Class 10 Maths Chapter 4 Partial Fractions MCQs - MCQs

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Practice Class 10 Maths Chapter 4 MCQs (Partial Fractions) based on FBISE pattern. These multiple choice questions help students prepare for board exams with conceptual and exam-oriented practice.

These Class 10 Maths Chapter 4 Partial Fractions MCQs are designed according to the FBISE syllabus. This chapter focuses on decomposition of rational expressions into partial fractions.

Students can use these MCQs to practice solving problems and prepare for exams. Answers are included to help with quick revision.

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1. A rational expression is:

A) Polynomial B) Ratio of two polynomials C) Integer D) Fraction of numbers

2. Partial fractions are used to:

A) Multiply expressions B) Simplify rational expressions C) Factor numbers D) Solve equations only

3. For decomposition, degree of numerator must be:

A) Greater than denominator B) Equal to denominator C) Less than denominator D) Zero always

4. If degree of numerator is higher, we use:

A) Addition B) Division C) Subtraction D) Factorization

5. (x+1)(x+2) are:

A) Repeated factors B) Linear distinct factors C) Quadratic factor D) Constant

6. For distinct linear factors, form is:

A) A/(x+a) B) A/(x+a) + B/(x+b) C) A + B D) ax + b

7. If factor repeats, form becomes:

A) A/(x+a) B) A/(x+a)² C) A/(x+a) + B/(x+a)² D) None

8. Irreducible quadratic factor is:

A) Factorable B) Cannot be factorized C) Linear D) Constant

9. For quadratic factor, numerator is:

A) Constant B) Linear expression C) Quadratic D) Zero

10. Cover-up method is used when:

A) Factors are distinct B) Repeated factors C) Quadratic factor D) Always

11. Partial fractions help in:

A) Integration B) Simplification C) Solving equations D) All of these

12. Degree condition ensures:

A) Proper fraction B) Improper fraction C) Polynomial D) None

13. A/(x−1) + B/(x−2) represents:

A) Quadratic factor B) Linear distinct C) Repeated D) Constant

14. (x+1)² is:

A) Distinct B) Repeated C) Linear D) Constant

15. Numerator for linear factor is:

A) Constant B) Linear C) Quadratic D) None

16. Partial fractions are:

A) Unique B) Non-unique C) Infinite D) Undefined

17. If denominator has 3 distinct linear factors, constants required are:

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

18. $x^2 + 1$ is:

A) Reducible B) Irreducible quadratic C) Linear D) Constant

19. Partial fractions simplify:

A) Division B) Multiplication C) Rational expressions D) Roots

20. Common methods to find constants are:

A) Comparison B) Cover-up C) Both A and B D) None

21. If denominator is (x−1)(x−2)(x−3), decomposition has:

A) 1 term B) 2 terms C) 3 terms D) 4 terms

22. Proper rational function means:

A) Degree numerator ≥ denominator B) Degree numerator < denominator C) Equal degrees D) None

23. Improper rational function is reduced by:

A) Addition B) Division C) Subtraction D) Multiplication

24. For (x−1)², partial fractions are:

A) A/(x−1) B) A/(x−1)² C) A/(x−1) + B/(x−1)² D) None

25. Numerator for irreducible quadratic is:

A) Constant B) Linear (Ax + B) C) Quadratic D) Zero

26. For (x−1)³, number of terms is:

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

27. Degree of numerator in (Ax + B) is:

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

28. Cover-up method is NOT suitable for:

A) Distinct factors B) Repeated factors C) Linear factors D) Simple expressions

29. Decomposition depends mainly on:

A) Numerator B) Denominator C) Constants D) Variables

30. Number of partial fractions equals:

A) Degree of numerator B) Number of factors C) Constant D) Roots only

31. If denominator has irreducible quadratic factor, numerator is:

A) Constant B) Linear expression C) Quadratic D) Zero

32. $x^2 + 4$ is:

A) Reducible B) Irreducible quadratic C) Linear D) Constant

33. Partial fractions are useful in integration of:

A) Polynomials B) Rational functions C) Integers D) Roots

34. Decomposition depends on:

A) Numerator B) Denominator C) Constants D) Variables

35. If denominator has repeated factors, we use:

A) Cover-up method B) Repeated factor form C) Division only D) Graph method

36. For linear factor, numerator is:

A) Constant B) Linear C) Quadratic D) Zero

37. Degree condition ensures uniqueness of:

A) Constants B) Variables C) Functions D) Roots

38. Example of rational function is:

A) $x^2 + 1$ B) $\frac{x+1}{x^2+1}$ C) $\sqrt{x}$ D) $\sin x$

39. Partial fractions simplify calculations of:

A) Limits B) Integrals C) Algebra D) All of these

40. Factorization is required before:

A) Addition B) Decomposition C) Division D) Multiplication

41. If denominator is prime (not factorable), decomposition is:

A) Possible B) Not possible C) Infinite D) Constant

42. Constants are found using:

A) Guessing B) Comparing coefficients C) Graphing D) Random method

43. Number of equations equals number of:

A) Roots B) Degrees C) Constants D) Variables

44. Partial fractions convert:

A) Complex fraction into simpler ones B) Simple into complex C) Integers into fractions D) Roots into numbers

45. Main purpose of partial fractions is:

A) Simplification B) Expansion C) Multiplication D) Division

46. Partial fraction decomposition is:

A) Exact method B) Approximation C) Guessing D) Random

47. If denominator has two distinct factors, constants required are:

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

48. Cover-up method is fastest for:

A) Repeated factors B) Distinct linear factors C) Quadratic factors D) Complex expressions

49. Repeated factors require:

A) One term B) Multiple terms C) No decomposition D) Constant only

50. First step in partial fractions is:

A) Factorize denominator B) Integrate C) Multiply D) Add fractions

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