### Mathematics Partial Fractions MCQS Online Preparation Sample Paper Questions with Answer

MCQs on Partial Fractions in Mathematics test the ability to break down complex fractions into simpler ones. These types of questions are frequently seen in exams such as ECAT (Engineering College Admission Test). The sample paper questions encompass different elements of Partial Fractions, covering decomposition methods and solution strategies. Nokryan.com, an online platform, provides extensive preparation resources, including sample papers, practice questions, and detailed answers, to support students in excelling in this subject.

1. An improper fraction can be reduced to 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

- Identity
**correct** - Equation
- Algebraic equation
- Algebraic relation

Question was not answered14. 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**