Algebra MCQ Questions and Solutions with Explanations

Section 1 Section 2 Section 3 Section 4 Section 5 Section 6

1.
If x + y + z = 19, x² + y² + z² = 133, and xz = y², x > z > 0, what is the value of (x - z)?

A. 0

B. 5

C. -2

D. -5

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2.
If $$c - d = \frac{{c + d}}{5} = \frac{{cd}}{3}$$ and c, d ≠ 0 then what is the value of cd?

A. $$\frac{1}{2}$$

B. $$\frac{3}{2}$$

C. $$\frac{5}{2}$$

D. $$\frac{5}{4}$$

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3.
If x² - 4x + 1 = 0, then what is the value of x⁹ + x⁷ - 194x⁵ - 194x³?

A. 4

B. -4

C. 1

D. -1

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4.
If $$A = \frac{{x - 1}}{{x + 1}},$$ then the value of $$A - \frac{1}{A}$$ is:

A. $$\frac{{{x^2} - 1}}{{ - 4\left( {2x + 1} \right)}}$$

B. $$\frac{{ - 4x}}{{{x^2} - 1}}$$

C. $$\frac{{{x^2} - 1}}{{ - 4\left( {2x - 1} \right)}}$$

D. $$\frac{{ - 4\left( {2x - 1} \right)}}{{{x^2} - 1}}$$

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5.
If x + y = 3, then what is the value of x³ + y³ + 9xy?

A. 15

B. 81

C. 27

D. 9

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6.
If $${x^2} + \frac{1}{{{x^2}}} = 7,$$ then the value of $${x^3} + \frac{1}{{{x^3}}}$$ where x > 0 is equal to:

A. 18

B. 12

C. 15

D. 16

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7.
If x = 5 + 2√6, then what is the value of $$\sqrt x + \frac{1}{{\sqrt x }}?$$

A. 2√3

B. 3√2

C. 2√6

D. 6√2

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8.
If x⁴ + x^-4 = 194, x > 0, then what is the value of $$x + \frac{1}{x} + 2?$$

A. 6

B. 8

C. 4

D. 14

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9.
If (a + 4)³ = a³ + 12a² + ka + 64, then what is the value of k?

A. 45

B. 46

C. 47

D. 48

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10.
If (135√5x² - 2√2y³) ÷ (3√5x - √2y) = Ax² + By² + $$\sqrt {10} $$ Cxy, then the value of (A + B - 9C) is:

A. 18

B. 12

C. 20

D. 10

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Algebra MCQ Questions and Solutions with Explanations | Math Aptitude

1. If x + y + z = 19, x2 + y2 + z2 = 133, and xz = y2, x > z > 0, what is the value of (x - z)?

Answer & Solution

2. If $$c - d = \frac{{c + d}}{5} = \frac{{cd}}{3}$$ and c, d ≠ 0 then what is the value of cd?

Answer & Solution

3. If x2 - 4x + 1 = 0, then what is the value of x9 + x7 - 194x5 - 194x3?

Answer & Solution

4. If $$A = \frac{{x - 1}}{{x + 1}},$$ then the value of $$A - \frac{1}{A}$$ is:

Answer & Solution

5. If x + y = 3, then what is the value of x3 + y3 + 9xy?

Answer & Solution

6. If $${x^2} + \frac{1}{{{x^2}}} = 7,$$ then the value of $${x^3} + \frac{1}{{{x^3}}}$$ where x > 0 is equal to:

Answer & Solution

7. If x = 5 + 2√6, then what is the value of $$\sqrt x + \frac{1}{{\sqrt x }}?$$

Answer & Solution

8. If x4 + x-4 = 194, x > 0, then what is the value of $$x + \frac{1}{x} + 2?$$

Answer & Solution

9. If (a + 4)3 = a3 + 12a2 + ka + 64, then what is the value of k?

Answer & Solution

10. If (135√5x2 - 2√2y3) ÷ (3√5x - √2y) = Ax2 + By2 + $$\sqrt {10} $$ Cxy, then the value of (A + B - 9C) is:

Answer & Solution

Read More Section(Algebra)

1.
If x + y + z = 19, x² + y² + z² = 133, and xz = y², x > z > 0, what is the value of (x - z)?

2.
If $$c - d = \frac{{c + d}}{5} = \frac{{cd}}{3}$$ and c, d ≠ 0 then what is the value of cd?

3.
If x² - 4x + 1 = 0, then what is the value of x⁹ + x⁷ - 194x⁵ - 194x³?

4.
If $$A = \frac{{x - 1}}{{x + 1}},$$ then the value of $$A - \frac{1}{A}$$ is:

5.
If x + y = 3, then what is the value of x³ + y³ + 9xy?

6.
If $${x^2} + \frac{1}{{{x^2}}} = 7,$$ then the value of $${x^3} + \frac{1}{{{x^3}}}$$ where x > 0 is equal to:

7.
If x = 5 + 2√6, then what is the value of $$\sqrt x + \frac{1}{{\sqrt x }}?$$

8.
If x⁴ + x^-4 = 194, x > 0, then what is the value of $$x + \frac{1}{x} + 2?$$

9.
If (a + 4)³ = a³ + 12a² + ka + 64, then what is the value of k?

10.
If (135√5x² - 2√2y³) ÷ (3√5x - √2y) = Ax² + By² + $$\sqrt {10} $$ Cxy, then the value of (A + B - 9C) is: