AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

AP EAMCET Mathematics - Partial Fractions MCQs

1. 91. The partial fraction decomposition of \( \frac{1}{(x - 1)(x + 2)} \) is:

   • A) \( \frac{A}{x - 1} + \frac{B}{x + 2} \)
   • B) \( \frac{A}{x - 1} + \frac{B}{x + 2} + \frac{C}{x + 1} \)
   • C) \( \frac{A}{x + 1} + \frac{B}{x - 2} \)
   • D) \( \frac{A}{x + 2} + \frac{B}{(x - 1)^2} \)

   Answer: A

2. 92. The partial fraction decomposition of \( \frac{2}{(x - 1)(x - 2)} \) is:

   • A) \( \frac{A}{x - 1} + \frac{B}{x - 2} \)
   • B) \( \frac{A}{x - 1} + \frac{B}{(x - 2)^2} \)
   • C) \( \frac{A}{(x - 1)^2} + \frac{B}{x - 2} \)
   • D) \( \frac{A}{(x - 1)^2} + \frac{B}{(x - 2)^2} \)

   Answer: A

3. 93. What is the partial fraction decomposition of \( \frac{1}{x(x + 1)} \)?

   • A) \( \frac{A}{x} + \frac{B}{x + 1} \)
   • B) \( \frac{A}{x + 1} + \frac{B}{x} \)
   • C) \( \frac{A}{x} + \frac{B}{(x + 1)^2} \)
   • D) \( \frac{A}{x} + \frac{B}{x + 1} + \frac{C}{(x + 1)^2} \)

   Answer: A

4. 94. For the partial fraction decomposition of \( \frac{P(x)}{(x - 2)^2(x + 3)} \), what is the form of the decomposition?

   • A) \( \frac{A}{x - 2} + \frac{B}{(x - 2)^2} + \frac{C}{x + 3} \)
   • B) \( \frac{A}{(x - 2)^2} + \frac{B}{x + 3} \)
   • C) \( \frac{A}{x - 2} + \frac{B}{x + 3} \)
   • D) \( \frac{A}{x - 2} + \frac{B}{(x + 3)^2} \)

   Answer: A

5. 95. The partial fraction decomposition of \( \frac{1}{x^2 + 3x + 2} \) is:

   • A) \( \frac{A}{x + 1} + \frac{B}{x + 2} \)
   • B) \( \frac{A}{x + 1} + \frac{B}{(x + 2)^2} \)
   • C) \( \frac{A}{x + 2} + \frac{B}{x + 3} \)
   • D) \( \frac{A}{x + 1} + \frac{B}{x^2 + 3} \)

   Answer: A

6. 96. The partial fraction decomposition of \( \frac{3}{(x + 2)(x^2 + 1)} \) is:

   • A) \( \frac{A}{x + 2} + \frac{Bx + C}{x^2 + 1} \)
   • B) \( \frac{A}{x + 2} + \frac{B}{x^2 + 1} \)
   • C) \( \frac{A}{(x + 2)^2} + \frac{Bx + C}{x^2 + 1} \)
   • D) \( \frac{A}{(x + 2)^2} + \frac{B}{x^2 + 1} \)

   Answer: A

7. 97. The partial fraction decomposition of \( \frac{x + 3}{(x - 2)(x + 5)} \) is:

   • A) \( \frac{A}{x - 2} + \frac{B}{x + 5} \)
   • B) \( \frac{A}{x + 5} + \frac{B}{x - 2} \)
   • C) \( \frac{A}{(x - 2)^2} + \frac{B}{x + 5} \)
   • D) \( \frac{A}{x - 2} + \frac{B}{(x + 5)^2} \)

   Answer: A

8. 98. The partial fraction decomposition of \( \frac{4}{(x - 1)(x + 1)(x + 2)} \) is:

   • A) \( \frac{A}{x - 1} + \frac{B}{x + 1} + \frac{C}{x + 2} \)
   • B) \( \frac{A}{x - 1} + \frac{B}{x + 1} \)
   • C) \( \frac{A}{x - 1} + \frac{B}{x + 1} + \frac{C}{(x + 2)^2} \)
   • D) \( \frac{A}{x - 1} + \frac{B}{x + 1} + \frac{C}{(x + 2)^2} \)

   Answer: A

9. 99. The partial fraction decomposition of \( \frac{1}{x^2(x + 1)} \) is:

   • A) \( \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x + 1} \)
   • B) \( \frac{A}{x^2} + \frac{B}{x + 1} \)
   • C) \( \frac{A}{x} + \frac{B}{x^2} \)
   • D) \( \frac{A}{x} + \frac{B}{(x + 1)^2} \)

   Answer: A

10. 100. The partial fraction decomposition of \( \frac{5}{(x - 3)(x^2 + 4x + 5)} \) is:

    • A) \( \frac{A}{x - 3} + \frac{Bx + C}{x^2 + 4x + 5} \)
    • B) \( \frac{A}{x - 3} + \frac{B}{x^2 + 4x + 5} \)
    • C) \( \frac{A}{x - 3} + \frac{Bx + C}{(x^2 + 4x + 5)^2} \)
    • D) \( \frac{A}{x^2 + 4x + 5} + \frac{B}{x - 3} \)

    Answer: A

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