MHT-CET Exam Prep Resources | Soulshift Education

MHT-CET

Chemistry Mathematics Physics

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)

A. 4 m
B. 2 m
C. 3 m
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)

A. 250 Hz
B. 500 Hz
C. 1000 Hz
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 through a medium with a speed of 500 m/s and has a wavelength of 5 m. What is its frequency? (2021)

A. 100 Hz
B. 50 Hz
C. 200 Hz
D. 250 Hz

Solution

Frequency (f) = speed (v) / wavelength (λ) = 500 m/s / 5 m = 100 Hz.

Correct Answer: A — 100 Hz

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Q. A wave travels with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength? (2020)

A. 2 m
B. 1.5 m
C. 3 m
D. 0.5 m

Solution

Wavelength (λ) = Speed (v) / Frequency (f) = 300 m/s / 150 Hz = 2 m.

Correct Answer: A — 2 m

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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)

A. 2.0 m
B. 1.0 m
C. 0.5 m
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)

A. 5 m/s
B. 10 m/s
C. 15 m/s
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)

A. ω₀ + αt
B. ω₀ - αt
C. αt²
D. ω₀t

Solution

Using the equation of motion for rotation, ω = ω₀ + αt.

Correct Answer: A — ω₀ + αt

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Q. According to Faraday's law of electromagnetic induction, the induced EMF in a circuit is directly proportional to the rate of change of which of the following? (2020)

A. Magnetic field strength
B. Magnetic flux
C. Electric current
D. Resistance

Solution

Faraday's law states that the induced EMF is proportional to the rate of change of magnetic flux through the circuit.

Correct Answer: B — Magnetic flux

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Q. According to Faraday's law of electromagnetic induction, the induced EMF in a circuit is proportional to the rate of change of which of the following? (2020)

A. Magnetic field strength
B. Magnetic flux
C. Electric field strength
D. Current

Solution

Faraday's law states that the induced EMF in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.

Correct Answer: B — Magnetic flux

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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
B. 8 s
C. 10 s
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 is lifted to a height of 10 m. If the mass of the object is 5 kg, what is the gravitational potential energy gained? (g = 9.8 m/s²)

A. 49 J
B. 98 J
C. 245 J
D. 490 J

Solution

Potential Energy (PE) = mgh = 5 kg * 9.8 m/s² * 10 m = 490 J.

Correct Answer: B — 98 J

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Q. An object is lifted vertically 10 m. If the mass of the object is 5 kg, what is the gravitational potential energy gained?

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Potential Energy (PE) = mgh = 5 kg * 9.8 m/s² * 10 m = 490 J.

Correct Answer: B — 100 J

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Q. An object is lifted vertically 4 m against gravity. If the mass of the object is 3 kg, what is the work done against gravity? (g = 9.8 m/s²)

A. 117.6 J
B. 29.4 J
C. 39.2 J
D. 78.4 J

Solution

Work done (W) = mgh = 3 kg × 9.8 m/s² × 4 m = 117.6 J.

Correct Answer: A — 117.6 J

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Q. An object is lifted vertically 4 m against gravity. If the mass of the object is 10 kg, what is the work done against gravity? (g = 9.8 m/s²)

A. 39.2 J
B. 78.4 J
C. 98 J
D. 196 J

Solution

Work done (W) = mgh = 10 kg × 9.8 m/s² × 4 m = 392 J.

Correct Answer: B — 78.4 J

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Q. An object is lifted vertically 4 m. If the weight of the object is 50 N, how much work is done against gravity?

A. 100 J
B. 200 J
C. 150 J
D. 50 J

Solution

Work done (W) = Force (F) × Distance (d) = 50 N × 4 m = 200 J.

Correct Answer: B — 200 J

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Q. An object is moving with a speed of 15 m/s and has a mass of 3 kg. What is its kinetic energy?

