Engineering Entrance
Q. If the concentration of Cu²⁺ in a cell is increased, what happens to the cell potential?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Increasing the concentration of Cu²⁺ increases the cell potential according to the Nernst equation.
Correct Answer: A — Increases
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Q. If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)
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Solution
Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.
Correct Answer: A — 5
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Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the length of CD? (2021)
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Solution
Length CD = |10 - 5| = 5.
Correct Answer: A — 5
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Q. If the coordinates of point C are (5, 5) and the slope of the line is 1, what is the equation of the line? (2021) 2021
A.
y = x
B.
y = 5
C.
y = 2x - 5
D.
y = x + 5
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Solution
Using point-slope form: y - 5 = 1(x - 5) => y = x.
Correct Answer: A — y = x
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Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020)
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Solution
The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.
Correct Answer: B — 8
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Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020) 2020
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Solution
The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.
Correct Answer: B — 8
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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 vibrating tuning fork is 440 Hz, what is the time period of the vibration? (2023)
A.
0.00227 s
B.
0.005 s
C.
0.01 s
D.
0.0227 s
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Solution
The time period T is the reciprocal of frequency f, T = 1/f. Therefore, T = 1/440 ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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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 point of intersection?
A.
(3, 0)
B.
(0, 2)
C.
(0, 3)
D.
(2, 0)
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Solution
Setting y = 0 gives 2x = 6, thus x = 3. The point of intersection is (3, 0).
Correct Answer: A — (3, 0)
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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 intersects the y-axis, what is the point of intersection? (2021)
A.
(0, 3)
B.
(0, 4)
C.
(0, 2)
D.
(0, 1)
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Solution
Setting x = 0 gives 4y = 12, thus y = 3. The point of intersection is (0, 3).
Correct Answer: A — (0, 3)
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Q. If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of intersection?
A.
(0, 3)
B.
(0, -3)
C.
(0, 4)
D.
(0, -4)
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Solution
Setting x = 0 gives -4y + 12 = 0, thus y = -3. The point of intersection is (0, -3).
Correct Answer: D — (0, -4)
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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 line 7x + 2y = 14 is transformed to slope-intercept form, what is the slope?
A.
-7/2
B.
7/2
C.
2/7
D.
-2/7
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Solution
Rearranging to y = -7/2x + 7 shows that the slope is -7/2.
Correct Answer: A — -7/2
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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 magnetic field strength is doubled, what happens to the force on a current-carrying conductor in that field? (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 field strength is doubled, the force also doubles.
Correct Answer: A — It doubles
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Q. If the mass of the Earth were to double, what would happen to the gravitational force experienced by an object on its surface?
A.
It doubles
B.
It halves
C.
It quadruples
D.
It remains the same
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Solution
Gravitational force is directly proportional to mass. If mass doubles, force also doubles.
Correct Answer: A — It doubles
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