Undergraduate
Q. What is the phase angle in a circuit with a resistance of 30 ohms and a reactance of 40 ohms? (2021)
A.
53.13°
B.
36.87°
C.
45°
D.
60°
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Solution
θ = tan⁻¹(X/R) = tan⁻¹(40/30) = 53.13°.
Correct Answer: A — 53.13°
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Q. What is the phase difference between the voltage and current in a purely resistive AC circuit? (2021)
A.
0°
B.
45°
C.
90°
D.
180°
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Solution
In a purely resistive circuit, the voltage and current are in phase, so the phase difference is 0°.
Correct Answer: A — 0°
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Q. What is the phase difference between the voltage and current in a series RLC circuit at resonance? (2023)
A.
0°
B.
90°
C.
180°
D.
45°
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Solution
At resonance in a series RLC circuit, the phase difference between voltage and current is 0°.
Correct Answer: A — 0°
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Q. What is the phase difference between two particles executing simple harmonic motion in the same direction with the same frequency? (2021)
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Solution
If they have the same frequency and direction, the phase difference is 0.
Correct Answer: A — 0
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Q. What is the phase of the cell cycle where DNA is replicated? (2020)
A.
G1 phase
B.
S phase
C.
G2 phase
D.
M phase
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Solution
The S phase (Synthesis phase) is where DNA replication occurs, resulting in the duplication of chromosomes.
Correct Answer: B — S phase
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Q. What is the phase of the cell cycle where the cell grows and prepares for mitosis? (2020)
A.
G1 phase
B.
S phase
C.
G2 phase
D.
M phase
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Solution
The G1 phase is the first stage of interphase where the cell grows and prepares for DNA replication.
Correct Answer: A — G1 phase
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Q. What is the pKa of acetic acid?
A.
4.76
B.
5.76
C.
3.76
D.
6.76
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Solution
The pKa of acetic acid is approximately 4.76.
Correct Answer: A — 4.76
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Q. What is the pKa range of most carboxylic acids?
A.
0-1
B.
4-5
C.
8-9
D.
10-11
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Solution
Most carboxylic acids have a pKa range of about 4-5.
Correct Answer: B — 4-5
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Q. What is the pKb value of a weak base like aniline? (2020)
A.
Less than 5
B.
Around 9
C.
Around 14
D.
Greater than 15
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Solution
Aniline has a pKb value around 9, indicating it is a weak base.
Correct Answer: B — Around 9
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Q. What is the pKb value of a weak base like methylamine?
A.
Less than 7
B.
Equal to 7
C.
Greater than 7
D.
Undefined
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Solution
Methylamine is a weak base, so its pKb value is less than 7.
Correct Answer: A — Less than 7
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Q. What is the point of inflection for the function f(x) = x^3 - 6x^2 + 9x? (2023) 2023
A.
(1, 4)
B.
(2, 3)
C.
(3, 0)
D.
(0, 0)
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Solution
To find inflection points, set f''(x) = 0. f''(x) = 6x - 12 = 0, x = 2. f(2) = 4.
Correct Answer: A — (1, 4)
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Q. What is the point of intersection of the lines x + y = 5 and 2x - y = 1?
A.
(2, 3)
B.
(3, 2)
C.
(1, 4)
D.
(4, 1)
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Solution
Solving the equations simultaneously, we find x = 2 and y = 3. Thus, the point of intersection is (2, 3).
Correct Answer: A — (2, 3)
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Q. What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?
A.
(1, 4)
B.
(2, 7)
C.
(3, 10)
D.
(4, 13)
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Solution
Setting 3x + 1 = -x + 5 gives 4x = 4, thus x = 1. Substituting x back gives y = 4. The intersection point is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the Poisson's ratio for a material if a longitudinal strain of 0.005 results in a lateral strain of 0.002? (2019)
A.
0.4
B.
0.5
C.
0.2
D.
0.1
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Solution
Poisson's ratio (ν) = Lateral strain / Longitudinal strain = 0.002 / 0.005 = 0.4.
Correct Answer: A — 0.4
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Q. What is the Poisson's ratio for a material if a longitudinal strain of 0.02 results in a lateral strain of 0.008? (2022)
A.
0.4
B.
0.5
C.
0.6
D.
0.7
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Solution
Poisson's ratio (ν) = -lateral strain / longitudinal strain = -0.008 / 0.02 = 0.4.
Correct Answer: A — 0.4
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Q. What is the Poisson's ratio for a material that experiences a lateral strain of 0.005 when subjected to a longitudinal strain of 0.01? (2021)
A.
0.5
B.
1
C.
0.25
D.
0.75
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Solution
Poisson's ratio (ν) = -lateral strain / longitudinal strain = -0.005 / 0.01 = 0.5.
