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Q. In the electrochemical cell, which electrode is the site of reduction? (2023)

A. Anode
B. Cathode
C. Salt bridge
D. Electrolyte

Solution

In an electrochemical cell, the cathode is the electrode where reduction occurs.

Correct Answer: B — Cathode

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Q. In the electrochemical series, which element is the best reducing agent? (2022)

A. Li
B. Na
C. K
D. Rb

Solution

Li is the best reducing agent among the given alkali metals due to its low ionization energy.

Correct Answer: A — Li

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Q. In the electrochemical series, which element is the strongest oxidizing agent? (2023)

A. Li
B. F2
C. Na
D. K

Solution

Fluorine (F2) is the strongest oxidizing agent in the electrochemical series due to its high electronegativity and tendency to gain electrons.

Correct Answer: B — F2

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Q. In the electrochemical series, which of the following has the highest reduction potential? (2022)

A. Li+
B. Na+
C. K+
D. F+

Solution

Fluorine (F+) has the highest reduction potential in the electrochemical series, indicating it is a strong oxidizing agent.

Correct Answer: D — F+

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Q. In the equation 3x + 4y = 12, what is the value of y when x = 0?

A. 0
B. 3
C. 4
D. 12

Solution

Substituting x = 0 gives 4y = 12, thus y = 3.

Correct Answer: C — 4

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Q. In the equation 4x + 5y = 20, what is the value of y when x = 0?

A. 0
B. 4
C. 5
D. 20

Solution

Setting x = 0 in the equation gives 5y = 20, leading to y = 4.

Correct Answer: C — 5

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Q. In the equation 4x - 2y = 8, what is the value of y when x = 2?

A. 0
B. 2
C. 4
D. 6

Solution

Substituting x = 2 into the equation gives 4(2) - 2y = 8, leading to y = 2.

Correct Answer: B — 2

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Q. In the equation 5x - 2y = 10, what is the value of y when x = 0?

A. 0
B. 5
C. -5
D. 2

Solution

Substituting x = 0 into the equation gives -2y = 10, leading to y = -5.

Correct Answer: B — 5

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Q. In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant is 0, which indicates that the roots are real and equal.

Correct Answer: B — Real and equal

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Q. In the equation y = mx + b, what does 'm' represent?

A. The y-intercept
B. The slope of the line
C. The x-intercept
D. The constant term

Solution

'm' represents the slope of the line, indicating how steep the line is.

Correct Answer: B — The slope of the line

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Q. In the equilibrium constant expression Kc, what is the unit for Kc if the reaction is A(g) + B(g) ⇌ C(g)?

A. mol/L
B. L/mol
C. dimensionless
D. mol^2/L^2

Solution

The equilibrium constant Kc is dimensionless because it is a ratio of concentrations raised to their stoichiometric coefficients.

Correct Answer: C — dimensionless

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Q. In the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), if SO2 is added, what will be the effect on the equilibrium?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in pressure

Solution

Adding SO2 will shift the equilibrium to the right to produce more SO3, according to Le Chatelier's principle.

Correct Answer: A — Shift to the right

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Q. In the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), what happens if SO3 is removed?

A. Shift to the right
B. Shift to the left
C. No change
D. Increase in pressure

Solution

Removing SO3 will shift the equilibrium to the right to produce more SO3.

Correct Answer: A — Shift to the right

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Q. In the expansion of (1 + x)^10, what is the coefficient of x^5?

A. 252
B. 210
C. 120
D. 300

Solution

The coefficient of x^5 is C(10,5) = 10! / (5!5!) = 252.

Correct Answer: A — 252

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Q. In the expansion of (1 + x)^n, what is the term containing x^4?

A. C(n, 4)x^4
B. C(n, 3)x^4
C. C(n, 5)x^4
D. C(n, 2)x^4

Solution

The term containing x^4 in the expansion of (1 + x)^n is C(n, 4)x^4.

Correct Answer: A — C(n, 4)x^4

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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x?

A. 12
B. 24
C. 36
D. 48

Solution

The coefficient of x is C(4,1) * 2^3 * 3 = 4 * 8 * 3 = 96.

Correct Answer: A — 12

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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x^2?

A. 36
B. 54
C. 72
D. 90

Solution

The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.

Correct Answer: B — 54

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Q. In the expansion of (2 + 3x)^5, what is the coefficient of x?

A. 15
B. 30
C. 45
D. 60

Solution

The coefficient of x is given by C(5, 1) * (2)^4 * (3) = 5 * 16 * 3 = 240.

Correct Answer: A — 15

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Q. In the expansion of (2 + 3x)^5, what is the coefficient of x^2?

A. 90
B. 180
C. 270
D. 360

Solution

The coefficient of x^2 is given by 5C2 * (3^2) * (2^3) = 10 * 9 * 8 = 720.

Correct Answer: B — 180

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Q. In the expansion of (2 - x)^5, what is the coefficient of x^3?

A. -80
B. -60
C. 60
D. 80

Solution

The coefficient of x^3 in (2 - x)^5 is given by 5C3 * 2^2 * (-1)^3 = 10 * 4 * (-1) = -40.

Correct Answer: A — -80

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Q. In the expansion of (2x + 3)^4, what is the coefficient of x? (2020)

A. 12
B. 36
C. 48
D. 72

Solution

The coefficient of x is given by 4C1 * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.

Correct Answer: B — 36

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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^0?

A. 81
B. 64
C. 36
D. 16

Solution

The coefficient of x^0 is given by 4C4 * (2x)^0 * (3)^4 = 1 * 81 = 81.

Correct Answer: A — 81

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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^1?

A. 72
B. 48
C. 36
D. 24

Solution

The coefficient of x^1 is C(4,1) * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.

Correct Answer: B — 48

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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^2?

A. 108
B. 72
C. 36
D. 144

Solution

The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.

Correct Answer: B — 72

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Q. In the expansion of (2x + 3)^6, what is the coefficient of x^4?

A. 540
B. 720
C. 810
D. 900

Solution

The coefficient of x^4 is C(6,4) * (2)^4 * (3)^2 = 15 * 16 * 9 = 2160.

Correct Answer: B — 720

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Q. In the expansion of (2x + 3y)^4, what is the coefficient of x^2y^2?

A. 108
B. 72
C. 36
D. 144

Solution

The coefficient is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.

Correct Answer: A — 108

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Q. In the expansion of (2x + 5)^3, what is the coefficient of x?

A. 30
B. 45
C. 60
D. 75

Solution

The coefficient of x is given by 3C1 * (2)^1 * (5)^2 = 3 * 2 * 25 = 150.

Correct Answer: B — 45

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Q. In the expansion of (2x + 5)^3, what is the coefficient of x^2?

A. 30
B. 60
C. 90
D. 120

Solution

The coefficient of x^2 in (2x + 5)^3 is given by 3C2 * (2x)^2 * 5^1 = 3 * 4 * 5 = 60.

Correct Answer: B — 60

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Q. In the expansion of (2x + 5)^4, what is the coefficient of x^2?

A. 300
B. 600
C. 450
D. 500

Solution

The coefficient of x^2 is C(4,2) * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.

Correct Answer: A — 300

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Q. In the expansion of (2x - 3)^3, what is the coefficient of x?

A. -9
B. -18
C. -27
D. -6

Solution

The coefficient of x is C(3,1) * (2)^1 * (-3)^2 = 3 * 2 * 9 = -54.

Correct Answer: B — -18

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Major Competitive Exams

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