MHT-CET Exam Prep Resources | Soulshift Education

MHT-CET

Chemistry Mathematics Physics

Q. If the circumference of a circle is 31.4 cm, what is the radius? (2020) 2020

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.

Correct Answer: A — 5 cm

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Q. If the concentration of a reactant is increased in a system at equilibrium, what will happen according to Le Chatelier's principle?

A. The equilibrium will shift to the right.
B. The equilibrium will shift to the left.
C. The equilibrium will not change.
D. The reaction will stop.

Solution

According to Le Chatelier's principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Increasing the concentration of a reactant will shift the equilibrium to the right, favoring the formation of products.

Correct Answer: A — The equilibrium will shift to the right.

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Q. If the concentration of a reactant is tripled in a second-order reaction, how does the rate change? (2023)

A. Increases by 3 times
B. Increases by 6 times
C. Increases by 9 times
D. Increases by 12 times

Solution

For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.

Correct Answer: C — Increases by 9 times

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Q. If the concentration of Cu²⁺ in a cell is increased, what happens to the cell potential?

A. Increases
B. Decreases
C. Remains the same
D. Becomes zero

Solution

Increasing the concentration of Cu²⁺ increases the cell potential according to the Nernst equation.

Correct Answer: A — Increases

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Q. If the coordinates of a point P are (1, -1, 2), what is the x-coordinate of the point Q if it is reflected across the yz-plane? (2023)

A. 1
B. -1
C. 2
D. 0

Solution

Reflection across the yz-plane changes the sign of the x-coordinate. So, Q = (-1, -1, 2).

Correct Answer: B — -1

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Q. If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)

A. 5
B. 4
C. 3
D. 6

Solution

Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and point D are (1, 1), what is the slope of CD? (2021)

A. 1
B. 0
C. 2
D. 3

Solution

Slope = (5-1)/(5-1) = 4/4 = 1

Correct Answer: A — 1

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Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the distance CD? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Distance CD = |10 - 5| = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the length of CD? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Length CD = |10 - 5| = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)

A. y = x
B. y = 5
C. y = x + 5
D. y = x - 5

Solution

Using point-slope form: y - 5 = 1(x - 5) => y = x

Correct Answer: A — y = x

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Q. If the coordinates of point C are (5, 5) and the slope of the line is 1, what is the equation of the line? (2021) 2021

A. y = x
B. y = 5
C. y = 2x - 5
D. y = x + 5

Solution

Using point-slope form: y - 5 = 1(x - 5) => y = x.

Correct Answer: A — y = x

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Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020)

A. 5
B. 8
C. 12
D. 10

Solution

The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.

Correct Answer: B — 8

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Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020) 2020

A. 5
B. 8
C. 12
D. 10

Solution

The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.

Correct Answer: B — 8

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Q. If the cost function is C(x) = 5x^2 + 20x + 100, find the minimum cost. (2020)

A. 100
B. 120
C. 140
D. 160

Solution

The minimum cost occurs at x = -b/(2a) = -20/(2*5) = -2. C(-2) = 5(-2)^2 + 20(-2) + 100 = 120.

Correct Answer: B — 120

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Q. If the current in an AC circuit is given by I(t) = I0 cos(ωt), what is the RMS current? (2023)

A. I0/√2
B. I0
C. 2I0
D. I0/2

Solution

RMS current I_rms = I0/√2 for a cosine function.

Correct Answer: A — I0/√2

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Q. If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS current? (2021)

A. 5 A
B. 2.5 A
C. 7.07 A
D. 3.54 A

Solution

The RMS current is I_rms = I_peak / √2 = 5√2 / √2 = 5 A.

Correct Answer: B — 2.5 A

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Q. If the current through a resistor is tripled, what happens to the power dissipated in the resistor? (2022)

A. Increases by 3 times
B. Increases by 9 times
C. Remains the same
D. Decreases by 3 times

Solution

Power is proportional to the square of the current (P = I²R). If I is tripled, P increases by 3² = 9 times.

Correct Answer: B — Increases by 9 times

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Q. If the diameter of a circle is 20 cm, what is its circumference? (2022)

A. 62.83 cm
B. 31.42 cm
C. 20 cm
D. 40 cm

Solution

Circumference = πd; C = π * 20 ≈ 62.83 cm.

Correct Answer: A — 62.83 cm

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Q. If the electric field at a point is 1000 N/C and the charge at that point is 5 µC, what is the force experienced by the charge?

A. 0.005 N
B. 0.05 N
C. 0.5 N
D. 5 N

Solution

F = E * q = 1000 N/C * 5 × 10^-6 C = 0.005 N.

Correct Answer: B — 0.05 N

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Q. If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?

A. 128
B. 256
C. 512
D. 1024

Solution

The nth term of a geometric series is given by a_n = ar^(n-1). Here, a = 4, r = 2, n = 7. So, a_7 = 4 * 2^(7-1) = 4 * 64 = 256.

Correct Answer: B — 256

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Q. If the first term of an arithmetic series is 12 and the last term is 48, what is the common difference if there are 10 terms?

A. 4
B. 3
C. 5
D. 6

Solution

In an arithmetic series, the last term can be expressed as a + (n-1)d. Here, 48 = 12 + (10-1)d. Thus, 48 - 12 = 9d, giving d = 4.

Correct Answer: A — 4

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Q. If the frequency of a vibrating tuning fork is 440 Hz, what is the time period of the vibration? (2023)

A. 0.00227 s
B. 0.005 s
C. 0.01 s
D. 0.0227 s

Solution

The time period T is the reciprocal of frequency f, T = 1/f. Therefore, T = 1/440 ≈ 0.00227 s.

Correct Answer: A — 0.00227 s

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Q. If the frequency of a wave is doubled, what happens to its wavelength, assuming the speed remains constant? (2021)

A. Doubles
B. Halves
C. Remains the same
D. Quadruples

Solution

Wavelength (λ) is inversely proportional to frequency (f) when speed (v) is constant: λ = v/f. If f is doubled, λ is halved.

Correct Answer: B — Halves

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Q. If the frequency of a wave is halved, what happens to its wavelength? (2015)

A. Halves
B. Doubles
C. Remains the same
D. Increases by four times

Solution

Wavelength is inversely proportional to frequency. If frequency is halved, wavelength doubles.

Correct Answer: B — Doubles

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Q. If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)

A. Doubles
B. Halves
C. Remains the same
D. Quadruples

Solution

Xl = 2πfL; if f is doubled, Xl also doubles.

Correct Answer: B — Halves

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Q. If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.

Correct Answer: B — It halves

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Q. If the frequency of an AC source is doubled, what happens to the inductive reactance of an inductor? (2021)

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Inductive reactance Xl = ωL, so if frequency is doubled, Xl halves.

Correct Answer: B — It halves

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Q. If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.

Correct Answer: B — It halves

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Q. If the frequency of an AC source is doubled, what happens to the reactance of an inductor? (2023)

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

The reactance of an inductor is given by XL = ωL. If frequency is doubled, reactance also doubles.

Correct Answer: A — It doubles

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Q. If the gravitational force between two objects is 20 N and the distance between them is doubled, what will be the new force?

A. 5 N
B. 10 N
C. 20 N
D. 40 N

Solution

F is inversely proportional to r². If r is doubled, F becomes F/4 = 20 N / 4 = 5 N.

Correct Answer: A — 5 N

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