Engineering & Architecture Admissions

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Q. What is the SI unit of thermal conductivity?

A. W/m·K
B. J/kg·K
C. K/W
D. J/m·s

Solution

The SI unit of thermal conductivity is Watts per meter per Kelvin (W/m·K).

Correct Answer: A — W/m·K

Q. What is the SI unit of viscosity?

A. Pascal-second
B. Newton-second
C. Kilogram-meter per second
D. Joule-second

Solution

The SI unit of viscosity is Pascal-second (Pa·s), which is equivalent to Newton-second per square meter.

Correct Answer: A — Pascal-second

Q. What is the significance of the BET theory in surface chemistry?

A. Describes physisorption
B. Describes chemisorption
C. Determines surface area of solids
D. Calculates adsorption energy

Solution

The BET theory is significant for determining the surface area of solids based on multilayer adsorption.

Correct Answer: C — Determines surface area of solids

Q. What is the significance of the Gibbs Free Energy in chemical thermodynamics?

A. It predicts the direction of a reaction.
B. It measures the heat of reaction.
C. It indicates the concentration of reactants.
D. It determines the rate of reaction.

Solution

Gibbs Free Energy is crucial for predicting the spontaneity and direction of a chemical reaction.

Correct Answer: A — It predicts the direction of a reaction.

Q. What is the significance of the photoelectric effect in modern physics?

A. It explains the wave nature of light
B. It supports the theory of relativity
C. It led to the development of quantum mechanics
D. It has no significance

Solution

The photoelectric effect was crucial in the development of quantum mechanics, as it provided evidence for the quantization of energy.

Correct Answer: C — It led to the development of quantum mechanics

Q. What is the simplest form of carbohydrate?

A. Disaccharide
B. Monosaccharide
C. Polysaccharide
D. Oligosaccharide

Solution

The simplest form of carbohydrate is a monosaccharide, which cannot be hydrolyzed into simpler sugars.

Correct Answer: B — Monosaccharide

Q. What is the slope of the line perpendicular to the line y = -2x + 3?

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

Solution

The slope of the given line is -2. The slope of the perpendicular line is the negative reciprocal, which is 1/2.

Correct Answer: B — 1/2

Q. What is the slope of the line perpendicular to the line y = -2x + 4?

A. 0.5
B. 2
C. -0.5
D. -2

Solution

The slope of the given line is -2. The slope of the perpendicular line is the negative reciprocal, which is 1/2.

Correct Answer: B — 2

Q. What is the slope of the line perpendicular to the line y = -3x + 4?

A. 1/3
B. -1/3
C. 3
D. -3

Solution

The slope of the given line is -3. The slope of the perpendicular line is the negative reciprocal: 1/3.

Correct Answer: C — 3

Q. What is the slope of the line represented by the equation 2x - 3y + 6 = 0?

A. 2/3
B. 3/2
C. -2/3
D. -3/2

Solution

Rearranging gives y = (2/3)x + 2, slope = 2/3.

Correct Answer: C — -2/3

Q. What is the slope of the line represented by the equation 3x - 4y + 12 = 0?

A. 3/4
B. 4/3
C. -3/4
D. -4/3

Solution

Rearranging gives y = (3/4)x + 3. Slope = 3/4.

Correct Answer: C — -3/4

Q. What is the slope of the line represented by the equation 5y - 10x = 20?

A. 2
B. 1
C. 0.5
D. 5

Solution

Rearranging to slope-intercept form: 5y = 10x + 20 => y = 2x + 4. The slope is 2.

Correct Answer: C — 0.5

Q. What is the slope of the lines represented by the equation 5x^2 - 10xy + 5y^2 = 0?

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

Solution

The equation can be factored to find the slopes, which are both 1.

Correct Answer: A — 1

Q. What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?

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

Solution

Factoring gives (x - 3y)^2 = 0, indicating a double root, hence the slope is 3.

Correct Answer: A — 3

Q. What is the solution for the inequality 4 - x < 2?

A. x > 2
B. x < 2
C. x > 4
D. x < 4

Solution

4 - x < 2 => -x < -2 => x > 2.

