Engineering Entrance
Q. What is the result of (15 + 5) × 2? (2023) 2023
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Solution
(15 + 5) = 20, so 20 × 2 = 40.
Correct Answer: A — 30
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Q. What is the result of (15 ÷ 3) × 4? (2020)
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Solution
15 ÷ 3 = 5, then 5 × 4 = 20.
Correct Answer: A — 20
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Q. What is the shape of a molecule with a tetrahedral geometry? (2023)
A.
Linear
B.
Trigonal planar
C.
Tetrahedral
D.
Octahedral
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Solution
A tetrahedral geometry has a central atom bonded to four other atoms, forming a shape like a pyramid with a triangular base.
Correct Answer: C — Tetrahedral
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Q. What is the shape of the methane (CH4) molecule? (2023)
A.
Linear
B.
Trigonal planar
C.
Tetrahedral
D.
Octahedral
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Solution
Methane (CH4) has a tetrahedral shape due to the four pairs of bonding electrons around the central carbon atom.
Correct Answer: C — Tetrahedral
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Q. What is the shape of the s orbital? (2021) 2021
A.
Spherical
B.
Dumbbell
C.
Double dumbbell
D.
Linear
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Solution
The s orbital has a spherical shape.
Correct Answer: A — Spherical
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Q. What is the SI unit of electric charge? (2020)
A.
Coulomb
B.
Ampere
C.
Volt
D.
Ohm
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Solution
The SI unit of electric charge is Coulomb (C).
Correct Answer: A — Coulomb
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Q. What is the simplest ketone?
A.
Acetaldehyde
B.
Acetone
C.
Butanone
D.
Propionaldehyde
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Solution
Acetone (CH3COCH3) is the simplest ketone.
Correct Answer: B — Acetone
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Q. What is the slope of the line passing through the points (1, 2) and (3, 6)? (2020) 2020
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Solution
Slope = (6-2)/(3-1) = 4/2 = 2.
Correct Answer: A — 2
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Q. What is the slope of the line perpendicular to the line 5x + 2y = 10?
A.
-2/5
B.
5/2
C.
2/5
D.
-5/2
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Solution
The slope of the line is -5/2. The slope of the perpendicular line is the negative reciprocal, which is 2/5.
Correct Answer: A — -2/5
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Q. What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?
A.
1/2
B.
-1/2
C.
2
D.
-2
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Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer: B — -1/2
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Q. What is the slope of the line perpendicular to the line 7x - 2y = 14?
A.
1/7
B.
-1/7
C.
2/7
D.
-2/7
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Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer: B — -1/7
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Q. What is the slope of the tangent line to f(x) = x^2 + 2x at x = 1? (2023)
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Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.
Correct Answer: B — 3
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Q. What is the slope of the tangent to the curve y = x^2 + 2x at x = 1? (2023)
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Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.
Correct Answer: B — 3
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Q. What is the solution of the differential equation y' = 2y + 3?
A.
y = Ce^(2x) - 3/2
B.
y = Ce^(2x) + 3/2
C.
y = 3e^(2x)
D.
y = 2e^(x) + C
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Solution
The integrating factor is e^(-2x). Solving gives y = Ce^(2x) + 3/2.
Correct Answer: B — y = Ce^(2x) + 3/2
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Q. What is the solution of the equation dy/dx = 3x^2?
A.
y = x^3 + C
B.
y = 3x^3 + C
C.
y = x^2 + C
D.
y = 3x^2 + C
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Solution
Integrating both sides gives y = ∫3x^2 dx = x^3 + C.
Correct Answer: A — y = x^3 + C
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Q. What is the solution of the equation dy/dx = 4y + 2? (2021)
A.
y = Ce^(4x) - 1/2
B.
y = Ce^(-4x) + 1/2
C.
y = 2e^(4x) + C
D.
y = 4e^(4x) + C
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Solution
Using an integrating factor, the solution is y = Ce^(4x) - 1/2.
Correct Answer: A — y = Ce^(4x) - 1/2
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Q. What is the solution of the equation dy/dx = 6 - 2y? (2021)
A.
y = 3 - Ce^(-2x)
B.
y = 3 + Ce^(-2x)
C.
y = 2 - Ce^(2x)
D.
y = 6 - Ce^(2x)
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Solution
Rearranging gives dy/(6 - 2y) = dx. Integrating both sides leads to y = 3 - Ce^(-2x).
Correct Answer: A — y = 3 - Ce^(-2x)
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Q. What is the solution to the differential equation dy/dx = -y/x?
