MHT CET PYQs for Integration by Parts with Solutions: Practice MHT CET Previous Year Questions

Integration by parts is a topic from Class 12 Mathematics, and it is part of the Mathematics section of the MHT CET for candidates who are preparing for the PCM (Physics, Chemistry, and Mathematics).

The key topics covered in Integration by parts PYQs are:

Indefinite integrals by parts
Definite integrals by parts
Integrals of logarithmic functions
Integrals with inverse trigonometric functions

Practising Integration by parts MHT CET PYQ helps candidates to understand question pattern, improve calculation speed, and identify concepts which were asked in previous exams.

Based on chapter-wise analysis of the MHT CET Mathematics paper, you can get about 1 mark per paper by covering Integration by parts. The chapter recorded 14 questions across the 80 shifts in the data, and 9 of them came in the 2025 and 2026 papers, which is fewer than 1 of the 50 Mathematics questions in a typical shift.

MHT CET Integration by parts Topic: Question Count, Marks and Weightage:

What it shows	Number
Questions in the PDF (2017-2026)	14
Questions in the 2025 and 2026 papers (33 shifts)	9
Questions in the 2018 to 2026 papers (80 shifts)	13
Typical number of Mathematics questions from this topic in one shift	Fewer than 1 out of 50
Marks for each question	2

The PDF holds 14 questions from MHT CET 2026 to 2017, newest first, each with its exam date and shift. Options are as printed and answer keys are not included.

Integration by parts PYQ Statistics (2022-2026)

The table below shows the number of questions asked in MHT CET Integration by parts PYQs. Every shift has 50 Mathematics questions, and the last column is the number of questions asked divided by the shifts held, rounded to a whole number.

Year	Questions Asked	Shifts Held	Typical Questions in One Shift
2026	6	16	Fewer than 1 out of 50
2025	3	17	Fewer than 1 out of 50
2024	1	18	Fewer than 1 out of 50
2023	0	12	Fewer than 1 out of 50
2022	0	1	Fewer than 1 out of 50

The 2018 to 2021 papers in the PDF add 3 more questions: 2021 had 2, 2020 had none, 2019 had none, 2018 had 1; the papers before 2018 add 1 from 2017.

Pair PYQs with Other Study Material for MHT CET 2027

Click on the link to practise problems and time management skills:

Resource	Link
MHT CET Sample Paper	Check Here
MHT CET Mock Test	Check Here

Question Style in MHT CET Integration by parts PYQs

Every question in this PDF is a single-correct MCQ. Each one asks for an integral that is solved by parts, and the answer is given with a constant of integration for indefinite integrals.

Question Style	What it Tests
Indefinite integrals	The integral of a product such as x cos x or x sin x, the integral of cos(log x) and the integral of x sec⁻¹ x
Definite integrals	The value of the integral of log(x + 1) from 0 to 1, and a definite integral of x with a trigonometric function between 0 and π/4
Integrals with e raised to a power	The value of the integral of (1 + x log x) eˣ type expressions between limits

How to Use the Integration by parts PYQ PDF for MHT CET

Start with the 2025 and 2026 papers first, because they hold 9 of the 14 questions.
Choose the first function in the order of inverse trigonometric, logarithmic, algebraic, trigonometric and exponential (ILATE).
Remember the formula for ∫eˣ[f(x) + f′(x)] dx, because it removes the need for repeated integration by parts.
Solve year-wise PYQs by timing yourself, as time management is crucial.
Re-attempt only the questions you got wrong, and note which formula or step you missed.

Video: Integration by parts PYQs and MCQs

Source: MATRIX SCIENCE ACADEMY

Integration by parts PYQ for MHT CET Mathematics FAQs

Ques. How many questions come from Integration by parts every year?

Ans. In this PDF, the questions are 6 from 2026, 3 from 2025, 1 from 2024, 2 from 2021 and 1 from 2018 and the rest from earlier papers. In 2025 and 2026 together the topic had 9 questions across 33 shifts, which is fewer than 1 in a typical shift.

Ques. What kind of questions are asked from Integration by parts?

Ans. Single-correct MCQs. Common ones ask for an indefinite integral of a product or a logarithmic function, or the value of a definite integral.

Ques. What is the best way to practise Integration by parts PYQs?

Ans. First solve the 2025 and 2026 questions completely, then the older ones, and finally re-attempt the questions you got wrong.

Ques. Can I score full marks from Integration by parts?

Ans. In 2025 and 2026 together the topic had 9 questions across 33 shifts. Learning the integration by parts formula and the ILATE rule is enough to secure it. Each Mathematics question in MHT CET is worth 2 marks.

Ques. Does the Integration by parts PYQ PDF include solutions?

Ans. No. The PDF contains the questions with their exam date and shift, without answer keys or solutions.