Correct Answer: D — x < 4

Q. What is the solution for the inequality 4x + 1 < 3x + 5?

A. x < 4
B. x > 4
C. x < 3
D. x > 3

Solution

4x + 1 < 3x + 5 => x < 4.

Correct Answer: A — x < 4

Q. What is the solution for the inequality 4x - 1 < 3x + 2?

A. x < 3
B. x > 3
C. x < 1
D. x > 1

Solution

4x - 1 < 3x + 2 => x < 3.

Correct Answer: A — x < 3

Q. What is the solution for the inequality 6 - 2x ≥ 0?

A. x ≤ 3
B. x > 3
C. x < 3
D. x ≥ 3

Solution

6 - 2x ≥ 0 => -2x ≥ -6 => x ≤ 3.

Correct Answer: A — x ≤ 3

Q. What is the solution for the inequality 7 - 4x < 3?

A. x > 1
B. x < 1
C. x > -1
D. x < -1

Solution

7 - 4x < 3 => -4x < -4 => x > 1.

Correct Answer: B — x < 1

Q. What is the solution for the inequality 7x + 2 ≤ 5x + 10?

A. x ≤ 4
B. x ≥ 4
C. x ≤ 3
D. x ≥ 3

Solution

7x + 2 ≤ 5x + 10 => 2x ≤ 8 => x ≤ 4.

Correct Answer: A — x ≤ 4

Q. What is the solution for the inequality 7x + 3 < 24?

A. x < 3
B. x > 3
C. x < 4
D. x > 4

Solution

7x + 3 < 24 => 7x < 21 => x < 3.

Correct Answer: C — x < 4

Q. What is the solution for the inequality 8 - 3x > 2?

A. x < 2
B. x > 2
C. x < 3
D. x > 3

Solution

8 - 3x > 2 => -3x > -6 => x < 2.

Correct Answer: C — x < 3

Q. What is the solution of the differential equation dy/dx = (x^2 + 1)y?

A. y = Ce^(x^3/3 + x)
B. y = Ce^(x^2 + 1)
C. y = Ce^(x^2/2)
D. y = Ce^(x^3)

Solution

This is a separable equation. Integrating gives y = Ce^(x^3/3 + x).

Correct Answer: A — y = Ce^(x^3/3 + x)

Q. What is the solution set for the inequality -x + 6 > 0?

A. x < 6
B. x > 6
C. x < 0
D. x > 0

Solution

-x + 6 > 0 => -x > -6 => x < 6.

Correct Answer: A — x < 6

Q. What is the solution set for the inequality 4x + 1 < 9?

A. x < 2
B. x > 2
C. x < 1
D. x > 1

Solution

4x + 1 < 9 => 4x < 8 => x < 2.

Correct Answer: A — x < 2

Q. What is the solution set for the inequality 4x - 1 < 3x + 2?

A. x < 3
B. x > 3
C. x < 1
D. x > 1

Solution

4x - 1 < 3x + 2 => x < 3.

Correct Answer: A — x < 3

Q. What is the solution set for the inequality 5 - 2x < 1?

A. x > 2
B. x < 2
C. x > 3
D. x < 3

Solution

5 - 2x < 1 => -2x < -4 => x > 2.

Correct Answer: A — x > 2

Q. What is the solution set for the inequality 7 - 4x ≤ 3?

A. x ≥ 1
B. x ≤ 1
C. x ≥ -1
D. x ≤ -1

Solution

7 - 4x ≤ 3 => -4x ≤ -4 => x ≥ 1.

Correct Answer: B — x ≤ 1

Q. What is the solution set for the inequality 7x - 5 > 2?

A. x > 1
B. x < 1
C. x > 2
D. x < 2

Solution

7x - 5 > 2 => 7x > 7 => x > 1.

Correct Answer: A — x > 1

Q. What is the solution to the compound inequality 1 < 2x + 3 < 7?

A. -1 < x < 2
B. 0 < x < 2
C. 1 < x < 2
D. 1 < x < 3

Solution

1 < 2x + 3 < 7 => -2 < 2x < 4 => -1 < x < 2.

Correct Answer: A — -1 < x < 2

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