Engineering Entrance Exam Preparation Resources

Engineering Entrance

MHT-CET

Q. What is the integrating factor for the equation dy/dx + (1/x)y = 2?

A. x
B. e^(ln(x))
C. e^(ln(x^2))
D. 1/x

Solution

The integrating factor is e^(∫(1/x)dx) = e^(ln(x)) = x.

Correct Answer: C — e^(ln(x^2))

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Q. What is the integrating factor for the equation dy/dx + 2y = 3?

A. e^(2x)
B. e^(-2x)
C. e^(3x)
D. e^(-3x)

Solution

The integrating factor is e^(∫2dx) = e^(2x).

Correct Answer: A — e^(2x)

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Q. What is the integrating factor for the equation dy/dx + 2y = 6?

A. e^(2x)
B. e^(-2x)
C. e^(6x)
D. e^(-6x)

Solution

The integrating factor is e^(∫2dx) = e^(2x).

Correct Answer: A — e^(2x)

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Q. What is the IUPAC name of CH3CH2Cl?

A. Chloroethane
B. Ethyl chloride
C. Ethane chloride
D. Chloromethane

Solution

The IUPAC name of CH3CH2Cl is Chloroethane, as it is a two-carbon alkane with a chlorine substituent.

Correct Answer: A — Chloroethane

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Q. What is the IUPAC name of CH3CH2OH? (2021) 2021

A. Ethanol
B. Methanol
C. Propanol
D. Butanol

Solution

The compound CH3CH2OH is an alcohol with two carbon atoms, which is named Ethanol.

Correct Answer: A — Ethanol

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Q. What is the IUPAC name of CH3CHO? (2023) 2023

A. Acetaldehyde
B. Ethanal
C. Ethyl aldehyde
D. Methyl ketone

Solution

The IUPAC name of CH3CHO is ethanal, which is the simplest aldehyde.

Correct Answer: B — Ethanal

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Q. What is the IUPAC name of the compound CH3CH2NH2? (2021)

A. Ethylamine
B. Dimethylamine
C. Propylamine
D. Methylamine

Solution

The IUPAC name of CH3CH2NH2 is Ethylamine, as it consists of an ethyl group attached to an amine.

Correct Answer: A — Ethylamine

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Q. What is the IUPAC name of the compound CH3COOH? (2020)

A. Methanoic acid
B. Ethanoic acid
C. Propanoic acid
D. Butanoic acid

Solution

The IUPAC name of CH3COOH is Ethanoic acid, which is commonly known as acetic acid.

Correct Answer: B — Ethanoic acid

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Q. What is the kinetic energy of a 3 kg object moving at a speed of 4 m/s? (2022)

A. 24 J
B. 12 J
C. 6 J
D. 48 J

Solution

Kinetic Energy (KE) = 0.5 × m × v² = 0.5 × 3 kg × (4 m/s)² = 24 J.

Correct Answer: B — 12 J

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Q. What is the kinetic energy of a 4 kg object moving at a speed of 3 m/s? (2015)

A. 18 J
B. 12 J
C. 24 J
D. 36 J

Solution

Kinetic Energy (KE) = 0.5 × mass × velocity² = 0.5 × 4 kg × (3 m/s)² = 18 J.

Correct Answer: B — 12 J

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Q. What is the Ksp expression for the salt AgCl? (2023)

A. [Ag+][Cl-]
B. [AgCl]
C. [Ag+][Cl-]^2
D. [AgCl]^2

Solution

The solubility product constant (Ksp) for AgCl is expressed as Ksp = [Ag+][Cl-], where [Ag+] and [Cl-] are the molar concentrations of the ions in a saturated solution.

Correct Answer: A — [Ag+][Cl-]

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Q. What is the Ksp of AgCl if the solubility of AgCl in water is 1.33 x 10^-5 M? (2023)

A. 1.78 x 10^-10
B. 1.33 x 10^-5
C. 1.33 x 10^-10
D. 1.78 x 10^-5

Solution

Ksp = [Ag+][Cl-] = (1.33 x 10^-5)(1.33 x 10^-5) = 1.78 x 10^-10.

Correct Answer: A — 1.78 x 10^-10

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Q. What is the latent heat of fusion if 2000 J of energy is required to melt 0.5 kg of ice? (2021)

A. 2000 J/kg
B. 4000 J/kg
C. 1000 J/kg
D. 500 J/kg

Solution

Latent heat of fusion (L) = Q / m = 2000 J / 0.5 kg = 4000 J/kg.

