MHT-CET Exam Prep Resources | Soulshift Education

MHT-CET

Chemistry Mathematics Physics

Q. What is the bond angle in a methane (CH4) molecule? (2023) 2023

A. 90 degrees
B. 109.5 degrees
C. 120 degrees
D. 180 degrees

Solution

The bond angle in methane (CH4) is approximately 109.5 degrees due to its tetrahedral geometry.

Correct Answer: B — 109.5 degrees

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Q. What is the capacitance of a capacitor that stores 10 µC of charge at a potential difference of 5 V?

A. 2 µF
B. 5 µF
C. 10 µF
D. 20 µF

Solution

C = Q/V = 10 × 10^-6 C / 5 V = 2 × 10^-6 F = 2 µF.

Correct Answer: A — 2 µF

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Q. What is the capacitive reactance of a capacitor of 10μF at a frequency of 60 Hz? (2016)

A. 265.26Ω
B. 159.15Ω
C. 100Ω
D. 50Ω

Solution

Capacitive reactance Xc = 1 / (2πfC) = 1 / (2π * 60 * 10e-6) = 265.26Ω.

Correct Answer: A — 265.26Ω

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Q. What is the capacitive reactance of a capacitor with a capacitance of 10μF at a frequency of 50Hz? (2020)

A. 318.31 ohms
B. 159.15 ohms
C. 31.83 ohms
D. 15.92 ohms

Solution

Xc = 1 / (2πfC) = 1 / (2π × 50 × 10 × 10^-6) = 318.31 ohms.

Correct Answer: A — 318.31 ohms

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Q. What is the cell potential of a Daniell cell at standard conditions?

A. 1.10 V
B. 1.96 V
C. 0.76 V
D. 0.34 V

Solution

The standard cell potential of a Daniell cell is 1.10 V.

Correct Answer: A — 1.10 V

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Q. What is the cell potential of a galvanic cell with E° = 1.5 V and Q = 10?

A. 1.2 V
B. 1.0 V
C. 1.3 V
D. 1.4 V

Solution

Using the Nernst equation, E = E° - (RT/nF)lnQ, we find E ≈ 1.0 V.

Correct Answer: B — 1.0 V

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Q. What is the change in entropy when 1 kg of water at 100°C is converted to steam at 100°C? (Latent heat of vaporization = 2260 kJ/kg) (2021)

A. 2260 J/K
B. 2260 kJ/K
C. 0 J/K
D. 1130 J/K

Solution

ΔS = Q/T = 2260 kJ / 373 K = 6.06 kJ/K.

Correct Answer: A — 2260 J/K

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Q. What is the change in internal energy (ΔU) for an ideal gas that expands isothermally? (2022)

A. 0
B. nRT
C. nRΔT
D. PV

Solution

For an isothermal process, the change in internal energy ΔU = 0 for an ideal gas.

Correct Answer: A — 0

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Q. What is the change in internal energy for an ideal gas that expands isothermally? (2019)

A. nRT
B. 0
C. -nRT
D. nR(Tf - Ti)

Solution

For an isothermal process, the change in internal energy (ΔU) for an ideal gas is zero, as ΔU depends only on temperature.

Correct Answer: B — 0

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Q. What is the change in internal energy of 1 mole of an ideal gas when it is heated at constant volume from 300 K to 600 K?

A. 0 J
B. 300 J
C. 600 J
D. 900 J

Solution

ΔU = nCvΔT. For a monatomic gas, Cv = (3/2)R. ΔU = 1 * (3/2)(8.31 J/mol K)(600 - 300) = 900 J.

Correct Answer: D — 900 J

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Q. What is the change in internal energy of a gas that absorbs 300 J of heat and does 100 J of work on the surroundings? (2020)

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

Solution

Change in internal energy (ΔU) = Q - W = 300 J - 100 J = 200 J.

Correct Answer: A — 200 J

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Q. What is the change in internal energy of a system if 200 J of heat is added and 50 J of work is done by the system?

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

Solution

Using the first law of thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.

Correct Answer: A — 150 J

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Q. What is the change in internal energy of a system if 300 J of heat is added and 100 J of work is done by the system? (2021)

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

Solution

Using the first law of thermodynamics: ΔU = Q - W = 300 J - 100 J = 200 J.

Correct Answer: A — 200 J

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Q. What is the change in internal energy of an ideal gas when it expands isothermally? (2021)

A. Zero
B. Positive
C. Negative
D. Depends on the gas

Solution

In an isothermal process for an ideal gas, the internal energy remains constant, hence the change in internal energy is zero.

