MHT CET PYQs for Limits with Solutions: Practice MHT CET Previous Year Questions

Limits is a Class 11 chapter in the Mathematics section of the MHT CET for candidates who are preparing for the PCM (Physics, Chemistry, and Mathematics).

The key topics covered in Limits PYQs are:

Standard limits: trigonometric, exponential and logarithmic
Algebraic limits and limits with surds
Limits at infinity
Limits of sums of series
Left hand and right hand limits of a modulus function

Practising Limits 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 2 marks per paper by covering Limits. The chapter recorded 67 questions across the 80 shifts in the data, and 31 of them came in the 2025 and 2026 papers, which is about 1 of the 50 Mathematics questions in a typical shift.

MHT CET Limits Chapter: Question Count, Marks and Weightage:

What it shows	Number
Questions in the PDF (2021-2026)	67
Questions in the 2025 and 2026 papers (33 shifts)	31
Questions in the 2018 to 2026 papers (80 shifts)	67
Typical number of Mathematics questions from this topic in one shift	About 1 out of 50
Marks for each question	2

The PDF holds 67 questions from MHT CET 2026 to 2021, newest first, each with its exam date and shift. Options are as printed and answer keys are not included.

Limits PYQ Statistics (2022-2026)

The table below shows the number of questions asked in MHT CET Limits 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	16	16	About 1 out of 50
2025	15	17	About 1 out of 50
2024	14	18	About 1 out of 50
2023	13	12	About 1 out of 50
2022	1	1	About 1 out of 50

The 2018 to 2021 papers in the PDF add 8 more questions: 2021 had 8, 2020 had none, 2019 had none, 2018 had none.

MHT CET Limits Important Questions: Topic-Wise Breakdown

The major types of questions asked from Limits in MHT CET cover the following topics:

Topic	Questions in the PDF	Share of the PDF
Standard limits	14	21%
Algebraic limits	8	12%
Standard limits trig	5	7%
Standard limits exponential	4	6%
Limits at infinity	3	4%
Limits of sums	2	3%
Modulus function limit	2	3%
Trigonometric Limits At Pi By Two	2	3%
Other topics tagged in the PDF	27	40%

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 Limits PYQs

Every question in this PDF is a single-correct MCQ. Each one asks for the value of a limit or of a constant that makes a limit exist.

Question Style	What it Tests
Trigonometric limits	The limit as x tends to 0 of expressions with 1 − cos 2x, x tan 2x − 2x tan x and sin x
Exponential and logarithmic limits	The limit of an expression such as log(1 + 2x) divided by a power of x, and the value of limits that contain e raised to a power
Limits at infinity	The limit of an expression with surds as x tends to infinity
Limits of sums	The limit as n tends to infinity of (1² + 2² + … + n²) divided by n³
Modulus function	The limit as x tends to 0 of an expression that contains \|x\|

How to Use the Limits PYQ PDF for MHT CET

Start with the 2025 and 2026 papers first, because they hold 31 of the 67 questions.
Memorise the standard limits for sin x / x, (eˣ − 1) / x and log(1 + x) / x as x tends to 0.
For limits at infinity with surds, multiply and divide by the conjugate before taking the limit.
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: Limits PYQs and MCQs

Source: PW MHT CET

Limits PYQ for MHT CET Mathematics FAQs

Ques. How many questions come from Limits every year?

Ans. In this PDF, the questions are 16 from 2026, 15 from 2025, 14 from 2024, 13 from 2023 and 1 from 2022 and the rest from earlier papers. In 2025 and 2026 together the chapter had 31 questions across 33 shifts, which is about 1 in a typical shift.

Ques. Which topics are asked most frequently in MHT CET Limits?

Ans. Standard limits is the largest topic tag in the PDF with 14 of the 67 questions, about 21%.

Ques. What kind of questions are asked from Limits?

Ans. Single-correct MCQs, mostly short calculations. Common ones ask for the value of a limit at 0 or at infinity, or the limit of a sum of a series.

Ques. What is the best way to practise Limits 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 Limits?

Ans. In 2025 and 2026 together the chapter had 31 questions across 33 shifts. Learning the standard limits and the rationalisation method is enough to secure it. Each Mathematics question in MHT CET is worth 2 marks.

Ques. Does the Limits 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 Limits with Solutions: Practice MHT CET Previous Year Questions

Limits PYQ Statistics (2022-2026)

MHT CET Limits Important Questions: Topic-Wise Breakdown

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Limits PYQs

How to Use the Limits PYQ PDF for MHT CET

Video: Limits PYQs and MCQs

Limits PYQ for MHT CET Mathematics FAQs

1.
If \(\underset{x\rightarrow 1}{lim}\frac{sin(3x^2-4x+1)-x^2+1}{2x^3-7x^2+ax+b} = -2\), then the quadratic equation having roots \(a\) and \(b\) is