A.
y = Cx
B.
y = C/x
C.
y = Cx^2
D.
y = Cx^(-1)
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Solution
This is a separable equation. Separating variables and integrating gives y = C/x.
Correct Answer: B — y = C/x
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Q. What is the solution to the equation dy/dx = -5y?
A.
y = Ce^(-5x)
B.
y = -5Ce^x
C.
y = Ce^(5x)
D.
y = 5Ce^(-x)
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Solution
This is a separable differential equation. The solution is y = Ce^(-5x), where C is a constant.
Correct Answer: A — y = Ce^(-5x)
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Q. What is the solution to the equation dy/dx = y^2? (2022)
A.
y = 1/(C - x)
B.
y = C/(x - 1)
C.
y = Cx^2
D.
y = ln(Cx)
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Solution
This is a separable equation. Integrating gives y = 1/(C - x).
Correct Answer: A — y = 1/(C - x)
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Q. What is the solution to the equation y' + 2y = 0?
A.
y = Ce^(-2x)
B.
y = Ce^(2x)
C.
y = 2Ce^x
D.
y = Ce^x
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Solution
This is a separable equation. The solution is y = Ce^(-2x).
Correct Answer: A — y = Ce^(-2x)
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Q. What is the solution to the equation y' + 3y = 0?
A.
y = Ce^(-3x)
B.
y = Ce^(3x)
C.
y = 3Ce^(-x)
D.
y = Ce^(-x/3)
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Solution
This is a first-order linear differential equation. The solution is y = Ce^(-3x).
Correct Answer: A — y = Ce^(-3x)
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Q. What is the solution to the equation y' = 3y + 6?
A.
y = Ce^(3x) - 2
B.
y = Ce^(3x) + 2
C.
y = 2e^(3x)
D.
y = 3Ce^(x)
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Solution
This is a first-order linear equation. The integrating factor is e^(3x), leading to the solution y = Ce^(3x) + 2.
Correct Answer: B — y = Ce^(3x) + 2
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Q. What is the solution to the equation y'' + 4y = 0?
A.
y = C1 cos(2x) + C2 sin(2x)
B.
y = C1 e^(2x) + C2 e^(-2x)
C.
y = C1 e^(4x) + C2 e^(-4x)
D.
y = C1 sin(4x) + C2 cos(4x)
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Solution
The characteristic equation is r^2 + 4 = 0, giving complex roots. The general solution is y = C1 cos(2x) + C2 sin(2x).
Correct Answer: A — y = C1 cos(2x) + C2 sin(2x)
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Q. What is the specific heat at constant volume (Cv) for a monatomic ideal gas? (2019)
A.
3R/2
B.
5R/2
C.
R
D.
2R
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Solution
For a monatomic ideal gas, the specific heat at constant volume (Cv) is 3R/2.
Correct Answer: A — 3R/2
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Q. What is the specific heat capacity of a substance if it requires 500 J to raise the temperature of 2 kg of the substance by 5°C? (2021)
A.
20 J/kg°C
B.
50 J/kg°C
C.
100 J/kg°C
D.
200 J/kg°C
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Solution
Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 5°C) = 50 J/kg°C.
Correct Answer: B — 50 J/kg°C
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Q. What is the specific heat capacity of water at constant pressure (C_p)? (2020)
A.
4.18 J/g°C
B.
2.09 J/g°C
C.
1.00 J/g°C
D.
3.00 J/g°C
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Solution
The specific heat capacity of water at constant pressure is approximately 4.18 J/g°C.
Correct Answer: A — 4.18 J/g°C
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Q. What is the specific heat capacity of water if it takes 4200 J to raise the temperature of 1 kg of water by 1°C? (2021)
A.
2100 J/kg°C
B.
4200 J/kg°C
C.
8400 J/kg°C
D.
1000 J/kg°C
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Solution
The specific heat capacity of water is defined as the amount of heat required to raise the temperature of 1 kg of water by 1°C, which is given as 4200 J/kg°C.
Correct Answer: B — 4200 J/kg°C
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Q. What is the specific heat capacity of water? (2021) 2021
A.
1 J/g°C
B.
4.18 J/g°C
C.
2 J/g°C
D.
0.9 J/g°C
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Solution
The specific heat capacity of water is approximately 4.18 J/g°C.
Correct Answer: B — 4.18 J/g°C
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Q. What is the speed of light in vacuum? (2020)
A.
3 x 10^8 m/s
B.
3 x 10^6 m/s
C.
3 x 10^7 m/s
D.
3 x 10^9 m/s
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Solution
The speed of light in vacuum is approximately 3 x 10^8 m/s.
Correct Answer: A — 3 x 10^8 m/s
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