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Previous year question hub

Differentiation - Calculus - Mathematics Previous Year Questions

Practice Differentiation - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

60Papers
7Years
164Questions
1Topics

Differentiation question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Differentiation. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 164 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 164 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
164 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
164 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differentiation
164 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

MHT CET 2025 19TH APRIL EVENING SHIFT
3 Qs
MHT CET 2025 20TH APRIL EVENING SHIFT
3 Qs
MHT CET 2025 20TH APRIL MORNING SHIFT
3 Qs
MHT CET 2025 21ST APRIL MORNING SHIFT
3 Qs
MHT CET 2025 23RD APRIL EVENING SHIFT
3 Qs
MHT CET 2025 23RD APRIL MORNING SHIFT
3 Qs
MHT CET 2025 19TH APRIL MORNING SHIFT
2 Qs
MHT CET 2025 21ST APRIL EVENING SHIFT
2 Qs
MHT CET 2025 22ND APRIL EVENING SHIFT
2 Qs
MHT CET 2025 22ND APRIL MORNING SHIFT
2 Qs
MHT CET 2025 25TH APRIL EVENING SHIFT
2 Qs
MHT CET 2025 26TH APRIL EVENING SHIFT
2 Qs
MHT CET 2025 26TH APRIL MORNING SHIFT
2 Qs
MHT CET 2025 5TH MAY EVENING SHIFT
2 Qs
MHT CET 2025 25TH APRIL MORNING SHIFT
1 Qs
MHT CET 2024 10TH MAY MORNING SHIFT
4 Qs
MHT CET 2024 15TH MAY EVENING SHIFT
4 Qs
MHT CET 2024 2ND MAY EVENING SHIFT
4 Qs
MHT CET 2024 10TH MAY EVENING SHIFT
3 Qs
MHT CET 2024 11TH MAY EVENING SHIFT
3 Qs
MHT CET 2024 11TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 15TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 2ND MAY MORNING SHIFT
3 Qs
MHT CET 2024 3RD MAY MORNING SHIFT
3 Qs
MHT CET 2024 9TH MAY EVENING SHIFT
3 Qs
MHT CET 2024 9TH MAY MORNING SHIFT
3 Qs
MHT CET 2024 16TH MAY EVENING SHIFT
2 Qs
MHT CET 2024 16TH MAY MORNING SHIFT
2 Qs
MHT CET 2024 3RD MAY EVENING SHIFT
2 Qs
MHT CET 2024 4TH MAY MORNING SHIFT
2 Qs
MHT CET 2024 4TH MAY EVENING SHIFT
1 Qs
MHT CET 2023 12TH MAY MORNING SHIFT
5 Qs
MHT CET 2023 10TH MAY EVENING SHIFT
4 Qs
MHT CET 2023 11TH MAY EVENING SHIFT
4 Qs
MHT CET 2023 14TH MAY EVENING SHIFT
4 Qs
MHT CET 2023 9TH MAY MORNING SHIFT
4 Qs
MHT CET 2023 10TH MAY MORNING SHIFT
3 Qs
MHT CET 2023 11TH MAY MORNING SHIFT
3 Qs
MHT CET 2023 12TH MAY EVENING SHIFT
3 Qs
MHT CET 2023 13TH MAY EVENING SHIFT
3 Qs
MHT CET 2023 13TH MAY MORNING SHIFT
3 Qs
MHT CET 2023 14TH MAY MORNING SHIFT
3 Qs
MHT CET 2023 9TH MAY EVENING SHIFT
3 Qs
MHT CET 2022 11TH AUGUST EVENING SHIFT
3 Qs
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT
3 Qs
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT
3 Qs
MHT CET 2021 21TH SEPTEMBER MORNING SHIFT
3 Qs
MHT CET 2021 23RD SEPTEMBER EVENING SHIFT
3 Qs
MHT CET 2021 23th September Morning Shift
3 Qs
MHT CET 2021 24TH SEPTEMBER EVENING SHIFT
3 Qs
MHT CET 2021 21TH SEPTEMBER EVENING SHIFT
2 Qs
MHT CET 2021 22TH SEPTEMBER EVENING SHIFT
2 Qs
MHT CET 2021 22TH SEPTEMBER MORNING SHIFT
2 Qs
MHT CET 2021 24TH SEPTEMBER MORNING SHIFT
2 Qs
MHT CET 2020 16TH OCTOBER MORNING SHIFT
3 Qs
MHT CET 2020 19TH OCTOBER EVENING SHIFT
3 Qs
MHT CET 2020 16TH OCTOBER EVENING SHIFT
1 Qs
MHT CET 2019 2ND MAY EVENING SHIFT
2 Qs
MHT CET 2019 2ND MAY MORNING SHIFT
2 Qs
MHT CET 2019 3RD MAY MORNING SHIFT
