Indices and Surds - Applications for Competitive Exams

Indices and Surds - Applications

Q. If 2x + 3y = 12 and y = 2, what is the value of x?

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

Solution

Step 1: Substitute y = 2 into the equation: 2x + 6 = 12. Step 2: Subtract 6: 2x = 6. Step 3: Divide by 2: x = 3.

Correct Answer: C — 2

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Q. If 5x + 2 > 12, what is the smallest integer value of x?

A. 1
B. 2
C. 3
D. 4

Solution

Subtract 2 from both sides: 5x > 10. Then divide by 5: x > 2.

Correct Answer: C — 3

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Q. Solve for x in the equation x^2 + 6x + 9 = 0.

A. x = -3
B. x = 3
C. x = 0
D. x = -9

Solution

Factor the equation: (x + 3)(x + 3) = 0. Thus, x = -3.

Correct Answer: A — x = -3

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Q. Solve for x: 2x^2 + 8x = 0.

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

Solution

Factor out 2x: 2x(x + 4) = 0. Thus, x = 0 or x = -4.

Correct Answer: B — -4

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Q. Solve the quadratic equation x^2 - 5x + 6 = 0.

A. x = 2, 3
B. x = 1, 6
C. x = -2, -3
D. x = 0, 5

Solution

Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.

Correct Answer: A — x = 2, 3

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Q. What is the solution to the equation 4(x - 1) = 12?

A. x = 4
B. x = 3
C. x = 5
D. x = 2

Solution

Divide both sides by 4: x - 1 = 3. Add 1 to both sides: x = 4.

Correct Answer: B — x = 3

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Q. What is the solution to the inequality 2x + 1 > 7?

A. x < 3
B. x > 3
C. x < 4
D. x > 4

Solution

Subtract 1 from both sides: 2x > 6. Then divide by 2: x > 3.

Correct Answer: B — x > 3

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Q. What is the value of x in the equation 3(x - 2) = 12?

A. 2
B. 4
C. 6
D. 8

Solution

Divide both sides by 3: x - 2 = 4. Then add 2: x = 6.

Correct Answer: C — 6

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Q. What is the value of x in the polynomial equation 3x^2 - 12 = 0?

A. x = 2
B. x = -2
C. x = 4
D. x = -4

Solution

Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Take the square root: x = ±4.

Correct Answer: C — x = 4

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Q. What is the value of x in the polynomial equation x^3 - 4x = 0?

A. x = 0, 2, -2
B. x = 1, -1, 0
C. x = 4, -4, 0
D. x = 3, -3, 0

Solution

Factor out x: x(x^2 - 4) = 0. Thus, x = 0 or x^2 - 4 = 0, giving x = 2 or x = -2.

Correct Answer: A — x = 0, 2, -2

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Q. Which expression represents the sum of the roots of the equation x^2 - 6x + 8 = 0?

A. 6
B. 8
C. 4
D. 2

Solution

Step 1: The sum of the roots is given by -b/a: 6/1 = 6.

Correct Answer: A — 6

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Q. Which of the following is a solution to the inequality 3x - 5 < 4?

A. x < 3
B. x > 3
C. x < 2
D. x > 2

Solution

Add 5 to both sides: 3x < 9. Then divide by 3: x < 3.

Correct Answer: A — x < 3

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Q. Which of the following is a solution to the inequality 5x - 7 < 8?

A. x < 3
B. x > 3
C. x < 2
D. x > 2

Solution

Add 7 to both sides: 5x < 15. Divide by 5: x < 3.

Correct Answer: A — x < 3

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Q. Which of the following is the result of (x + 2)(x - 2)?

A. x^2 - 4
B. x^2 + 4
C. x^2 - 2
D. x^2 + 2

Solution

Use the difference of squares: (x + 2)(x - 2) = x^2 - 4.

Correct Answer: A — x^2 - 4

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Showing 1 to 14 of 14 (1 Pages)

Indices and Surds - Applications

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