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Q. What is the value of the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant of matrix A is 0 because the rows are linearly dependent.

Correct Answer: A — 0

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Q. What is the value of the determinant of the matrix \( \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant of the matrix is 0 because the rows are linearly dependent.

Correct Answer: A — 0

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Q. What is the value of the determinant \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant is 0 because the first column is repeated.

Correct Answer: A — 0

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Q. What is the value of the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) when \( a = 1, b = 2, c = 3, d = 4 \)?

A. -2
B. 2
C. 0
D. 1

Solution

The determinant is \( 1*4 - 2*3 = 4 - 6 = -2 \).

Correct Answer: A — -2

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Q. What is the value of the determinant | 1 2 3 | | 0 1 4 | | 5 6 0 |?

A. -12
B. 12
C. 0
D. 6

Solution

Calculating the determinant gives -12.

Correct Answer: A — -12

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Q. What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4, d = 5?

A. -2
B. 1
C. 2
D. 7

Solution

det = (2)(5) - (3)(4) = 10 - 12 = -2.

Correct Answer: C — 2

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Q. What is the value of the discriminant for the equation 3x^2 + 12x + 12 = 0?

A. 0
B. 12
C. 36
D. 24

Solution

The discriminant is b^2 - 4ac = 12^2 - 4(3)(12) = 144 - 144 = 0.

Correct Answer: A — 0

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Q. What is the value of the discriminant for the equation 3x^2 + 12x + 9 = 0?

A. 0
B. 36
C. 12
D. 24

Solution

The discriminant is b^2 - 4ac = 12^2 - 4*3*9 = 144 - 108 = 36.

Correct Answer: A — 0

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Q. What is the value of the discriminant for the equation 3x² + 6x + 2 = 0? (2020)

A. 0
B. 4
C. 12
D. 6

Solution

The discriminant D = b² - 4ac = 6² - 4*3*2 = 36 - 24 = 12.

Correct Answer: B — 4

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Q. What is the value of the discriminant for the equation 3x² - 12x + 12 = 0? (2020)

A. 0
B. 12
C. 36
D. 24

Solution

The discriminant D = b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.

Correct Answer: A — 0

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Q. What is the value of the discriminant for the equation x² - 2x + 1 = 0? (2022)

A. 0
B. 1
C. 2
D. 4

Solution

The discriminant is b² - 4ac = (-2)² - 4*1*1 = 0.

Correct Answer: A — 0

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Q. What is the value of the discriminant for the equation x² - 4x + 4 = 0? (2022)

A. 0
B. 4
C. 8
D. 16

Solution

The discriminant is b² - 4ac = (-4)² - 4*1*4 = 0.

Correct Answer: A — 0

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Q. What is the value of the discriminant for the quadratic equation 3x^2 + 12x + 9 = 0? (2019)

A. 0
B. 9
C. 36
D. 27

Solution

The discriminant D = b^2 - 4ac = 12^2 - 4*3*9 = 0, indicating equal roots.

Correct Answer: A — 0

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Q. What is the value of the discriminant for the quadratic equation 3x^2 + 6x + 2 = 0? (2023)

A. 0
B. 4
C. 12
D. 36

Solution

The discriminant is b^2 - 4ac = 6^2 - 4(3)(2) = 36 - 24 = 12.

Correct Answer: B — 4

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Q. What is the value of the equilibrium constant Kc for the reaction A + B ⇌ C + D at 25°C if the concentrations are [A]=0.1 M, [B]=0.2 M, [C]=0.3 M, [D]=0.4 M?

A. 0.5
B. 1.0
C. 2.0
D. 4.0

Solution

Kc = ([C][D]) / ([A][B]) = (0.3 * 0.4) / (0.1 * 0.2) = 2.0

Correct Answer: C — 2.0

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Q. What is the value of the equilibrium constant Kc for the reaction A + B ⇌ C at 25°C if the concentrations are [A] = 0.1 M, [B] = 0.2 M, and [C] = 0.3 M?

A. 0.5
B. 1.0
C. 1.5
D. 2.0

Solution

Kc = [C]/([A][B]) = 0.3/(0.1*0.2) = 1.5

Correct Answer: B — 1.0

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Q. What is the value of the equilibrium constant Kc for the reaction: 2A ⇌ B + C if at equilibrium [A] = 0.5 M, [B] = 0.2 M, and [C] = 0.3 M?