Correct Answer: A — Zero

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Q. What is the change in internal energy of an ideal gas when it is heated at constant volume? (2021) 2021

A. Zero
B. Equal to heat added
C. Equal to work done
D. Equal to pressure times volume

Solution

At constant volume, the change in internal energy (ΔU) is equal to the heat added (Q). Therefore, ΔU = Q.

Correct Answer: B — Equal to heat added

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Q. What is the chemical formula for sodium chloride? (2023) 2023

A. NaCl
B. Na2Cl
C. NaCl2
D. Na2Cl2

Solution

The chemical formula for sodium chloride is NaCl.

Correct Answer: A — NaCl

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Q. What is the chemical formula for table salt? (2019)

A. NaCl
B. KCl
C. CaCl2
D. MgCl2

Solution

Table salt is chemically known as sodium chloride, which has the formula NaCl.

Correct Answer: A — NaCl

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Q. What is the coefficient of x^0 in the expansion of (2x - 3)^5? (2022)

A. -243
B. 243
C. -81
D. 81

Solution

The constant term is C(5,5)(-3)^5 = -243.

Correct Answer: A — -243

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Q. What is the coefficient of x^0 in the expansion of (3x + 2)^5? (2022)

A. 32
B. 48
C. 64
D. 80

Solution

The coefficient of x^0 is C(5,5) * (3x)^0 * (2)^5 = 1 * 32 = 32.

Correct Answer: C — 64

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Q. What is the coefficient of x^0 in the expansion of (x + 1/x)^8? (2021)

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

Solution

The coefficient of x^0 occurs when k=4, which gives us 8C4 = 70.

Correct Answer: C — 70

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Q. What is the coefficient of x^1 in the expansion of (x + 1)^10? (2021)

A. 10
B. 90
C. 100
D. 1

Solution

The coefficient of x^1 is C(10,1)(1)^9 = 10.

Correct Answer: A — 10

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Q. What is the coefficient of x^1 in the expansion of (x + 5)^6?

A. 30
B. 60
C. 90
D. 120

Solution

The coefficient of x^1 is C(6,1) * 5^5 = 6 * 3125 = 18750.

Correct Answer: C — 90

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Q. What is the coefficient of x^1 in the expansion of (x - 1)^5?

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

Solution

The coefficient of x^1 is given by 5C1 * (-1)^4 = 5 * 1 = 5.

Correct Answer: A — -5

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Q. What is the coefficient of x^2 in the expansion of (2x + 1)^6?

A. 15
B. 30
C. 45
D. 60

Solution

The coefficient of x^2 is C(6,2) * (2)^2 * (1)^4 = 15 * 4 = 60.

Correct Answer: B — 30

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Q. What is the coefficient of x^2 in the expansion of (2x - 1)^5? (2021)

A. 10
B. 20
C. 30
D. 40

Solution

The coefficient of x^2 is C(5,2) * (2)^2 * (-1)^3 = 10 * 4 * (-1) = -40.

Correct Answer: B — 20

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Q. What is the coefficient of x^2 in the expansion of (3x - 4)^6?

A. 540
B. 720
C. 1080
D. 1440

Solution

The coefficient of x^2 is C(6,2) * (3)^2 * (-4)^(6-2) = 15 * 9 * 256 = 34560.

Correct Answer: C — 1080

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Q. What is the coefficient of x^2 in the expansion of (x + 1/2)^8?

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

Solution

The coefficient of x^2 is C(8,2) * (1/2)^2 = 28 * 1/4 = 7.

Correct Answer: C — 70

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Q. What is the coefficient of x^2 in the expansion of (x + 3)^5?

A. 45
B. 60
C. 75
D. 90

Solution

The coefficient of x^2 is given by 5C2 * (3)^3 = 10 * 27 = 270.

Correct Answer: A — 45

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Q. What is the coefficient of x^2 in the expansion of (x + 4)^5?

A. 80
B. 100
C. 120
D. 160

Solution

The coefficient of x^2 is C(5,2) * 4^3 = 10 * 64 = 640.

Correct Answer: A — 80

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Q. What is the coefficient of x^2 in the expansion of (x + 5)^4?

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

Solution

The coefficient of x^2 is C(4,2) * (5)^2 = 6 * 25 = 150.

Correct Answer: B — 100

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