Undergraduate
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 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 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, 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 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 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 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 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 roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)
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Solution
Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.
Correct Answer: C — 3
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Q. If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)
A.
k > 1
B.
k < 1
C.
k > 4
D.
k < 4
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Solution
The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.
Correct Answer: C — k > 4
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Q. If the roots of the equation x² + 5x + k = 0 are 1 and 4, find k. (2020)
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Solution
Using the sum and product of roots: k = 1*4 = 4, and sum = 1 + 4 = 5, thus k = 7.
Correct Answer: D — 7
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Q. If the roots of the equation x² + 7x + p = 0 are -3 and -4, find p. (2019)
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Solution
Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find p = 12.
Correct Answer: A — 12
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Q. If the voltage across a resistor is 240V and the resistance is 60 ohms, what is the current flowing through it? (2020)
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Solution
I = V / R = 240V / 60Ω = 4A.
Correct Answer: C — 6A
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Q. If two dice are rolled, what is the probability that the sum is 7?
A.
1/6
B.
1/12
C.
1/36
D.
5/36
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Solution
Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.
Correct Answer: D — 5/36
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Q. If two identical capacitors of 4 µF each are connected in series, what is the equivalent capacitance?
A.
2 µF
B.
4 µF
C.
6 µF
D.
8 µF
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Solution
C_eq = 1 / (1/C1 + 1/C2) = 1 / (1/4 + 1/4) = 2 µF.
Correct Answer: A — 2 µF
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Q. If x = 3, what is the value of 2x^2 - 5x + 1? (2022)
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Solution
2(3^2) - 5(3) + 1 = 18 - 15 + 1 = 4.
Correct Answer: D — 6
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Q. If x = 5, what is the value of 2x + 3? (2022)
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Solution
Substituting x = 5, we get 2(5) + 3 = 10 + 3 = 13.
Correct Answer: B — 13
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Q. If x = 5, what is the value of 3x + 2? (2022)
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Solution
3(5) + 2 = 15 + 2 = 17.
Correct Answer: A — 17
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Q. If you have 0.25 moles of sulfuric acid (H2SO4), what is its mass? (2023)
A.
49 g
B.
98 g
C.
25 g
D.
12.5 g
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Solution
Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 0.25 moles x 98 g/mol = 24.5 g.
Correct Answer: B — 98 g
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Q. If z = -2 + 2i, what is the value of |z|? (2019)
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Solution
|z| = √((-2)^2 + (2)^2) = √(4 + 4) = √8 = 2√2.
Correct Answer: A — 2√2
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Q. If z = 1 + i, what is the value of z^2? (2022)
A.
2i
B.
1 + 2i
C.
2
D.
0
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Solution
z^2 = (1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.
Correct Answer: B — 1 + 2i
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