MHT CET PYQs for Integration by Parts with Solutions: Practice MHT CET Previous Year Questions

Integration by parts PYQ Statistics (2022-2026)

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Integration by parts PYQs

How to Use the Integration by parts PYQ PDF for MHT CET

Video: Integration by parts PYQs and MCQs

Integration by parts PYQ for MHT CET Mathematics FAQs

1.
Evaluate the integral: \[ \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \] (where \(C\) is a constant of integration)

2.
$\int x^{2}\cos x~dx=$

3.
\(\int \text{cosec}^{-1}(\sqrt{\frac{a+x}{x}})\,\text{d}x =\)

4.
\(\int \frac{logx}{(1+logx)^2}dx =\)

5.
\(\int sin(logx)\,dx =\)

6.
The value of integral \(\int x^3cosx\,dx\) is...

7.
\(\int (e^{log(sinx)}+cosx)x\,dx =\)

8.
The value of the integral \( \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \) is:

9.
If an antiderivative of \(f(x)\) is \(e^x\) and an antiderivative of \(g(x)\) is \(cosx\), then \(\int f(x)cosx\,dx+\int g(x)e^x\,dx =\)

10.
If \(f(x) = \frac{sin^{-1}x}{\sqrt{1-x^2}}\) and \(g(x) = e^{sin^{-1}x}\), then the value of \(\int f(x)g(x)\,dx = \ldots\)

11.
If \(f(x)\) and \(g(x)\) are integrable functions then \([\int f(x)dx][\int g(x)dx] =\)

12.
The value of integral \(\int \frac{\sqrt{x^2+1}\,[log(x^2+1)-2logx]}{x^4}\,dx\) is equal to...

13.
\(\int x^3logx\,dx =\)

14.
If \(\int x^2\cdot e^xdx = e^xf(x)+c\), then the minimum value of \(f(x)\) is ...

15.
$\int x^{2}\cos x~dx=$

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Integration by parts PYQ Statistics (2022-2026)

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Integration by parts PYQs

How to Use the Integration by parts PYQ PDF for MHT CET

Video: Integration by parts PYQs and MCQs

Integration by parts PYQ for MHT CET Mathematics FAQs

1.Evaluate the integral: \[ \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \] (where \(C\) is a constant of integration)

2.$\int x^{2}\cos x~dx=$

3.\(\int \text{cosec}^{-1}(\sqrt{\frac{a+x}{x}})\,\text{d}x =\)

4.\(\int \frac{logx}{(1+logx)^2}dx =\)

5.\(\int sin(logx)\,dx =\)

6.The value of integral \(\int x^3cosx\,dx\) is...

7.\(\int (e^{log(sinx)}+cosx)x\,dx =\)

8.The value of the integral \( \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \) is:

9.If an antiderivative of \(f(x)\) is \(e^x\) and an antiderivative of \(g(x)\) is \(cosx\), then \(\int f(x)cosx\,dx+\int g(x)e^x\,dx =\)

10.If \(f(x) = \frac{sin^{-1}x}{\sqrt{1-x^2}}\) and \(g(x) = e^{sin^{-1}x}\), then the value of \(\int f(x)g(x)\,dx = \ldots\)

11.If \(f(x)\) and \(g(x)\) are integrable functions then \([\int f(x)dx][\int g(x)dx] =\)

12.The value of integral \(\int \frac{\sqrt{x^2+1}\,[log(x^2+1)-2logx]}{x^4}\,dx\) is equal to...

13.\(\int x^3logx\,dx =\)

14.If \(\int x^2\cdot e^xdx = e^xf(x)+c\), then the minimum value of \(f(x)\) is ...

15.$\int x^{2}\cos x~dx=$

Comments

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1.
Evaluate the integral: \[ \int \frac{4x^2 \cot^{-1}(x^3)}{1+x^6}\,dx \] (where \(C\) is a constant of integration)

2.
$\int x^{2}\cos x~dx=$

3.
\(\int \text{cosec}^{-1}(\sqrt{\frac{a+x}{x}})\,\text{d}x =\)

4.
\(\int \frac{logx}{(1+logx)^2}dx =\)

5.
\(\int sin(logx)\,dx =\)

6.
The value of integral \(\int x^3cosx\,dx\) is...

7.
\(\int (e^{log(sinx)}+cosx)x\,dx =\)

8.
The value of the integral \( \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \) is:

9.
If an antiderivative of \(f(x)\) is \(e^x\) and an antiderivative of \(g(x)\) is \(cosx\), then \(\int f(x)cosx\,dx+\int g(x)e^x\,dx =\)

10.
If \(f(x) = \frac{sin^{-1}x}{\sqrt{1-x^2}}\) and \(g(x) = e^{sin^{-1}x}\), then the value of \(\int f(x)g(x)\,dx = \ldots\)

11.
If \(f(x)\) and \(g(x)\) are integrable functions then \([\int f(x)dx][\int g(x)dx] =\)

12.
The value of integral \(\int \frac{\sqrt{x^2+1}\,[log(x^2+1)-2logx]}{x^4}\,dx\) is equal to...

13.
\(\int x^3logx\,dx =\)

14.
If \(\int x^2\cdot e^xdx = e^xf(x)+c\), then the minimum value of \(f(x)\) is ...

15.
$\int x^{2}\cos x~dx=$