Application of Derivatives PYQs - Last 5 Years
IAT (IISER) / Mathematics / Calculus / 7 recent questions
MathematicsCalculus2020-2024
Practice 7 IAT (IISER) Mathematics questions from Application of Derivatives. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Calculus
2022-2024
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7 in last 5 years7 in last 10 years
Last 5 Years Application of Derivatives Questions
Showing 7 of 7 filtered questions.
1Application Of Derivatives
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?
MCQ+4 / -12024
2Application Of Derivatives
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...
MCQ+4 / -12024
3Application Of Derivatives
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 $y^2=1$ ?
MCQ+4 / -12023
4Application Of Derivatives
Let $f(x)=\sin (3 x), x \in\left[0, \frac{\pi}{2}\right]$. Which of the following statements is true
MCQ+4 / -12023
5Application Of Derivatives
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
MCQ+4 / -12022
6Application Of Derivatives
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 $f(5)=$
\(\left.\left.\frac{d f}{d x}\right]_{x=0}=1, \frac{d^2 f}{d x^2}\right]_{x=0}=4\)
and
\(\frac{d^3 f}{d x^3}=\frac{d^5 f}{d x^5}\)
Then $f(5)=$
MCQ+4 / -12022
7Application Of Derivatives
The function given by $f(x)=2 x^3-15 x^2+36 x-5$ is
MCQ+4 / -12022