A. 0.12
B. 0.30
C. 0.60
D. 1.20

Solution

Kc = [B][C] / [A]^2 = (0.2)(0.3) / (0.5)^2 = 0.12 / 0.25 = 0.48.

Correct Answer: C — 0.60

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Q. What is the value of the equilibrium constant Kp for the reaction 2NO2(g) ⇌ N2O4(g) at a certain temperature?

A. Kp = (P_N2O4) / (P_NO2)^2
B. Kp = (P_NO2)^2 / (P_N2O4)
C. Kp = (P_N2O4)^2 / (P_NO2)
D. Kp = (P_NO2) / (P_N2O4)^2

Solution

Kp is defined as the partial pressure of products over reactants, raised to the power of their coefficients.

Correct Answer: A — Kp = (P_N2O4) / (P_NO2)^2

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Q. What is the value of the equilibrium constant Kp for the reaction: N2(g) + 3H2(g) ⇌ 2NH3(g) at 25°C?

A. 0.5
B. 1.0
C. 0.1
D. Depends on the initial concentrations

Solution

The value of Kp is specific to the reaction conditions and cannot be determined without knowing the initial concentrations or the extent of the reaction.

Correct Answer: D — Depends on the initial concentrations

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Q. What is the value of the expression (2 + 3) × (4 - 1)? (2019)

A. 15
B. 20
C. 25
D. 10

Solution

Calculating inside the parentheses first: (2 + 3) = 5 and (4 - 1) = 3. Therefore, 5 × 3 = 15.

Correct Answer: A — 15

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Q. What is the value of the expression (3 + 5) × (2 - 1)? (2019)

A. 8
B. 6
C. 10
D. 4

Solution

Calculating inside the parentheses first: (3 + 5) = 8 and (2 - 1) = 1. Therefore, (3 + 5) × (2 - 1) = 8 × 1 = 8.

Correct Answer: A — 8

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Q. What is the value of the expression (4 + 5) × 2? (2023)

A. 18
B. 20
C. 16
D. 14

Solution

First, we calculate the sum inside the parentheses: 4 + 5 = 9. Then we multiply by 2: 9 × 2 = 18.

Correct Answer: A — 18

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Q. What is the value of the expression (8 + 4) ÷ 2 × 3? (2022)

A. 18
B. 12
C. 24
D. 6

Solution

First, calculate inside the parentheses: 8 + 4 = 12. Then divide by 2: 12 ÷ 2 = 6. Finally, multiply by 3: 6 × 3 = 18.

Correct Answer: B — 12

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Q. What is the value of the expression 10 - (3 + 2) × 2?

A. 0
B. 1
C. 2
D. 3

Solution

First calculate inside the parentheses: 3 + 2 = 5. Then, 5 × 2 = 10. Finally, 10 - 10 = 0.

Correct Answer: B — 1

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Q. What is the value of the expression 10 - 2 × 3 + 4? (2023)

A. 8
B. 10
C. 12
D. 14

Solution

Following the order of operations: 10 - 6 + 4 = 8.

Correct Answer: A — 8

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Q. What is the value of the expression 2 + 3 × 4?

A. 14
B. 20
C. 12
D. 10

Solution

According to the order of operations, we first multiply: 3 × 4 = 12, then add: 2 + 12 = 14.

Correct Answer: C — 12

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Q. What is the value of the expression 2(3 + 4) - 5? (2019)

A. 9
B. 10
C. 11
D. 12

Solution

Calculating gives 2(7) - 5 = 14 - 5 = 9.

Correct Answer: B — 10

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Q. What is the value of the expression 2^3 + 3^2 - 4? (2021)

A. 5
B. 7
C. 9
D. 11

Solution

2^3 = 8, 3^2 = 9, so 8 + 9 - 4 = 13. The correct answer is 7.

Correct Answer: B — 7

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Q. What is the value of the expression 2^3 + 3^2? (2023)

A. 17
B. 11
C. 9
D. 8

Solution

Calculating gives 2^3 = 8 and 3^2 = 9. Therefore, 2^3 + 3^2 = 8 + 9 = 17.

Correct Answer: A — 17

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Q. What is the value of the expression 3(2 + 4) - 5? (2022)

A. 10
B. 15
C. 12
D. 8

Solution

First, calculate the expression inside the parentheses: 2 + 4 = 6. Then, multiply by 3: 3 × 6 = 18. Finally, subtract 5: 18 - 5 = 13.

Correct Answer: A — 10

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Major Competitive Exams

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