MHT-CET
Q. A sound wave travels through air at a speed of 340 m/s. If the frequency of the sound is 170 Hz, what is the wavelength?
-
A.
1 m
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B.
2 m
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C.
3 m
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D.
4 m
Solution
The wavelength λ is given by λ = v/f. Thus, λ = 340/170 = 2 m.
Correct Answer: B — 2 m
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Q. A stone is thrown horizontally from a height of 45 m. How long will it take to hit the ground? (Take g = 10 m/s²) (2023)
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A.
3 s
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B.
4.5 s
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C.
5 s
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D.
6 s
Solution
Using h = 0.5 * g * t^2, we have 45 = 0.5 * 10 * t^2. Solving gives t^2 = 9, so t = 3 s.
Correct Answer: A — 3 s
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Q. A train moving at 72 km/h applies brakes and comes to a stop in 5 seconds. What is the deceleration? (2023)
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A.
2 m/s²
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B.
3 m/s²
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C.
4 m/s²
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D.
5 m/s²
Solution
First convert speed to m/s: 72 km/h = 20 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 20) / 5 = -4 m/s².
Correct Answer: C — 4 m/s²
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Q. A tuning fork produces a sound wave of frequency 440 Hz. What is the period of the wave? (2019)
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A.
0.00227 s
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B.
0.005 s
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C.
0.01 s
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D.
0.001 s
Solution
Period 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 time period of this sound wave? (2021)
-
A.
0.00227 s
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B.
0.0045 s
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C.
0.01 s
-
D.
0.005 s
Solution
Time period (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 time period of the sound wave?
-
A.
0.00227 s
-
B.
0.005 s
-
C.
0.01 s
-
D.
0.02 s
Solution
The time period T is the reciprocal of frequency f. Thus, T = 1/f = 1/440 ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. A tuning fork vibrates at a frequency of 440 Hz. What is the time period of the fork? (2020)
-
A.
0.00227 s
-
B.
0.0045 s
-
C.
0.01 s
-
D.
0.005 s
Solution
Time period T = 1/f = 1/440 Hz ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. A uniform rod of length L is pivoted at one end and released from rest. What is the angular speed just before it hits the ground? (2019)
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A.
√(3g/L)
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B.
√(2g/L)
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C.
√(g/L)
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D.
√(4g/L)
Solution
Using conservation of energy, potential energy converts to rotational kinetic energy. Angular speed ω = √(3g/L).
Correct Answer: B — √(2g/L)
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Q. A uniform rod of length L is pivoted at one end and released from rest. What is the angular speed when it reaches the vertical position? (2019)
-
A.
√(3g/L)
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B.
√(2g/L)
-
C.
√(g/L)
-
D.
√(4g/L)
Solution
Using conservation of energy, potential energy converts to rotational kinetic energy. Angular speed ω = √(3g/L).
Correct Answer: B — √(2g/L)
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Q. A vehicle travels with a uniform speed of 60 km/h. How far will it travel in 2 hours? (2023)
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A.
80 km
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B.
100 km
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C.
120 km
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D.
140 km
Solution
Distance = speed * time = 60 km/h * 2 h = 120 km.
Correct Answer: C — 120 km
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Q. A wave has a frequency of 10 Hz and a wavelength of 5 m. What is its speed? (2020)
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A.
50 m/s
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B.
10 m/s
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C.
2 m/s
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D.
5 m/s
Solution
Speed (v) = frequency (f) × wavelength (λ) = 10 Hz × 5 m = 50 m/s.
Correct Answer: A — 50 m/s
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Q. A wave has a frequency of 500 Hz and a wavelength of 0.6 m. What is the speed of the wave? (2022)
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A.
300 m/s
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B.
500 m/s
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C.
600 m/s
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D.
400 m/s
Solution
Using the wave equation v = fλ, we find v = 500 Hz * 0.6 m = 300 m/s.
Correct Answer: A — 300 m/s
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Q. A wave has a frequency of 60 Hz and a wavelength of 3 m. What is its speed? (2016)
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A.
180 m/s
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B.
120 m/s
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C.
60 m/s
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D.
90 m/s
Solution
Speed v = f × λ = 60 Hz × 3 m = 180 m/s.
Correct Answer: A — 180 m/s
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Q. A wave has a frequency of 60 Hz and a wavelength of 3 m. What is the speed of the wave?
-
A.
180 m/s
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B.
120 m/s
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C.
60 m/s
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D.
30 m/s
Solution
The speed v of a wave is given by v = fλ. Thus, v = 60 * 3 = 180 m/s.
Correct Answer: B — 120 m/s
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Q. A wave has a speed of 300 m/s and a frequency of 150 Hz. What is its wavelength? (2022)
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A.
1 m
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B.
2 m
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C.
3 m
-
D.
4 m
Solution
Wavelength λ can be calculated using the formula λ = v/f. Therefore, λ = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. A wave on a string has a speed of 50 m/s and a wavelength of 2 m. What is its frequency? (2018)
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A.
