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JEE • MATHEMATICS • PARTIAL FRACTIONS

Partial fractions practice · Mixed difficulty

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Easy

1 of 11

Application +4 | -1

If a real valued function

f

of a real variable

x

is such that

\frac{1}{{\left( {1 + x} \right)\left( {1 + {x^2}} \right)}} = \frac{A}{{1 + x}} + \frac{{f\left( x \right)}}{{1 + {x^2}}}

then

f\left( x \right)

is equal to

View answer and explanation

Correct option: A

\frac{{1 - x}}{2}

Option A (

\frac{{1 - x}}{2}

) is correct because by performing partial fraction decomposition, we can find the function

f(x)

that satisfies the given equation.

2 Easy

2 of 11

Analyzing +4 | -1

\frac{{{x^3}}}{{\left( {2x - 1} \right)\left( {x + 2} \right)\left( {x - 3} \right)}} = A + \frac{B}{{2x - 1}} + \frac{C}{{x + 2}} + \frac{D}{{x - 3}}

, then

A

is equal to

View answer and explanation

Correct option: A

\frac{1}{2}

Option C (

{x^3} + 4x - 1 = 0

) is correct because it is derived from transforming the roots of the original equation and using Vieta's formulas.

3 Easy

3 of 11

Analyzing +4 | -1

\frac{{{x^2} + x + 1}}{{{x^2} + 2x + 1}} = A + \frac{B}{{x + 1}} + \frac{C}{{{{\left( {x + 1} \right)}^2}}}

, then

A - B

is equal to

View answer and explanation

Correct option: D

2C

The correct answer is D (

2C

) because after simplifying the given equation and comparing coefficients, we find that

A - B = 2C

4 Medium

4 of 11

Application +4 | -1

\frac{{x - 4}}{{{x^2} - 5x + 6}}

can be expanded in the ascending powers of

x

, then the coeficient of

{x^3}

View answer and explanation

Correct option: A

- \frac{{73}}{{648}}

Option A ( - 73/648) is correct because it is the coefficient of x³ in the expansion of the given expression.

5 Easy

5 of 11

Application +4 | -1

Let

a,b

and

c

be such that

\frac{1}{{\left( {1 - x} \right)\left( {1 - 2x} \right)\left( {1 - 3x} \right)}} = \frac{a}{{1 - x}} + \frac{b}{{1 - 2x}} + \frac{c}{{1 - 3x}}

then

\frac{a}{1} + \frac{b}{3} + \frac{c}{5}

is equal to

View answer and explanation

Correct option: A

\frac{1}{{15}}

Option A (

\frac{1}{{15}}

) is correct because it is the result of partial fraction decomposition and subsequent substitution to find the value of the expression.

6 Easy

6 of 11

Analyzing +4 | -1

\frac{{3{x^2} + 1}}{{{x^2} - 6x + 8}}

is equal to

View answer and explanation

Correct option: A

3 + \frac{{49}}{{2\left( {x - 4} \right)}} - \frac{{13}}{{2\left( {x - 2} \right)}}

Option A (

3 + \frac{{49}}{{2\left( {x - 4} \right)}} - \frac{{13}}{{2\left( {x - 2} \right)}}

) is correct because it is the result of polynomial long division and partial fraction decomposition.

7 Easy

7 of 11

Application +4 | -1

The partial fractions of

\frac{3 x^{3}-8 x^{2}+10}{(x-1)^{4}}

View answer and explanation

Correct option: C

\frac{3}{(x-1)}+\frac{1}{(x-1)^{2}}-\frac{7}{(x-1)^{3}}+\frac{5}{(x-1)^{4}}

Option B (

\frac{3}{(x-1)}+\frac{1}{(x-1)^{2}}-\frac{7}{(x-1)^{3}}+\frac{5}{(x-1)^{4}}

) is correct because it represents the correct partial fraction decomposition of the given expression.

8 Easy

8 of 11

Application +4 | -1

The partial fraction of

\frac{{3{x^3} - 8{x^2} + 10}}{{{{\left( {x - 1} \right)}^4}}}

View answer and explanation

Correct option: B

\frac{3}{{\left( {x - 1} \right)}} + \frac{1}{{{{\left( {x - 1} \right)}^2}}} - \frac{7}{{{{\left( {x - 1} \right)}^3}}} + \frac{5}{{{{\left( {x - 1} \right)}^4}}}

Option B (

\frac{3}{{\left( {x - 1} \right)}} + \frac{1}{{{{\left( {x - 1} \right)}^2}}} - \frac{7}{{{{\left( {x - 1} \right)}^3}}} + \frac{5}{{{{\left( {x - 1} \right)}^4}}}

) is correct because it represents the correct partial fraction decomposition of the given expression.

9 Easy

9 of 11

Application +4 | -1

\frac{{3x + 2}}{{\left( {x + 1} \right)\left( {2{x^2} + 3} \right)}} = \frac{A}{{x + 1}} + \frac{{Bx + C}}{{2{x^2} + 3}}

, then

A + C - B

is equal to

View answer and explanation

Correct option: B

Option B (2) is correct because solving for A, B, and C and then calculating A + C - B results in 2.

10 Easy

10 of 11

Analyzing +4 | -1

\frac{{3x}}{{\left( {x - a} \right)\left( {x - b} \right)}} = \frac{2}{{x - a}} + \frac{1}{{x - b}}

, then

a:b

is equal to

View answer and explanation

Correct option: B

- 2:1

Option B (

- 2:1

) is correct because solving for a and b by comparing coefficients leads to the ratio a:b = -2:1.

11 Easy

11 of 11

Application +4 | -1

\frac{{\left( {x + 1} \right)}}{{\left( {2x - 1} \right)\left( {3x + 1} \right)}} = \frac{A}{{\left( {2x - 1} \right)}} + \frac{B}{{\left( {3x + 1} \right)}}

, then

16A + 9B

is equal to

View answer and explanation

Correct option: C

Option C (6) is correct because after performing partial fraction decomposition and solving for A and B, substituting these values into 16A + 9B yields 6.

Revision notes and key takeaways

Review PARTIAL FRACTIONS in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 11 single-correct-answer MCQs on PARTIAL FRACTIONS.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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