2 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
MHT CET 2025 19TH APRIL EVENING SHIFT20253View paper
MHT CET 2025 19TH APRIL MORNING SHIFT20252View paper
MHT CET 2025 20TH APRIL EVENING SHIFT20253View paper
MHT CET 2025 20TH APRIL MORNING SHIFT20253View paper
MHT CET 2025 21ST APRIL EVENING SHIFT20252View paper
MHT CET 2025 21ST APRIL MORNING SHIFT20253View paper
MHT CET 2025 22ND APRIL EVENING SHIFT20252View paper
MHT CET 2025 22ND APRIL MORNING SHIFT20252View paper
MHT CET 2025 23RD APRIL EVENING SHIFT20253View paper
MHT CET 2025 23RD APRIL MORNING SHIFT20253View paper
MHT CET 2025 25TH APRIL EVENING SHIFT20252View paper
MHT CET 2025 25TH APRIL MORNING SHIFT20251View paper
MHT CET 2025 26TH APRIL EVENING SHIFT20252View paper
MHT CET 2025 26TH APRIL MORNING SHIFT20252View paper
MHT CET 2025 5TH MAY EVENING SHIFT20252View paper
MHT CET 2024 10TH MAY EVENING SHIFT20243View paper
MHT CET 2024 10TH MAY MORNING SHIFT20244View paper
MHT CET 2024 11TH MAY EVENING SHIFT20243View paper
MHT CET 2024 11TH MAY MORNING SHIFT20243View paper
MHT CET 2024 15TH MAY EVENING SHIFT20244View paper
MHT CET 2024 15TH MAY MORNING SHIFT20243View paper
MHT CET 2024 16TH MAY EVENING SHIFT20242View paper
MHT CET 2024 16TH MAY MORNING SHIFT20242View paper
MHT CET 2024 2ND MAY EVENING SHIFT20244View paper
MHT CET 2024 2ND MAY MORNING SHIFT20243View paper
MHT CET 2024 3RD MAY EVENING SHIFT20242View paper
MHT CET 2024 3RD MAY MORNING SHIFT20243View paper
MHT CET 2024 4TH MAY EVENING SHIFT20241View paper
MHT CET 2024 4TH MAY MORNING SHIFT20242View paper
MHT CET 2024 9TH MAY EVENING SHIFT20243View paper
MHT CET 2024 9TH MAY MORNING SHIFT20243View paper
MHT CET 2023 10TH MAY EVENING SHIFT20234View paper
MHT CET 2023 10TH MAY MORNING SHIFT20233View paper
MHT CET 2023 11TH MAY EVENING SHIFT20234View paper
MHT CET 2023 11TH MAY MORNING SHIFT20233View paper
MHT CET 2023 12TH MAY EVENING SHIFT20233View paper
MHT CET 2023 12TH MAY MORNING SHIFT20235View paper
MHT CET 2023 13TH MAY EVENING SHIFT20233View paper
MHT CET 2023 13TH MAY MORNING SHIFT20233View paper
MHT CET 2023 14TH MAY EVENING SHIFT20234View paper
MHT CET 2023 14TH MAY MORNING SHIFT20233View paper
MHT CET 2023 9TH MAY EVENING SHIFT20233View paper
MHT CET 2023 9TH MAY MORNING SHIFT20234View paper
MHT CET 2022 11TH AUGUST EVENING SHIFT20223View paper
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT20213View paper
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT20213View paper
MHT CET 2021 21TH SEPTEMBER EVENING SHIFT20212View paper
MHT CET 2021 21TH SEPTEMBER MORNING SHIFT20213View paper
MHT CET 2021 22TH SEPTEMBER EVENING SHIFT20212View paper
MHT CET 2021 22TH SEPTEMBER MORNING SHIFT20212View paper
MHT CET 2021 23RD SEPTEMBER EVENING SHIFT20213View paper
MHT CET 2021 23th September Morning Shift20213View paper
MHT CET 2021 24TH SEPTEMBER EVENING SHIFT20213View paper
MHT CET 2021 24TH SEPTEMBER MORNING SHIFT20212View paper
MHT CET 2020 16TH OCTOBER EVENING SHIFT20201View paper
MHT CET 2020 16TH OCTOBER MORNING SHIFT20203View paper
MHT CET 2020 19TH OCTOBER EVENING SHIFT20203View paper
MHT CET 2019 2ND MAY EVENING SHIFT20192View paper
MHT CET 2019 2ND MAY MORNING SHIFT20192View paper
MHT CET 2019 3RD MAY MORNING SHIFT20192View paper

All Differentiation previous year questions

Practice every matching question in batches of 20, with every available option.

