Q. What is the standard entropy change (ΔS°) for the reaction: 2SO2(g) + O2(g) → 2SO3(g)?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Cannot be determined
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Solution
The reaction decreases the number of gas molecules from 3 to 2, leading to a decrease in entropy.
Correct Answer: B — Decreases
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Q. What is the standard form of the equation of a parabola that opens upwards with vertex at the origin?
A.
y^2 = 4ax
B.
x^2 = 4ay
C.
y^2 = -4ax
D.
x^2 = -4ay
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Solution
The standard form of a parabola that opens upwards is given by x^2 = 4ay.
Correct Answer: B — x^2 = 4ay
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Q. What is the standard Gibbs Free Energy change (ΔG°) for a reaction at standard conditions?
A.
Always zero
B.
Depends on the reaction
C.
Is a constant value
D.
Is always positive
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Solution
ΔG° depends on the specific reaction and its conditions.
Correct Answer: B — Depends on the reaction
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Q. What is the standard molar entropy of a substance?
A.
Entropy at 0 K
B.
Entropy at 25 °C and 1 atm
C.
Entropy at boiling point
D.
Entropy at melting point
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Solution
Standard molar entropy is defined as the entropy of 1 mole of a substance at 25 °C and 1 atm pressure.
Correct Answer: B — Entropy at 25 °C and 1 atm
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Q. What is the standard state of a substance?
A.
The most stable form at 1 atm and 25°C
B.
Any form of the substance
C.
The gaseous form only
D.
The liquid form only
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Solution
The standard state of a substance is defined as its most stable form at 1 atm pressure and 25°C.
Correct Answer: A — The most stable form at 1 atm and 25°C
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Q. What is the standard unit of temperature in the SI system?
A.
Celsius
B.
Fahrenheit
C.
Kelvin
D.
Rankine
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Solution
The standard unit of temperature in the SI system is Kelvin (K).
Correct Answer: C — Kelvin
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Q. What is the Stefan-Boltzmann law related to?
A.
Conduction
B.
Convection
C.
Radiation
D.
Thermal expansion
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Solution
The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.
Correct Answer: C — Radiation
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Q. What is the structural formula for 2-methylpropane?
A.
CH3-CH2-CH(CH3)-CH3
B.
CH3-CH(CH3)-CH2-CH3
C.
CH3-CH2-CH2-CH3
D.
CH3-CH2-CH(CH2)-CH3
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Solution
The structural formula for 2-methylpropane is CH3-CH(CH3)-CH2-CH3.
Correct Answer: B — CH3-CH(CH3)-CH2-CH3
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Q. What is the structural formula for hexane?
A.
C6H14
B.
C5H12
C.
C4H10
D.
C3H8
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Solution
The structural formula for hexane is C6H14.
Correct Answer: A — C6H14
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Q. What is the structural formula of 2-methylpropane?
A.
CH3-CH2-CH(CH3)-CH3
B.
CH3-CH(CH3)-CH2-CH3
C.
CH3-CH2-CH2-CH3
D.
CH3-CH2-CH(CH2)-CH3
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Solution
The structural formula of 2-methylpropane is CH3-CH(CH3)-CH2-CH3.
Correct Answer: B — CH3-CH(CH3)-CH2-CH3
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Q. What is the structural formula of propane?
A.
C3H8
B.
C2H6
C.
C4H10
D.
C5H12
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Solution
The structural formula of propane is C3H8, indicating three carbon atoms.
Correct Answer: A — C3H8
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Q. What is the structure of DNA?
A.
Single-stranded
B.
Double helix
C.
Triple helix
D.
Linear
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Solution
DNA has a double helix structure, consisting of two strands that coil around each other.
Correct Answer: B — Double helix
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Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?
A.
81
B.
64
C.
100
D.
125
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Solution
The sum of the coefficients is found by substituting x = 1: (2 + 3*1)^4 = 5^4 = 625.
Correct Answer: A — 81
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Q. What is the sum of the coefficients in the expansion of (x + 1)^5?
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Solution
The sum of the coefficients is found by substituting x = 1, so (1 + 1)^5 = 2^5 = 32.
Correct Answer: D — 32
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Q. What is the sum of the coefficients in the expansion of (x + 1)^7?
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Solution
The sum of the coefficients is found by substituting x = 1, giving (1 + 1)^7 = 2^7 = 128.
Correct Answer: A — 128
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Q. What is the sum of the complex numbers 2 + 3i and 4 - 5i?
A.
6 - 2i
B.
6 + 2i
C.
2 - 2i
D.
2 + 2i
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Solution
The sum is (2 + 4) + (3 - 5)i = 6 - 2i.
Correct Answer: A — 6 - 2i
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Q. What is the sum of the first 5 natural numbers?
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Solution
Sum = 1 + 2 + 3 + 4 + 5 = 15.
Correct Answer: B — 15
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Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
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Solution
S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.
Correct Answer: A — 1.5
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Q. What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?
A.
90
B.
100
C.
110
D.
120
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Solution
The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.
Correct Answer: A — 90
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Q. What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?
A.
n/2 * (2 + (n-1) * 3)
B.
n * (2 + 3n)/2
C.
3n^2/2 + n/2
D.
n * (n + 1)
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Solution
The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).
Correct Answer: A — n/2 * (2 + (n-1) * 3)
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Q. What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?
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Solution
The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.
Correct Answer: A — 2
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Q. What is the sum of the roots of the equation 2x^2 - 3x + 1 = 0?
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Solution
The sum of the roots is given by -b/a = 3/2.
Correct Answer: B — 3/2
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Q. What is the sum of the roots of the equation 2x^2 - 4x + 1 = 0?
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Solution
The sum of the roots is given by -b/a = 4/2 = 2.
Correct Answer: B — 1
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Q. What is the sum of the roots of the equation 3x^2 - 12x + 9 = 0?
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Solution
Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.
Correct Answer: B — 4
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Q. What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?
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Solution
The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the equation x^2 - 4x + 3 = 0?
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Solution
The sum of the roots is given by -b/a = 4/1 = 4.
Correct Answer: D — 4
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Q. What is the sum of the roots of the quadratic equation f(x) = x^2 - 5x + 6?
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Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the quadratic equation x^2 - 4x + 3 = 0?
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Solution
The sum of the roots is given by -b/a = 4/1 = 4.
Correct Answer: D — 4
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Q. What is the sum of the roots of the quadratic equation x^2 - 5x + 6 = 0?
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Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the quadratic equation x^2 - 7x + 10 = 0?
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Solution
The sum of the roots is given by -b/a = 7/1 = 7.
Correct Answer: C — 7
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