A. 67.5 J
B. 45 J
C. 90 J
D. 135 J

Solution

Kinetic Energy (KE) = 0.5 × m × v² = 0.5 × 3 kg × (15 m/s)² = 0.5 × 3 × 225 = 337.5 J.

Correct Answer: C — 90 J

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Q. An object is thrown vertically upwards with a velocity of 20 m/s. How high will it rise? (Assume g = 10 m/s²) (2020)

A. 20 m
B. 30 m
C. 40 m
D. 50 m

Solution

Using h = v²/(2g) = (20 m/s)² / (2 × 10 m/s²) = 20 m.

Correct Answer: A — 20 m

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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)

A. 0 N
B. 10 N
C. 20 N
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. An object moves with a uniform acceleration of 2 m/s². If it starts from rest, what will be its velocity after 5 seconds?

A. 5 m/s
B. 10 m/s
C. 15 m/s
D. 20 m/s

Solution

Using the formula: v = u + at, where u = 0, a = 2 m/s², t = 5 s. v = 0 + 2 * 5 = 10 m/s.

Correct Answer: B — 10 m/s

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Q. An object moves with a uniform speed of 10 m/s. How far will it travel in 15 seconds?

A. 100 m
B. 150 m
C. 200 m
D. 250 m

Solution

Distance = speed * time = 10 m/s * 15 s = 150 m.

Correct Answer: B — 150 m

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Q. An object moves with a uniform speed of 20 m/s. How far will it travel in 15 seconds?

A. 200 m
B. 300 m
C. 400 m
D. 500 m

Solution

Distance = speed * time = 20 m/s * 15 s = 300 m.

Correct Answer: C — 400 m

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Q. At what point does the function f(x) = x^3 - 3x^2 + 4 have a local minimum? (2020)

A. (1, 2)
B. (2, 1)
C. (0, 4)
D. (3, 0)

Solution

To find local minima, we find f'(x) = 3x^2 - 6x. Setting f'(x) = 0 gives x = 0 and x = 2. Checking the second derivative, f''(2) = 6 > 0, so (2, 1) is a local minimum.

Correct Answer: A — (1, 2)

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Q. At which point does the function f(x) = -x^3 + 3x^2 + 4 have a local maximum? (2023)

A. (0, 4)
B. (1, 6)
C. (2, 5)
D. (3, 4)

Solution

Setting f'(x) = -3x^2 + 6x = 0 gives x = 0 and x = 2. f''(2) < 0 indicates a local maximum at (2, 5).

Correct Answer: B — (1, 6)

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Q. Calculate 15% of 200. (2015)

A. 30
B. 25
C. 20
D. 15

Solution

15% of 200 = (15/100) × 200 = 30.

Correct Answer: A — 30

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Q. Calculate 18 - (3 × 4). (2015)

A. 6
B. 12
C. 10
D. 8

Solution

3 × 4 = 12, then 18 - 12 = 6.

Correct Answer: B — 12

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Q. Calculate the area of a triangle with base 10 cm and height 5 cm. (2021)

A. 25 cm²
B. 50 cm²
C. 15 cm²
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 (2x + 3)^4.

A. 36
B. 48
C. 54
D. 64

Solution

The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.

Correct Answer: B — 48

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Q. Calculate the coefficient of x^2 in the expansion of (x + 1/2)^6.

A. 15/4
B. 45/8
C. 15/8
D. 5/4

Solution

The coefficient of x^2 is C(6,2) * (1/2)^2 = 15 * 1/4 = 15/4.

Correct Answer: B — 45/8

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Q. Calculate the coefficient of x^2 in the expansion of (x + 1/2)^8. (2021)

A. 28
B. 56
C. 70
D. 84

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^2 in the expansion of (x + 1/x)^6. (2019)

A. 15
B. 30
C. 20
D. 10

Solution

The coefficient of x^2 is given by 6C2 * (1)^4 = 15.

Correct Answer: A — 15

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