Engineering Entrance
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
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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 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
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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
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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
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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
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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 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
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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
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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
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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 reactance of a capacitor? (2023)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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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 inductance of a coil is 0.5H and the frequency is 60Hz, what is the inductive reactance? (2023)
A.
31.42 ohms
B.
18.85 ohms
C.
37.70 ohms
D.
25.13 ohms
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Solution
Xl = 2πfL = 2π × 60 × 0.5 = 31.42 ohms.
Correct Answer: A — 31.42 ohms
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Q. If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)
A.
10Ω
B.
30Ω
C.
33.33Ω
D.
40Ω
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Solution
Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.
Correct Answer: C — 33.33Ω
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Q. If the latent heat of fusion of ice is 334 J/g, how much heat is required to melt 50 g of ice? (2019)
A.
1670 J
B.
3340 J
C.
5000 J
D.
1000 J
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Solution
Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.
Correct Answer: A — 1670 J
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Q. If the line 2x + 3y = 6 intersects the x-axis, what is the x-coordinate of the intersection point?
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Solution
Setting y = 0 gives 2x = 6, thus x = 3. The x-coordinate of the intersection point is 3.
Correct Answer: B — 2
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Q. If the line 3x - 4y + 12 = 0 is parallel to another line, what is the slope of the parallel line?
A.
3/4
B.
-3/4
C.
4/3
D.
-4/3
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Solution
Rearranging gives y = (3/4)x + 3. The slope of the line is 3/4, so the slope of the parallel line is -3/4.
Correct Answer: B — -3/4
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Q. If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?
A.
6x - 8y + 24 = 0
B.
3x + 4y - 12 = 0
C.
x + 2y - 5 = 0
D.
2x - 3y + 6 = 0
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Solution
Parallel lines have the same slope. The slope of the given line is 3/4, which is the same as the slope of 6x - 8y + 24 = 0.
Correct Answer: A — 6x - 8y + 24 = 0
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Q. If the magnetic field strength is doubled, what happens to the force experienced by a current-carrying conductor? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The force experienced by a current-carrying conductor in a magnetic field is directly proportional to the magnetic field strength. Therefore, if the magnetic field strength is doubled, the force also doubles.
Correct Answer: A — It doubles
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Q. If the magnetic field strength is doubled, what happens to the force on a current-carrying conductor? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The force on a current-carrying conductor is directly proportional to the magnetic field strength, so if the magnetic field strength is doubled, the force also doubles.
Correct Answer: A — It doubles
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Q. If the perimeter of a square is 40 cm, what is the length of one side? (2018)
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Perimeter = 4 × side, so side = 40/4 = 10 cm.
Correct Answer: A — 10 cm
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Q. If the pH of a solution is 3, what is the concentration of H+ ions? (2023)
A.
0.001 M
B.
0.01 M
C.
0.1 M
D.
0.0001 M
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Solution
pH = 3 means [H+] = 10^-3 M = 0.001 M.
Correct Answer: B — 0.01 M
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Q. If the pKa of acetic acid is 4.76, what is the pH of a 0.1 M solution?
A.
4.76
B.
5.76
C.
6.76
D.
3.76
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Solution
For a weak acid, pH ≈ pKa for a 0.1 M solution, so pH ≈ 4.76.
Correct Answer: A — 4.76
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Q. If the radius of a circle is 7 cm, what is its circumference? (Use π = 22/7) (2014)
A.
44 cm
B.
22 cm
C.
14 cm
D.
28 cm
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Solution
Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.
Correct Answer: A — 44 cm
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Q. If the radius of a circle is doubled, how does the area change? (2021)
A.
It doubles
B.
It triples
C.
It quadruples
D.
It remains the same
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Solution
Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Correct Answer: C — It quadruples
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Q. If the radius of a circle is halved, how does the circumference change? (2021)
A.
Halved
B.
Remains the same
C.
Doubled
D.
Tripled
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Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer: A — Halved
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Q. If the radius of a circle is halved, how does the circumference change? (2022) 2022
A.
Halved
B.
Remains the same
C.
Doubled
D.
Quadrupled
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Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer: A — Halved
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Q. If the radius of a circle is tripled, by what factor does the area increase? (2021)
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Solution
Area increases by a factor of (3r)²/r² = 9.
Correct Answer: C — 9
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Q. If the rate of a reaction doubles when the temperature increases by 10°C, what is the approximate activation energy? (2020)
A.
20 kJ/mol
B.
40 kJ/mol
C.
60 kJ/mol
D.
80 kJ/mol
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Solution
Using the Arrhenius equation, if the rate doubles for a 10°C increase, Ea is approximately 40 kJ/mol.
Correct Answer: B — 40 kJ/mol
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Q. If the rate of a reaction is directly proportional to the concentration of one reactant raised to the power of 3, what is the order of the reaction? (2023)
A.
Zero
B.
First
C.
Second
D.
Third
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Solution
The order of the reaction is third because the rate is proportional to the concentration raised to the power of 3.
Correct Answer: D — Third
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Q. If the rate of a reaction is given by rate = k[A]², what is the order of the reaction? (2021)
A.
Zero
B.
First
C.
Second
D.
Third
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Solution
The reaction is second-order because the rate depends on the square of the concentration of A.
Correct Answer: C — Second
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Q. If the resistance of a conductor is doubled, what happens to the current flowing through it when the voltage remains constant? (2022)
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases by 1.5 times
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Solution
According to Ohm's law, I = V/R. If R is doubled, I will be halved.
Correct Answer: B — Halves
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Q. If the revenue function is R(x) = 100x - 2x^2, find the number of units that maximizes revenue. (2021)
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Solution
Max revenue occurs at x = -b/(2a) = 100/(2*2) = 25.
Correct Answer: B — 50
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