
5 hours
Show solution
Solution
Time = Distance / Speed = 270 km / 90 km/h = 3 hours.
Correct Answer: B — 3 hours
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Q. A train travels at a speed of 90 km/h. How long will it take to cover 450 km? (2019)
A.
4 hours
B.
5 hours
C.
6 hours
D.
7 hours
Show solution
Solution
Time = Distance / Speed = 450 km / 90 km/h = 5 hours.
Correct Answer: C — 6 hours
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Q. A train travels at a speed of 90 km/h. How long will it take to cover a distance of 270 km? (2021)
A.
2.5 hours
B.
3 hours
C.
3.5 hours
D.
4 hours
Show solution
Solution
Time = Distance / Speed = 270 km / 90 km/h = 3 hours.
Correct Answer: B — 3 hours
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Q. A train travels at a speed of 90 km/h. How long will it take to cover a distance of 450 km?
A.
4 hours
B.
5 hours
C.
6 hours
D.
7 hours
Show solution
Solution
Time = Distance/Speed = 450 km / 90 km/h = 5 hours.
Correct Answer: B — 5 hours
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Q. A train travels from City A to City B at a speed of 60 km/h and returns at a speed of 90 km/h. What is the average speed of the train for the entire journey?
A.
72 km/h
B.
75 km/h
C.
80 km/h
D.
85 km/h
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Solution
Average speed = 2xy / (x + y) = 2 * 60 * 90 / (60 + 90) = 72 km/h.
Correct Answer: A — 72 km/h
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Q. A train travels from station A to station B, a distance of 300 km, at a speed of 75 km/h. How long does the journey take? (2019)
A.
3 hours
B.
4 hours
C.
5 hours
D.
6 hours
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Solution
Time = Distance / Speed = 300 km / 75 km/h = 4 hours.
Correct Answer: C — 5 hours
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Q. A transformer has 200 turns in the primary coil and 50 turns in the secondary coil. If the primary voltage is 240 V, what is the secondary voltage? (2023)
A.
60 V
B.
120 V
C.
240 V
D.
480 V
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Solution
Using the transformer equation Vp/Vs = Np/Ns, we find Vs = Vp × (Ns/Np) = 240 V × (50/200) = 60 V.
Correct Answer: A — 60 V
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Q. A transformer operates on the principle of electromagnetic induction. If the primary coil has 100 turns and the secondary coil has 50 turns, what is the relationship between the primary and secondary voltages?
A.
V_primary = 2 * V_secondary
B.
V_primary = 0.5 * V_secondary
C.
V_primary = V_secondary
D.
V_primary = 4 * V_secondary
Show solution
Solution
The voltage ratio in a transformer is given by the turns ratio. Therefore, V_primary/V_secondary = N_primary/N_secondary = 100/50 = 2, which means V_primary = 2 * V_secondary.
Correct Answer: A — V_primary = 2 * V_secondary
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Q. A transformer operates on the principle of electromagnetic induction. What is the primary function of a transformer?
A.
To increase voltage
B.
To decrease voltage
C.
To convert AC to DC
D.
To store energy
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Solution
A transformer is designed to increase or decrease the voltage in an AC circuit through electromagnetic induction, depending on the turns ratio of the primary and secondary coils.
Correct Answer: A — To increase voltage
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Q. A transformer operates on the principle of electromagnetic induction. What is the main purpose of a transformer?
A.
To increase or decrease voltage
B.
To store electrical energy
C.
To convert AC to DC
D.
To measure current
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Solution
A transformer is used to increase or decrease the voltage in an AC circuit based on the turns ratio of its coils.
Correct Answer: A — To increase or decrease voltage
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Q. A transformer steps down voltage from 240 V to 120 V. If the primary coil has 100 turns, how many turns does the secondary coil have? (2023)
A.
50 turns
B.
100 turns
C.
200 turns
D.
300 turns
Show solution
Solution
Using the transformer equation Vp/Vs = Np/Ns, we have 240/120 = 100/Ns, giving Ns = 50 turns.
Correct Answer: A — 50 turns
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Q. A transformer works on the principle of:
A.
Electromagnetic induction
B.
Electrostatics
C.
Magnetic resonance
D.
Thermal conduction
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Solution
A transformer operates on the principle of electromagnetic induction, transferring energy between coils through a changing magnetic field.
Correct Answer: A — Electromagnetic induction
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Q. A transversal intersects two parallel lines creating a pair of corresponding angles. If one of the angles measures 120 degrees, what is the measure of the corresponding angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
30 degrees
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Solution
Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the corresponding angle also measures 120 degrees.