2.
If \(\underset{x\rightarrow \infty }{lim}[\frac{x^2+x+1}{x+1}-ax-b] = 3\), then \(a-b =\)...

3.
\(\underset{x\rightarrow 0}{lim}\frac{(5^x-1)^4\,\text{cosec}\,(xlog5)}{tan(xlog5)\cdot log(1+x^2log25)} = \ldots \ldots\)

4.
\(\underset{x\rightarrow 0}{lim}[\frac{x\cdot log(1+4x)}{(e^{4x}-1)^2}] = \cdots\)

5.
If \(\underset{x\rightarrow 0}{lim}\frac{45^x-9^x-5^x+1}{(k^x-1)(3^x-1)} = 2\), then the value of \(k\) is ...

6.
The value of \(\underset{x\rightarrow 0}{lim}(\frac{8}{x^8})[1-cos\frac{x^2}{2}-cos\frac{x^2}{4}+cos\frac{x^2}{2}\cdot cos\frac{x^2}{4}]\) is equal to ...

7.
The quadratic polynomial \(p(x)\) has roots \(1\) and \(α\), while quadratic polynomial \(q(x)\) has roots \(1\) and \(β\). Let \(α\) and \(β\) be the roots of \(r(x) = p(x)+q(x)\). Then \(\underset{x\rightarrow \infty }{lim}[\sqrt{p(x)}-\sqrt{q(x)}] =\)

8.
If \(\underset{x\rightarrow k}{lim}\frac{x^3-k^3}{x^2-k^2} = \underset{x\rightarrow 0}{lim}\frac{1-cos(2x)}{xsinx}\), then the value of \(k\) is \(\ldots\)

9.
The value of \(\underset{n\rightarrow \infty }{lim}\frac{(n+2)!+(n+1)!}{(n+2)!-(n+1)!}\) is ____

10.
If \(\underset{x\rightarrow \infty }{lim}\frac{(2x-1)^{19}\cdot (3x+2)^{11}}{(6x-5)^{30}} = 2^a\cdot 3^b\), then \(a+b =\)

11.
If \(\underset{x\rightarrow 0}{lim}\frac{(4^x-1)^3}{tan(\frac{x}{4})log(1+\frac{x^2}{3})} = 96(loga)^b\), then \((a+b) =\)

12.
If \(A = \left[ \begin{array}{cc}1 & -tan\frac{θ}{2} \\ tan\frac{θ}{2} & 1\end{array} \right]\) and \(B = \left[ \begin{array}{cc}1 & tan\frac{θ}{2} \\ -tan\frac{θ}{2} & 1\end{array} \right]\) then \(A^{-1}B\) is equal to

13.
If \(\underset{x\rightarrow 1}{lim}\frac{x^3+ax^2+bx+c}{x^2-2x+1} = 2026\) then the value of \(a-c\) is...

14.
The value of \(\underset{n\rightarrow \infty }{lim}[\frac{1}{1-n^2}+\frac{2}{1-n^2}+\ldots +\frac{n}{1-n^2}]^3\) is

15.
\(\underset{x\rightarrow 0}{lim}[\frac{log|2+x|-log|2-x|}{tanx}] =\) .......

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Limits PYQ Statistics (2022-2026)

MHT CET Limits Important Questions: Topic-Wise Breakdown

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Limits PYQs

How to Use the Limits PYQ PDF for MHT CET

Video: Limits PYQs and MCQs

Limits PYQ for MHT CET Mathematics FAQs

1.If \(\underset{x\rightarrow 1}{lim}\frac{sin(3x^2-4x+1)-x^2+1}{2x^3-7x^2+ax+b} = -2\), then the quadratic equation having roots \(a\) and \(b\) is

2.If \(\underset{x\rightarrow \infty }{lim}[\frac{x^2+x+1}{x+1}-ax-b] = 3\), then \(a-b =\)...

3.\(\underset{x\rightarrow 0}{lim}\frac{(5^x-1)^4\,\text{cosec}\,(xlog5)}{tan(xlog5)\cdot log(1+x^2log25)} = \ldots \ldots\)

4.\(\underset{x\rightarrow 0}{lim}[\frac{x\cdot log(1+4x)}{(e^{4x}-1)^2}] = \cdots\)

5.If \(\underset{x\rightarrow 0}{lim}\frac{45^x-9^x-5^x+1}{(k^x-1)(3^x-1)} = 2\), then the value of \(k\) is ...

6.The value of \(\underset{x\rightarrow 0}{lim}(\frac{8}{x^8})[1-cos\frac{x^2}{2}-cos\frac{x^2}{4}+cos\frac{x^2}{2}\cdot cos\frac{x^2}{4}]\) is equal to ...

