Mathematics Partial Fractions MCQS Online Preparation Sample Paper Questions with Answer
Partial fractions play a crucial role in algebra and calculus, helping to break down complex rational expressions into simpler components. In ECAT Engineering Entry Test Mathematics, understanding Mathematics Partial Fractions is essential for solving integrals, differential equations, and algebraic simplifications.
This guide provides Mathematics Partial Fractions MCQs to help students master decomposition methods, proper and improper fractions, and their real-world applications. Each multiple-choice question comes with a detailed solution, allowing students to enhance their problem-solving skills for the ECAT exam.
Key Concepts in Partial Fractions
1. Understanding Partial Fractions
A rational function P(x) / Q(x) is expressed as a sum of simpler fractions when degree of P(x) < degree of Q(x). If the numerator’s degree is equal to or greater than the denominator’s degree, the fraction is first converted into a proper fraction using polynomial division.
2. Types of Partial Fractions
- Linear Factors: ( A / x+a ) + ( B / x-b )
- Repeated Linear Factors: ( A / x+a ) + ( B / (x+a)2 )
- Quadratic Factors: ( Ax+B ) / ( x2+a2 )
3. Steps for Partial Fraction Decomposition
- Factorizing the denominator
- Setting up the equation using unknown constants
- Multiplying both sides by the denominator
- Solving for constants (A, B, C, etc.)
ECAT Mathematics Partial Fractions MCQs
1. An improper fraction can be reduced to a proper fraction by
- Subtraction
- Multiplication
- Divisions correct
- Addition
2. (x – 4)² =x² – 8x + 16 is
- Cubic equation
- A transcendental equation
- An identity correct
- An equation
3. Partial fractions of 1/x³+1 will be of the form
- Ax+B/x+1 + C/x²-x+1
- A/x-1 – B/x²-x+1
- A/x+1 – B/x²-x+1
- A/x+1 + Bx+C/x²-x+1 correct
4. A fraction in which the degree of the numerator is less than the degree of the denominator is called
- A proper fraction correct
- Equation
- An improper fraction
- Algebraic relation
5. The function of the form f (x) = p(x)/q(x), q(x) ≠ 0, where p(x) and q(x) are polynomials in x is called the
- Equation
- Identity
- Algebraic relation
- Fraction correct
6. x/(x+a)(x-a) =
- ½(x-a) + ½(x²+a) correct
- None of these
- ½(x²- a) + ½(x+a)
- ½(x-a) + ½(x²+a)
7. ax+b/(cx+d)(ex+f) =
- A/cx+d + B/ex+f correct
- None of these
- Ax+B/cx+d + C/ex+f
- A/cx+d + B/(ex+f)²
8. Partial fractions of 1/x³-1 will be of the form
- A/x-1 + Bx+C/x²+x+1 correct
- A/x-1 + B/x²+x+1
- A/x+1 + B/x²+x+1
- None of these
9. Partial fractions of 1/x²-1 are equivalent to
- B/x-1
- Ax+B/x²-1
- A/x+1
- A/x+1 + B/x-1 correct
10. To resolve a combined fraction into its parts is called
- Partial fraction correct
- Combined fraction
- None of these
- Rational fraction
11. Partial fractions of 1/(x+1)(x²-1) will be of the form
- A/x+1 + B/(x+1)² + C/x-1 correct
- None of these
- A/x+1 + B/x+1 + C/x-1
- A/x+1 + Bx+0/x²-1
12. A fraction in which the degree of the numerator is greater than or equal to the degree of the denominator is called:
- Algebraic relation
- An improper fraction correct
- Equation
- A proper fraction
13. A relation in which the equality is true for any value of unknowns is called an
- Identify correct
- Equation
- Algebraic equation
- Algebraic relation
The question was not answered
14. 1/(x-3)(x-2) =
- 1/x-3 – 1/x-2 correct
- 1/x²-3 – 1/x²-2
- 1/x+3 – 1/x+2
- 1/x² – 3 – 1/x-2
15. The rational fraction P(x)/Q(x) is a proper fraction if
- None of these
- Degree of Q(x) < degree of P(x)
- Degree of P(x) < degree of Q(x) correct
- Degree of P(x) = degree of Q(x)
16. ax+b/(cx+d)²=
- A/cx+d + B/(cx+d) ² correct
- None of these
- Ax+B/(cx+d)²
- A/cx+d + B/cx+d
17. The identity (x + 3)(x + 4) = x² + 7x + 12 is true for
- One values of x
- All values of x correct
- Two values of x
- None of these
18. The partial fraction of x + 5/(x – 1)(x² + 1) are of the form
- A/x – 1 + B/x² + 1
- A/x-1 + Bx+C/x² +1 correct
- None of these
- Ax/x-1 + B/x²+1
19. x+3/x(x+1) =
- 4/3(x-4) – 1/3(x-1)
- 3/x – 2/x+1 correct
- None of these
- 3/4(x+2) + 1/4(x-2)
20. x + 3/x = 4 is
- A transcendental equation
- An identity
- Cubic equation
- An equation correct
21. 1/(x²+5)(x²+4)=
- 1/x²+4 – 1/x² + 5 correct
- None of these
- 1/x²+4 – 1/x²- 5
- 1/x² – 4 – 1/x² + 5
22. A relation in which the equality is true only for a number of unknowns is called an:
- Equation correct
- Identity
- Algebraic equation
- Algebraic relation
23. (x + 2)² = x² + 4x + 4 is
- A linear equation
- Cubic equation
- An equation
- An identity correct
24. 1/(x+3)(x+2) =
- 1/x-3 – 1/x-2
- None of these
- 1/x²-3 – 1/x²-2
- 1/x + 3 – 1/x+2 correct
25. Partial fractions of 1/x²-4 will be of the form
- None of these
- A/x+2 + B/(x-2) ²
- A/x-2 + B/(x+2) ²
- A/x+2 + B/x-2 correct
Conclusion
Mastering Mathematics Partial Fractions is a key step toward excelling in ECAT Engineering Entry Test Mathematics. Understanding decomposition methods, solving algebraic fractions, and applying polynomial division techniques are essential for answering MCQs correctly.
For more ECAT practice questions, solved MCQs, and expert preparation guides, visit Nokryan.com and enhance your exam readiness with free study resources!