Correct Answer: B — 120 degrees
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Q. A trapezium has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is its area? (2023)
A.
32 cm²
B.
36 cm²
C.
40 cm²
D.
44 cm²
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Solution
Area = (1/2) * (base1 + base2) * height = (1/2) * (10 + 6) * 4 = 32 cm².
Correct Answer: A — 32 cm²
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Q. A trapezium has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is the area of the trapezium?
A.
32 cm²
B.
40 cm²
C.
36 cm²
D.
28 cm²
Show solution
Solution
Area of a trapezium = (1/2) × (base1 + base2) × height = (1/2) × (10 + 6) × 4 = 32 cm².
Correct Answer: A — 32 cm²
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Q. A tree casts a shadow of 20 m when the angle of elevation of the sun is 30 degrees. What is the height of the tree?
A.
10 m
B.
15 m
C.
20 m
D.
25 m
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Solution
Using tan(30°) = height/20, we have 1/√3 = height/20. Therefore, height = 20/√3 ≈ 11.55 m.
Correct Answer: A — 10 m
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Q. A tree casts a shadow of 20 m when the angle of elevation of the sun is 45 degrees. What is the height of the tree?
A.
10 m
B.
20 m
C.
30 m
D.
40 m
Show solution
Solution
Using tan(45°) = height/shadow, we have 1 = height/20. Therefore, height = 20 m.
Correct Answer: B — 20 m
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Q. A tree casts a shadow of 20 meters when the angle of elevation of the sun is 30 degrees. What is the height of the tree?
A.
20√3 meters
B.
10√3 meters
C.
30 meters
D.
40 meters
Show solution
Solution
Height = shadow * tan(angle) = 20 * tan(30°) = 20 * (1/√3) = 20√3 meters.
Correct Answer: A — 20√3 meters
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Q. A tree is 15 meters tall. From a point on the ground, the angle of elevation to the top of the tree is 30 degrees. How far is the point from the base of the tree?
A.
15√3 meters
B.
30 meters
C.
45 meters
D.
10 meters
Show solution
Solution
Distance = height / tan(angle) = 15 / tan(30°) = 15√3 meters.
Correct Answer: A — 15√3 meters
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Q. A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is the area of the triangle?
A.
24 cm²
B.
30 cm²
C.
36 cm²
D.
20 cm²
Show solution
Solution
Using Heron's formula, s = (6 + 8 + 10)/2 = 12. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12 × 6 × 4 × 2] = 24 cm².
Correct Answer: A — 24 cm²
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Q. A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle? (2019)
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angles are known
Show solution
Solution
Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625, which is equal to 25^2. Therefore, it is a right triangle.
Correct Answer: A — Yes
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Q. A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle? (2021)
A.
84 cm²
B.
96 cm²
C.
120 cm²
D.
168 cm²
Show solution
Solution
The triangle is a right triangle (7² + 24² = 25²). The area is (1/2) * base * height = (1/2) * 7 * 24 = 84 cm².
Correct Answer: A — 84 cm²
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Q. A tuning fork produces a sound wave of frequency 440 Hz. If the speed of sound in air is 340 m/s, what is the wavelength of the sound wave?
A.
0.77 m
B.
0.85 m
C.
0.90 m
D.
1.00 m
Show solution
Solution
Using the formula λ = v/f, we find λ = 340 m/s / 440 Hz = 0.7727 m, approximately 0.77 m.
Correct Answer: A — 0.77 m
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Q. A tuning fork produces a sound wave of frequency 440 Hz. What is the period of this wave?
A.
0.00227 s
B.
0.0025 s
C.
0.0023 s
D.
0.0020 s
Show solution
Solution
The period T is the reciprocal of frequency f. T = 1/f = 1/440 Hz = 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. A tuning fork produces a sound wave of frequency 440 Hz. What is the period of this sound wave?
A.
0.00227 s
B.
0.00455 s
C.
0.005 s
D.
0.01 s
Show solution
Solution
The period T is the reciprocal of frequency f. T = 1/f = 1/440 Hz = 0.00227 s.
Correct Answer: B — 0.00455 s
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Q. A tuning fork produces a sound wave of frequency 440 Hz. What is the period of the wave? (2019)
A.
0.00227 s
B.
0.005 s
C.
0.01 s
D.
0.001 s
Show solution
Solution
Period T = 1/f = 1/440 Hz ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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