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Previous year question hub

Application Of Derivatives - Calculus - Mathematics Previous Year Questions

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

3Papers
3Years
7Questions
1Topics

Application Of Derivatives question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Application Of Derivatives. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 7 100%

Question type distribution

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

Multiple Choices 7 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
7 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
7 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Derivatives
7 Qs

Paper coverage

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

IAT IISER 2024
2 Qs
IAT IISER 2023
2 Qs
IAT IISER 2022
3 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
IAT IISER 202420242View paper
IAT IISER 202320232View paper
IAT IISER 202220223View paper

All Application Of Derivatives previous year questions

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

1
2022 · Mathematics · Calculus · Application Of Derivatives
IAT IISER 2022
Let $a$ be a nonzero real number and $f: \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function such that $f^{\prime}(x)>0$ for all $x \in R$. Consider $g(x)=f\left(2 a^2 x-a x^2\right)$. Then $g$ has
A
Local maxima at $x=a$ if $a>0$
B
Local maxima at $x=a$ if $a<0$
C
Local minima at $x=a$ if $a>0$
D
A point of inflection at $x=a$
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2
2022 · Mathematics · Calculus · Application Of Derivatives
IAT IISER 2022
The function given by $f(x)=2 x^3-15 x^2+36 x-5$ is
A
Increasing on the interval $(0,2)$
B
Decreasing on the interval $(-3,0)$
C
Increasing on the interval $(2,3)$
D
Decreasing on the interval $(3, \infty)$
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3
2022 · Mathematics · Calculus · Application Of Derivatives
IAT IISER 2022

Let $f(x)=a_n x^n+a_{n-1} x^{n-1}+\cdots+a_1 x+a_0$ be a polynomial. Suppose that $f(0)=0$,

$$\left.\left.\frac{d f}{d x}\right]_{x=0}=1, \frac{d^2 f}{d x^2}\right]_{x=0}=4$$

and

$$\frac{d^3 f}{d x^3}=\frac{d^5 f}{d x^5}$$

Then $f(5)=$

A
25
B
35
C
55
D
105
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4
2023 · Mathematics · Calculus · Application Of Derivatives
IAT IISER 2023
Let $f(x)=\sin (3 x), x \in\left[0, \frac{\pi}{2}\right]$. Which of the following statements is true
A
$f$ is increasing on $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$.
B
$f$ is decreasing on $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$
C
$f$ is increasing on $\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$ and decreasing on $\left(\frac{\pi}{3}, \frac{\pi}{2}\right)$.
D
$f$ is decreasing on $\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$ and increasing on $\left(\frac{\pi}{3}, \frac{\pi}{2}\right)$.
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5
2023 · Mathematics · Calculus · Application Of Derivatives
IAT IISER 2023
Let $\alpha$ be a real number. What is the total number of distinct point(s) of intersection between the parabola $y=x^2+4 x \sin \alpha+6$ and the pair of lines $y^2=1$ ?
A
Zero
B
One
C
Two
D
Four
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6
2024 · Mathematics · Calculus · Application Of Derivatives
IAT IISER 2024
What is the largest area of a rectangle, whose sides are parallel to the coordinate axes, that can be inscribed under the graph of the curve $y=1-x^2$ and above the $x$-axis?
A
$\frac{2}{3 \sqrt{3}}$
B
$\frac{4}{3 \sqrt{3}}$
C
$\frac{1}{3}$
D
$\frac{4}{3}$
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7
2024 · Mathematics · Calculus · Application Of Derivatives
IAT IISER 2024
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a strictly decreasing function with $|f(t)|<\pi / 2$ for all $t \in \mathbf{R}$. Let $g:[0, \pi] \rightarrow$ R be a function defined by $g(t)=\sin (f(t))$. Which one of the following statements is Correct?
A
$g$ is increasing on $[0, \pi]$.
B
$g$ is decreasing on $[0, \pi]$.
C
$g$ is increasing on $(0, \pi / 2)$ and decreasing on $(\pi / 2, \pi)$.
D
$g$ is decreasing on $(0, \pi / 2)$ and increasing on $(\pi / 2, \pi)$.
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