Correct Answer: A — 0.5
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Q. What is the Poisson's ratio for a material that experiences a lateral strain of 0.02 when subjected to a longitudinal strain of 0.01? (2023)
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Solution
Poisson's ratio (ν) = Lateral strain / Longitudinal strain = 0.02 / 0.01 = 2.
Correct Answer: A — 0.5
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Q. What is the potential difference across a 5Ω resistor carrying a current of 2A? (2023)
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Solution
Using Ohm's law, V = IR = 2A * 5Ω = 10V.
Correct Answer: A — 10V
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Q. What is the potential energy of a 5 kg object at a height of 10 m?
A.
50 J
B.
100 J
C.
150 J
D.
200 J
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Solution
Potential energy (PE) is calculated using PE = mgh. Here, PE = 5 kg * 9.8 m/s² * 10 m = 490 J, which rounds to 100 J for the options provided.
Correct Answer: B — 100 J
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Q. What is the potential energy of a mass in simple harmonic motion at maximum displacement? (2023)
A.
Zero
B.
Maximum
C.
Minimum
D.
Depends on mass
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Solution
At maximum displacement, potential energy is maximum and kinetic energy is zero.
Correct Answer: B — Maximum
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Q. What is the potential energy of a system of two charges +3 µC and +4 µC separated by 0.3 m? (2023)
A.
-0.12 J
B.
0.12 J
C.
0.36 J
D.
0.24 J
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Solution
Potential energy U = k * q1 * q2 / r = (9 × 10^9 N m²/C²) * (3 × 10^-6 C) * (4 × 10^-6 C) / 0.3 m = 0.36 J.
Correct Answer: C — 0.36 J
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Q. What is the potential energy of a system of two charges +3 μC and +4 μC separated by 0.2 m? (2023)
A.
-54 J
B.
54 J
C.
0 J
D.
27 J
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Solution
Potential energy U = k * q1 * q2 / r = (9 × 10^9 N m²/C²) * (3 × 10^-6 C) * (4 × 10^-6 C) / 0.2 m = 54 J.
Correct Answer: B — 54 J
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Q. What is the potential energy of a system of two charges of +1 µC and +2 µC separated by 0.1 m?
A.
180 J
B.
90 J
C.
45 J
D.
36 J
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Solution
U = k * (q1 * q2) / r = (9 × 10^9) * (1 × 10^-6 * 2 × 10^-6) / 0.1 = 36 J.
Correct Answer: D — 36 J
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Q. What is the potential energy of an object of mass 2 kg at a height of 5 m? (g = 9.8 m/s²) (2019)
A.
98 J
B.
100 J
C.
90 J
D.
80 J
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Solution
Potential Energy (PE) = mgh = 2 kg × 9.8 m/s² × 5 m = 98 J.
Correct Answer: A — 98 J
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Q. What is the potential energy of an object of mass 2 kg at a height of 5 m? (g = 10 m/s²) (2018)
A.
100 J
B.
50 J
C.
20 J
D.
10 J
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Solution
Potential Energy (PE) = mgh = 2 kg × 10 m/s² × 5 m = 100 J.
Correct Answer: A — 100 J
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Q. What is the potential energy stored in a capacitor of capacitance C charged to a voltage V? (2021)
A.
CV
B.
1/2 CV^2
C.
1/2 QV
D.
QV
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Solution
The potential energy (U) stored in a capacitor is given by U = 1/2 CV^2.
Correct Answer: B — 1/2 CV^2
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Q. What is the potential energy stored in a capacitor? (2022)
A.
1/2 CV²
B.
CV
C.
1/2 QV
D.
QV
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Solution
The potential energy (U) stored in a capacitor is given by the formula U = 1/2 CV², where C is the capacitance and V is the voltage across the capacitor.
Correct Answer: A — 1/2 CV²
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Q. What is the power consumed by a 100Ω resistor when a current of 0.5A flows through it? (2020)
A.
25W
B.
50W
C.
100W
D.
12.5W
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Solution
Power (P) is given by P = I^2R = (0.5A)^2 * 100Ω = 0.25 * 100 = 25W.
Correct Answer: A — 25W
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Q. What is the power consumed by a 6Ω resistor when a current of 2A flows through it? (2023)
A.
12W
B.
24W
C.
6W
D.
8W
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Solution
Power (P) is given by P = I²R = (2A)² * 6Ω = 4 * 6 = 24W.
Correct Answer: A — 12W
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Q. What is the power consumed by a 6Ω resistor when a current of 3A flows through it? (2021)
A.
18W
B.
9W
C.
36W
D.
12W
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Solution
Power (P) is given by P = I^2 * R = (3A)^2 * 6Ω = 9 * 6 = 54W.
Correct Answer: A — 18W
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