7.The quadratic polynomial \(p(x)\) has roots \(1\) and \(α\), while quadratic polynomial \(q(x)\) has roots \(1\) and \(β\). Let \(α\) and \(β\) be the roots of \(r(x) = p(x)+q(x)\). Then \(\underset{x\rightarrow \infty }{lim}[\sqrt{p(x)}-\sqrt{q(x)}] =\)

8.If \(\underset{x\rightarrow k}{lim}\frac{x^3-k^3}{x^2-k^2} = \underset{x\rightarrow 0}{lim}\frac{1-cos(2x)}{xsinx}\), then the value of \(k\) is \(\ldots\)

9.The value of \(\underset{n\rightarrow \infty }{lim}\frac{(n+2)!+(n+1)!}{(n+2)!-(n+1)!}\) is ____

10.If \(\underset{x\rightarrow \infty }{lim}\frac{(2x-1)^{19}\cdot (3x+2)^{11}}{(6x-5)^{30}} = 2^a\cdot 3^b\), then \(a+b =\)

11.If \(\underset{x\rightarrow 0}{lim}\frac{(4^x-1)^3}{tan(\frac{x}{4})log(1+\frac{x^2}{3})} = 96(loga)^b\), then \((a+b) =\)

12.If \(A = \left[ \begin{array}{cc}1 & -tan\frac{θ}{2} \\ tan\frac{θ}{2} & 1\end{array} \right]\) and \(B = \left[ \begin{array}{cc}1 & tan\frac{θ}{2} \\ -tan\frac{θ}{2} & 1\end{array} \right]\) then \(A^{-1}B\) is equal to

13.If \(\underset{x\rightarrow 1}{lim}\frac{x^3+ax^2+bx+c}{x^2-2x+1} = 2026\) then the value of \(a-c\) is...

14.The value of \(\underset{n\rightarrow \infty }{lim}[\frac{1}{1-n^2}+\frac{2}{1-n^2}+\ldots +\frac{n}{1-n^2}]^3\) is

15.\(\underset{x\rightarrow 0}{lim}[\frac{log|2+x|-log|2-x|}{tanx}] =\) .......

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1.
If \(\underset{x\rightarrow 1}{lim}\frac{sin(3x^2-4x+1)-x^2+1}{2x^3-7x^2+ax+b} = -2\), then the quadratic equation having roots \(a\) and \(b\) is

2.
If \(\underset{x\rightarrow \infty }{lim}[\frac{x^2+x+1}{x+1}-ax-b] = 3\), then \(a-b =\)...

3.
\(\underset{x\rightarrow 0}{lim}\frac{(5^x-1)^4\,\text{cosec}\,(xlog5)}{tan(xlog5)\cdot log(1+x^2log25)} = \ldots \ldots\)

4.
\(\underset{x\rightarrow 0}{lim}[\frac{x\cdot log(1+4x)}{(e^{4x}-1)^2}] = \cdots\)

5.
If \(\underset{x\rightarrow 0}{lim}\frac{45^x-9^x-5^x+1}{(k^x-1)(3^x-1)} = 2\), then the value of \(k\) is ...

6.
The value of \(\underset{x\rightarrow 0}{lim}(\frac{8}{x^8})[1-cos\frac{x^2}{2}-cos\frac{x^2}{4}+cos\frac{x^2}{2}\cdot cos\frac{x^2}{4}]\) is equal to ...

7.
The quadratic polynomial \(p(x)\) has roots \(1\) and \(α\), while quadratic polynomial \(q(x)\) has roots \(1\) and \(β\). Let \(α\) and \(β\) be the roots of \(r(x) = p(x)+q(x)\). Then \(\underset{x\rightarrow \infty }{lim}[\sqrt{p(x)}-\sqrt{q(x)}] =\)

8.
If \(\underset{x\rightarrow k}{lim}\frac{x^3-k^3}{x^2-k^2} = \underset{x\rightarrow 0}{lim}\frac{1-cos(2x)}{xsinx}\), then the value of \(k\) is \(\ldots\)

9.
The value of \(\underset{n\rightarrow \infty }{lim}\frac{(n+2)!+(n+1)!}{(n+2)!-(n+1)!}\) is ____

10.
If \(\underset{x\rightarrow \infty }{lim}\frac{(2x-1)^{19}\cdot (3x+2)^{11}}{(6x-5)^{30}} = 2^a\cdot 3^b\), then \(a+b =\)

11.
If \(\underset{x\rightarrow 0}{lim}\frac{(4^x-1)^3}{tan(\frac{x}{4})log(1+\frac{x^2}{3})} = 96(loga)^b\), then \((a+b) =\)

12.
If \(A = \left[ \begin{array}{cc}1 & -tan\frac{θ}{2} \\ tan\frac{θ}{2} & 1\end{array} \right]\) and \(B = \left[ \begin{array}{cc}1 & tan\frac{θ}{2} \\ -tan\frac{θ}{2} & 1\end{array} \right]\) then \(A^{-1}B\) is equal to

13.
If \(\underset{x\rightarrow 1}{lim}\frac{x^3+ax^2+bx+c}{x^2-2x+1} = 2026\) then the value of \(a-c\) is...

14.
The value of \(\underset{n\rightarrow \infty }{lim}[\frac{1}{1-n^2}+\frac{2}{1-n^2}+\ldots +\frac{n}{1-n^2}]^3\) is

15.
\(\underset{x\rightarrow 0}{lim}[\frac{log|2+x|-log|2-x|}{tanx}] =\) .......