1
2019 · Mathematics · Calculus · Differentiation
MHT CET 2019 2ND MAY EVENING SHIFT

If $x=\sin \theta, y=\sin ^3 \theta$ then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{2}$ is ............

A
3
B
6
C
$\frac{1}{6}$
D
$\frac{1}{3}$
Open complete paper
2
2019 · Mathematics · Calculus · Differentiation
MHT CET 2019 2ND MAY EVENING SHIFT

If $x^y=e^{x-y}$, then $\frac{d y}{d x}$ at $x=1$ is ...........

A
$e$
B
1
C
0
D
$-$1
Open complete paper
3
2019 · Mathematics · Calculus · Differentiation
MHT CET 2019 2ND MAY MORNING SHIFT

If $x=\sqrt{a^{\sin ^{-1} t}}, y=\sqrt{a^{\cos ^{-1} t}}$, then $\frac{d y}{d x}=\ldots .$.

A
$\frac{-y}{x}$
B
$\frac{x}{y}$
C
$\frac{y}{x}$
D
$\frac{-x}{y}$
Open complete paper
4
2019 · Mathematics · Calculus · Differentiation
MHT CET 2019 2ND MAY MORNING SHIFT

Derivative of $\log _{e^2}(\log x)$ with respect to $x$ is

A
$\frac{2}{x \log x}$
B
$\frac{1}{x \log x}$
C
$\frac{1}{x \cdot \log x^2}$
D
$\frac{2}{\log x}$
Open complete paper
5
2019 · Mathematics · Calculus · Differentiation
MHT CET 2019 3RD MAY MORNING SHIFT

If $y=\tan ^{-1}\left(\frac{1-\cos 3 x}{\sin 3 x}\right)$, then $\frac{d y}{d x}=$ .......

A
$-\frac{3}{2}$
B
$-\frac{1}{2}$
C
$\frac{3}{2}$
D
$\frac{1}{2}$
Open complete paper
6
2019 · Mathematics · Calculus · Differentiation
MHT CET 2019 3RD MAY MORNING SHIFT

If $y=\log \left[\frac{x+\sqrt{x^2+25}}{\sqrt{x^2+25}-x}\right]$ then $\frac{d y}{d x}=\ldots \ldots$

A
$\frac{1}{\sqrt{x^2+25}}$
B
$\frac{2}{\sqrt{x^2+25}}$
C
$\frac{-1}{\sqrt{x^2+25}}$
D
$\frac{-2}{\sqrt{x^2+25}}$
Open complete paper
7
2020 · Mathematics · Calculus · Differentiation
MHT CET 2020 16TH OCTOBER EVENING SHIFT

If \(f(x)=\sin ^{-1}\left(\sqrt{\frac{1-x}{2}}\right)\), then \(f^{\prime}(x)=\)

A
\(\frac{1}{2 \sqrt{1+x^2}}\)
B
\(\frac{-1}{2 \sqrt{1+x^2}}\)
C
\(\frac{1}{\sqrt{1-x^2}}\)
D
\(\frac{-1}{2 \sqrt{1-x^2}}\)
Open complete paper
8
2020 · Mathematics · Calculus · Differentiation
MHT CET 2020 16TH OCTOBER MORNING SHIFT

If \(f(x)=\log (\sec x+\tan x)\), then \(f^{\prime}\left(\frac{\pi}{4}\right)=\)

A
\(\frac{1}{\sqrt{2}}\)
B
\(\sqrt{2}\)
C
1
D
\(\frac{2}{\sqrt{3}}\)
Open complete paper
9
2020 · Mathematics · Calculus · Differentiation
MHT CET 2020 16TH OCTOBER MORNING SHIFT

If \(\frac{x}{\sqrt{1+x}}+\frac{y}{\sqrt{1+y}}=0, x \neq y\), then \((1+x)^2 \frac{d y}{d x}=\)

A
1
B
\(\frac{1}{2}\)
C
\(-\)1
D
0
Open complete paper
10
2020 · Mathematics · Calculus · Differentiation
MHT CET 2020 16TH OCTOBER MORNING SHIFT

If \(\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=4\), then \(\frac{d y}{d x}=\)

A
\(\frac{7 y-x}{y-7 x}\)
B
\(\frac{y-7 x}{7 x-y}\)
C
\(\frac{y+7 x}{7 y-x}\)
D
\(\frac{7 x+y}{x-7 y}\)
Open complete paper
11
2020 · Mathematics · Calculus · Differentiation
MHT CET 2020 19TH OCTOBER EVENING SHIFT