25 Hz
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B.
50 Hz
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C.
100 Hz
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D.
75 Hz
Solution
Frequency f = v/λ = 50 m/s / 2 m = 25 Hz.
Correct Answer: A — 25 Hz
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Q. A wave on a string is described by the equation y(x, t) = 0.05 sin(2π(0.1x - 5t)). What is the amplitude of the wave?
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A.
0.01 m
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B.
0.05 m
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C.
0.1 m
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D.
0.2 m
Solution
The amplitude of the wave is the coefficient in front of the sine function. Here, the amplitude is 0.05 m.
Correct Answer: B — 0.05 m
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Q. A wave traveling along a string has a frequency of 50 Hz and a wavelength of 2 m. What is the speed of the wave? (2020)
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A.
25 m/s
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B.
50 m/s
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C.
100 m/s
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D.
75 m/s
Solution
Speed (v) = frequency (f) × wavelength (λ) = 50 Hz × 2 m = 100 m/s.
Correct Answer: C — 100 m/s
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Q. A wave travels in a medium with a speed of 300 m/s and has a frequency of 75 Hz. What is the wavelength? (2021)
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A.
4 m
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B.
2 m
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C.
3 m
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D.
1 m
Solution
Wavelength λ = v/f = 300 m/s / 75 Hz = 4 m.
Correct Answer: A — 4 m
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Q. A wave travels through a medium with a speed of 500 m/s and has a wavelength of 2 m. What is its frequency? (2022)
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A.
250 Hz
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B.
500 Hz
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C.
1000 Hz
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D.
2000 Hz
Solution
Using the wave equation v = fλ, we can find frequency f = v/λ = 500 m/s / 2 m = 250 Hz.
Correct Answer: A — 250 Hz
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Q. A wave travels with a speed of 340 m/s and has a frequency of 170 Hz. What is its wavelength? (2022)
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A.
2.0 m
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B.
1.0 m
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C.
0.5 m
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D.
3.0 m
Solution
Wavelength λ = v/f = 340 m/s / 170 Hz = 2.0 m.
Correct Answer: A — 2.0 m
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Q. A wheel of radius 0.5 m is rotating with an angular speed of 10 rad/s. What is the linear speed of a point on the edge of the wheel? (2022)
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A.
5 m/s
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B.
10 m/s
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C.
15 m/s
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D.
20 m/s
Solution
Linear speed v = rω = 0.5 m * 10 rad/s = 5 m/s.
Correct Answer: B — 10 m/s
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Q. A wheel rotates with a constant angular acceleration α. If its initial angular velocity is ω₀, what is its angular velocity after time t? (2023)
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A.
ω₀ + αt
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B.
ω₀ - αt
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C.
αt²
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D.
ω₀t
Solution
Using the equation of motion for rotation, ω = ω₀ + αt.
Correct Answer: A — ω₀ + αt
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Q. An object is dropped from a height of 80 m. How long will it take to reach the ground? (Take g = 10 m/s²) (2023)
-
A.
4 s
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B.
8 s
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C.
10 s
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D.
12 s
Solution
Using the formula: h = 0.5 * g * t^2. Rearranging gives t = sqrt(2h/g) = sqrt(2*80/10) = sqrt(16) = 4 s.
Correct Answer: B — 8 s
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Q. An object moves with a constant velocity of 10 m/s. What is the net force acting on it? (2023)
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A.
0 N
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B.
10 N
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C.
20 N
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D.
100 N
Solution
If the object moves with constant velocity, the net force acting on it is 0 N.
Correct Answer: A — 0 N
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Q. Calculate 15% of 200. (2015)
Solution
15% of 200 = (15/100) × 200 = 30.
Correct Answer: A — 30
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Q. Calculate the area of a triangle with base 10 cm and height 5 cm. (2021)
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A.
25 cm²
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B.
50 cm²
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C.
15 cm²
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D.
30 cm²
Solution
Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 cm².
Correct Answer: A — 25 cm²
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Q. Calculate the coefficient of x^2 in the expansion of (x + 1/2)^8. (2021)
Solution
The coefficient of x^2 is C(8,2) * (1/2)^6 = 28 * 1/64 = 28/64 = 7/16.
Correct Answer: C — 70
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Q. Calculate the coefficient of x^4 in the expansion of (3x - 2)^6.
-
A.
540
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B.
720
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C.
810
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D.
960
Solution
The coefficient of x^4 is C(6,4) * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.
Correct Answer: A — 540
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Q. Calculate the coefficient of x^4 in the expansion of (x + 1/2)^6. (2021)
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A.
15/8
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B.
45/8
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C.
5/8
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D.
1/8
Solution
The coefficient of x^4 is C(6,4)(1/2)^2 = 15 * 1/4 = 15/4.
Correct Answer: B — 45/8
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