Undergraduate
Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020)
Show solution
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
Learn More →
Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020) 2020
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
The RMS current is I_rms = I_peak / √2 = 5√2 / √2 = 5 A.
Correct Answer: B — 2.5 A
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
Circumference = πd; C = π * 20 ≈ 62.83 cm.
Correct Answer: A — 62.83 cm
Learn More →
Q. If the distance between the plates of a capacitor is halved, what happens to the capacitance? (2019)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
If the distance d is halved, the capacitance C = εA/d will double.
Correct Answer: A — It doubles
Learn More →
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
Show solution
Solution
F = E * q = 1000 N/C * 5 × 10^-6 C = 0.005 N.
Correct Answer: B — 0.05 N
Learn More →
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
Show solution
Solution
Wavelength is inversely proportional to frequency. If frequency is halved, wavelength doubles.
Correct Answer: B — Doubles
Learn More →
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
Show solution
Solution
Xl = 2πfL; if f is doubled, Xl also doubles.
Correct Answer: B — Halves
Learn More →
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
Show solution
Solution
Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.
Correct Answer: B — It halves
Learn More →
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
Show solution
Solution
The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.
Correct Answer: B — It halves
Learn More →
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
Show solution
Solution
Xl = 2πfL = 2π × 60 × 0.5 = 31.42 ohms.
Correct Answer: A — 31.42 ohms
Learn More →
Q. If the inductance of a coil is doubled, what happens to its inductive reactance at a constant frequency? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
Inductive reactance (X_L) is given by X_L = 2πfL. If the inductance (L) is doubled, X_L will also double.
Correct Answer: A — It doubles
Learn More →
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
Show solution
Solution
Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.
Correct Answer: C — 33.33Ω
Learn More →
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
Show solution
Solution
Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.
Correct Answer: A — 1670 J
Learn More →
Q. If the length of a wire is doubled while keeping the diameter constant, what happens to its resistance? (2019)
A.
It doubles
B.
It halves
C.
It quadruples
D.
It remains the same
Show solution
Solution
Resistance (R) is directly proportional to length (L). If length is doubled, resistance also doubles.
Correct Answer: A — It doubles
Learn More →
Q. If the line 2x + 3y = 6 intersects the x-axis, what is the x-coordinate of the intersection point?
Show solution
Solution
Setting y = 0 gives 2x = 6, thus x = 3. The x-coordinate of the intersection point is 3.
Correct Answer: B — 2
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
Q. If the magnetic flux through a coil changes from 0.5 Wb to 0.2 Wb in 2 seconds, what is the average induced emf? (2023)
A.
150 V
B.
100 V
C.
75 V
D.
50 V
Show solution
Solution
Average induced emf = -ΔΦ/Δt = -(0.2 - 0.5)/2 = 0.15 V = 150 V.
Correct Answer: B — 100 V
Learn More →
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
Show solution
Solution
Perimeter = 4 × side, so side = 40/4 = 10 cm.
Correct Answer: A — 10 cm
Learn More →
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
Show solution
Solution
pH = 3 means [H+] = 10^-3 M = 0.001 M.
Correct Answer: B — 0.01 M
Learn More →
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
Show solution
Solution
For a weak acid, pH ≈ pKa for a 0.1 M solution, so pH ≈ 4.76.
Correct Answer: A — 4.76
Learn More →
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
Show solution
Solution
Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.
Correct Answer: A — 44 cm
Learn More →
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
Show solution
Solution
Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Correct Answer: C — It quadruples
Learn More →
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
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer: A — Halved
Learn More →
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
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer: A — Halved
Learn More →
Showing 511 to 540 of 2215 (74 Pages)