If $x=a \sin t-b \cos t, y=a \cos t+b \sin t$, then $y^3 \frac{d^2 y}{d x^2}+x^2+y^2=$

A
2
B
1
C
0
D
$-$1
Open complete paper
12
2020 · Mathematics · Calculus · Differentiation
MHT CET 2020 19TH OCTOBER EVENING SHIFT

If $y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]$, then $\frac{d y}{d x}=$

A
$\left(\frac{1}{4}\right) \frac{1}{\sqrt{x^2-1}}$
B
$\left(-\frac{1}{2}\right) \frac{1}{\sqrt{x^2-1}}$
C
$\left(-\frac{1}{2}\right) \frac{1}{\sqrt{1-x^2}}$
D
$\left(\frac{1}{4}\right) \frac{1}{\sqrt{1-x^2}}$
Open complete paper
13
2020 · Mathematics · Calculus · Differentiation
MHT CET 2020 19TH OCTOBER EVENING SHIFT

If $x^2 y^2=\sin ^{-1} \sqrt{x^2+y^2}+\cos ^{-1} \sqrt{x^2+y^2}$ then $\frac{d y}{d x}=$

A
$\frac{-x}{y}$
B
$\frac{x}{y}$
C
$\frac{-y}{x}$
D
$\frac{y}{x}$
Open complete paper
14
2021 · Mathematics · Calculus · Differentiation
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT

If \(x=a(t+\sin t), y=a(1-\cos t)\), then \(\frac{d y}{d x}=\)

A
\(\tan \frac{t}{2}\)
B
\(-\frac{1}{2} \tan \mathrm{t}\)
C
\(\frac{1}{2} \tan \mathrm{t}\)
D
\(-\tan \frac{t}{2}\)
Open complete paper
15
2021 · Mathematics · Calculus · Differentiation
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT

\(y=\sqrt{e^{\sqrt{x}}}\), then \(\frac{d y}{d x}=\)

A
\(\frac{e^{\sqrt{x}}}{4 \sqrt{x}}\)
B
\(\frac{\mathrm{e}^{\sqrt{x}}}{4 x}\)
C
\(\frac{e^{\frac{\sqrt{x}}{2}}}{4 \sqrt{x}}\)
D
\(\frac{e^{\sqrt{x}}}{2 \sqrt{x}}\)
Open complete paper
16
2021 · Mathematics · Calculus · Differentiation
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT

If \(y=\sin ^{-1}\left[\cos \sqrt{\frac{1+x}{2}}\right]+x^x\), then \(\frac{d y}{d x}\) at \(x=1\) is

A
\(\frac{5}{4}\)
B
\(\frac{-1}{4}\)
C
\(\frac{3}{4}\)
D
\(\frac{-5}{4}\)
Open complete paper
17
2021 · Mathematics · Calculus · Differentiation
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT

If \(y=\log \tan \left(\frac{x}{2}\right)+\sin ^{-1}(\cos x)\), then \(\frac{d y}{d x}=\)

A
\(\operatorname{cosec} x\)
B
\(\sin x+1\)
C
\(x\)
D
\(\operatorname{cosec} x-1\)
Open complete paper
18
2021 · Mathematics · Calculus · Differentiation
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT

If \(x=a \cos \theta, y=b \sin \theta\), then \(\left[\frac{d^2 y}{d x^2}\right]_{\theta=\frac{\pi}{4}}=\)

A
\(2\left(\frac{a^2}{b}\right)\)
B
\(\sqrt{2}\left(\frac{\mathrm{a}^2}{\mathrm{~b}}\right)\)
C
\(-2 \sqrt{2}\left(\frac{b}{a^2}\right)\)
D
\(2 \sqrt{2}\left(\frac{\mathrm{b}}{\mathrm{a}^2}\right)\)
Open complete paper
19
2021 · Mathematics · Calculus · Differentiation
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT

If \(h(x)=\sqrt{4 f(x)+3 g(x)}, f(1)=4, g(1)=3, f^{\prime}(1)=3, g^{\prime}(1)=4\), then \(h^{\prime}(1)=\)

A
\(\frac{5}{12}\)
B
\(\frac{12}{5}\)
C
\(\frac{-5}{12}\)
D
\(\frac{-12}{7}\)
Open complete paper
20
2021 · Mathematics · Calculus · Differentiation
MHT CET 2021 21TH SEPTEMBER EVENING SHIFT

If \(y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}\), then \({{dy} \over {dx}}\)

A
\({1 \over {1 + {x^2}}}\)
B
\({1 \over {\sqrt {1 - {x^2}} }}\)
C
\(- 1\)
D
None of these
Open complete paper

Showing 20 of 164 questions