Engineering Entrance
Q. If sin(θ) = 1/√2, what is θ in degrees?
A.
30°
B.
45°
C.
60°
D.
90°
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Solution
sin(45°) = 1/√2, so θ = 45°
Correct Answer: B — 45°
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Q. If tan(θ) = 1, what is the value of θ? (2020)
A.
0°
B.
30°
C.
45°
D.
60°
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Solution
tan(45°) = 1, so θ = 45°.
Correct Answer: C — 45°
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Q. If the amplitude of a wave is doubled, how does it affect the energy of the wave? (2020)
A.
Remains the same
B.
Doubles
C.
Increases by four times
D.
Halves
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Solution
Energy of a wave is proportional to the square of the amplitude. If amplitude is doubled, energy increases by (2^2) = 4 times.
Correct Answer: C — Increases by four times
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Q. If the amplitude of a wave is doubled, how does this affect the energy carried by the wave? (2021)
A.
Energy is halved
B.
Energy remains the same
C.
Energy is doubled
D.
Energy is quadrupled
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Solution
The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.
Correct Answer: D — Energy is quadrupled
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Q. If the capacitance in an AC circuit is increased, what happens to the capacitive reactance? (2023)
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
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Solution
Capacitive reactance XC = 1/(ωC). If capacitance C increases, XC decreases.
Correct Answer: B — It decreases
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Q. If the charge on a capacitor is doubled, what happens to the energy stored? (2019)
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
The energy stored in a capacitor is proportional to the square of the charge (U = Q^2/(2C)). Doubling the charge increases the energy by a factor of 4.
Correct Answer: C — It quadruples
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Q. If the circumference of a circle is 31.4 cm, what is its radius? (2022)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.
Correct Answer: A — 5 cm
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Q. If the circumference of a circle is 31.4 cm, what is its radius? (Use π = 3.14) (2015)
A.
5 cm
B.
7 cm
C.
10 cm
D.
8 cm
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Solution
Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.
Correct Answer: A — 5 cm
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Q. If the circumference of a circle is 31.4 cm, what is the radius? (2020) 2020
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.
Correct Answer: A — 5 cm
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Q. If the concentration of a reactant is increased in a system at equilibrium, what will happen according to Le Chatelier's principle?
A.
The equilibrium will shift to the right.
B.
The equilibrium will shift to the left.
C.
The equilibrium will not change.
D.
The reaction will stop.
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Solution
According to Le Chatelier's principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Increasing the concentration of a reactant will shift the equilibrium to the right, favoring the formation of products.
Correct Answer: A — The equilibrium will shift to the right.
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Q. If the concentration of a reactant is tripled in a second-order reaction, how does the rate change? (2023)
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Increases by 12 times
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Solution
For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.
Correct Answer: C — Increases by 9 times
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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 distance CD? (2021)
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Solution
Distance CD = |10 - 5| = 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 given by I(t) = I0 cos(ωt), what is the RMS current? (2023)
A.
I0/√2
B.
I0
C.
2I0
D.
I0/2
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Solution
RMS current I_rms = I0/√2 for a cosine function.
Correct Answer: A — I0/√2
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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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