Correct Answer: A — 2000 J/kg

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Q. What is the latent heat of fusion if 2000 J of heat is required to melt 500 g of ice? (2022)

A. 2000 J/kg
B. 4000 J/kg
C. 1000 J/kg
D. 3000 J/kg

Solution

Latent heat of fusion (L) = Q/m = 2000 J / 0.5 kg = 4000 J/kg.

Correct Answer: A — 2000 J/kg

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Q. What is the latent heat of fusion of ice if 80 calories are required to melt 20 grams of ice? (2020)

A. 40 cal/g
B. 60 cal/g
C. 80 cal/g
D. 100 cal/g

Solution

Latent heat of fusion (L_f) = Q / m = 80 cal / 20 g = 4 cal/g.

Correct Answer: C — 80 cal/g

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Q. What is the latent heat of fusion of ice if 80 g of ice at 0°C melts to water at 0°C, absorbing 3360 J of heat? (2022)

A. 40 J/g
B. 60 J/g
C. 80 J/g
D. 100 J/g

Solution

Latent heat of fusion (L) = Q/m = 3360 J / 80 g = 42 J/g.

Correct Answer: C — 80 J/g

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Q. What is the latent heat of vaporization if 500 g of water at 100°C is converted to steam at the same temperature, absorbing 2260 kJ of heat? (2023)

A. 2260 J/g
B. 450 J/g
C. 334 J/g
D. 1000 J/g

Solution

Latent heat of vaporization (L) = Q / m = 2260 kJ / 500 g = 4.52 kJ/g = 2260 J/g.

Correct Answer: A — 2260 J/g

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Q. What is the latent heat of vaporization of water if 540 J of energy is required to convert 100 g of water at 100°C to steam? (2021)

A. 540 J/g
B. 54 J/g
C. 5.4 J/g
D. 0.54 J/g

Solution

Latent heat of vaporization (L) = Q/m = 540 J / 100 g = 5.4 J/g.

Correct Answer: A — 540 J/g

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Q. What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)

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

Solution

Using Pythagoras: (radius)² = (distance from center)² + (half chord)²; 10² = 6² + (half chord)²; half chord = 8 cm, so full chord = 16 cm.

Correct Answer: A — 8 cm

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Q. What is the length of a chord that is 6 cm from the center of a circle with a radius of 10 cm? (2019)

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

Solution

Using Pythagoras: chord length = 2√(r² - d²) = 2√(10² - 6²) = 2√(100 - 36) = 2√64 = 16 cm.

Correct Answer: A — 8 cm

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Q. What is the length of a diameter of a circle with a radius of 7 cm? (2022)

A. 14 cm
B. 21 cm
C. 7 cm
D. 28 cm

Solution

Diameter = 2 × radius; Diameter = 2 × 7 cm = 14 cm.

Correct Answer: A — 14 cm

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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021

A. 10.47 cm
B. 15.71 cm
C. 20.94 cm
D. 25.13 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.

Correct Answer: A — 10.47 cm

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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (Use π = 3.14) (2023)

A. 10.47 cm
B. 15.71 cm
C. 20.94 cm
D. 25.13 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.

Correct Answer: A — 10.47 cm

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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021)

A. 10.47 cm
B. 12.57 cm
C. 15.71 cm
D. 20.94 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.

Correct Answer: B — 12.57 cm

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Q. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)

A. 2π cm
B. 4π cm
C. π cm
D. 8 cm

Solution

Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.

Correct Answer: A — 2π cm

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Q. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)

A. 5.24 cm
B. 3.14 cm
C. 5.00 cm
D. 10.47 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.

Correct Answer: A — 5.24 cm

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Q. What is the length of an arc of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14) (2020)

A. 6.28 cm
B. 3.14 cm
C. 12.56 cm
D. 9.42 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 6 cm = 6.28 cm.

Correct Answer: A — 6.28 cm

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Q. What is the length of an arc of a circle with radius 5 cm and angle 60 degrees? (2020)

A. 5.24 cm
B. 3.14 cm
C. 5.00 cm
D. 6.00 cm

Solution

Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.

Correct Answer: A — 5.24 cm

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Q. What is the length of the diagonal of a cuboid with dimensions 2, 3, and 6? (2022)

A. √49
B. √45
C. √36
D. √50

Solution

Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.

Correct Answer: A — √49

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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3), (4, 0), and (4, 3)? (2022)

A. 5
B. 6
C. 7
D. 8

Solution

Diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.

Correct Answer: A — 5

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Engineering Entrance

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