Engineering Entrance
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 the sound wave?
-
A.
0.00227 s
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B.
0.005 s
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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)
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A.
0.00227 s
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B.
0.0045 s
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C.
0.01 s
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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 when it reaches the vertical position? (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 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 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 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?
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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.
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
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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 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)
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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 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.
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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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Q. Calculate the coefficient of x^4 in the expansion of (x + 3)^6. (2021)
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A.
54
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B.
81
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C.
108
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D.
729
Solution
The coefficient of x^4 is C(6,4)(3)^2 = 15 * 9 = 135.
Correct Answer: C — 108
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Q. Calculate the derivative of f(x) = 5x^5. (2016)
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A.
25x^4
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B.
5x^4
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C.
20x^4
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D.
10x^4
Solution
The derivative f'(x) = d/dx(5x^5) = 25x^4.
Correct Answer: A — 25x^4
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Q. Calculate the derivative of f(x) = ln(x^2 + 1).
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A.
2x/(x^2 + 1)
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B.
1/(x^2 + 1)
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C.
2/(x^2 + 1)
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D.
x/(x^2 + 1)
Solution
Using the chain rule, f'(x) = d/dx(ln(x^2 + 1)) = (2x)/(x^2 + 1).
Correct Answer: A — 2x/(x^2 + 1)
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Q. Calculate the derivative of f(x) = x^2 * e^x. (2023) 2023
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A.
e^x(2x + 1)
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B.
e^x(2x - 1)
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C.
2xe^x
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D.
x^2e^x
Solution
Using the product rule, f'(x) = d/dx(x^2 * e^x) = e^x(2x + 1).
Correct Answer: A — e^x(2x + 1)
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Q. Calculate the determinant of D = [[2, 3, 1], [1, 0, 2], [4, 1, 0]]. (2020)
Solution
Det(D) = 2(0*0 - 2*1) - 3(1*0 - 2*4) + 1(1*1 - 0*4) = 2(0 - 2) - 3(0 - 8) + 1(1) = -4 + 24 + 1 = 21.
Correct Answer: A — -10
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Q. Calculate the determinant of D = [[3, 2, 1], [1, 0, 2], [0, 1, 3]]. (2023)
Solution
Det(D) = 3(0*3 - 2*1) - 2(1*3 - 0*2) + 1(1*1 - 0*0) = 3(0 - 2) - 2(3) + 1(1) = -6 - 6 + 1 = -11.
Correct Answer: A — 1
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Q. Calculate the determinant of D = [[4, 2], [1, 3]]. (2020)
Solution
Determinant of D = (4*3) - (2*1) = 12 - 2 = 10.
Correct Answer: A — 10
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