Application of Derivatives PYQs - Last 10 Years
TS EAMCET / Mathematics / Calculus / 112 recent questions
MathematicsCalculus2016-2025
Practice 112 TS EAMCET 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
2020-2025
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Last 10 Years Application of Derivatives Questions
Showing 12 of 112 filtered questions.
1Application Of Derivatives
Consider the following statements
Statement I If $a_0+\frac{a_1}{2}+\frac{a_2}{3}+\ldots .+\frac{a_n}{n+1}=0$, where $a_0, a_1, \ldots, a_n$ are real numbers, then the polynomial $a_0+a_1 x+a_2 x^2+\ldots .+a_n x^n$ has a zero in the interv...
Statement I If $a_0+\frac{a_1}{2}+\frac{a_2}{3}+\ldots .+\frac{a_n}{n+1}=0$, where $a_0, a_1, \ldots, a_n$ are real numbers, then the polynomial $a_0+a_1 x+a_2 x^2+\ldots .+a_n x^n$ has a zero in the interv...
MCQ+1 / -02020
2Application Of Derivatives
$x_1, x_2 \in \mathbf{N}$. If a line having slope 2 is a tangent to the curve $y=x^4-6 x^3+13 x^2-10 x+5$ at points $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right)$, then $x_1 x_2+y_1 y_2=$
MCQ+1 / -02020
3Application Of Derivatives
If the tangent and normal drawn to the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$ at $P\left(\theta=\frac{\pi}{2}\right)$ cuts the $X$-axis at $A$ and $B$ respectively, then the area (in sq. units) of $\triangle P A B$ is
MCQ+1 / -02020
4Application Of Derivatives
Assertion (A) The function $f(x)=x-\log \left(\frac{1+x}{x}\right), x>0$ has no maximum.
Reason (R) If a function $f(x)$ is strictly increasing in an interval $(a, b)$, then at any point in $(a, b) f^{\prime}(x) \neq 0$
The correct option a...
Reason (R) If a function $f(x)$ is strictly increasing in an interval $(a, b)$, then at any point in $(a, b) f^{\prime}(x) \neq 0$
The correct option a...
MCQ+1 / -02020
5Application Of Derivatives
The volume of a sphere is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$. When its volume is $288 \pi \mathrm{cc}$, the rate of increase (in $\mathrm{cm} / \mathrm{sec}$ ) in its radius is
MCQ+1 / -02020
6Application Of Derivatives
The radius of a sphere is changing. At an instant of time the rate of change in its volume and its surface area are equal. Then the value of radius at that instant is?
MCQ+1 / -02020
7Application Of Derivatives
Let $P(x)$ be a polynomial of degree 3 having extreme value at $x=1$. If $\mathop {\lim }\limits_{x \to 0}\left(\frac{P(x)+4}{x^2}+2\right)=6$, then $\left(\frac{d P}{d x}\right)_{x=\frac{1}{2}}=$
MCQ+1 / -02020
8Application Of Derivatives
Let $a$ be a fixed positive real number and $n$ be an arbitrary constant. For the curve $y=\frac{x^n}{a^{n-1}}$, if the length of the subnormal at any point $(\alpha, \beta)$ is proportional to $a^2$, then $n=$
MCQ+1 / -02020
9Application Of Derivatives
If the area of a circle increases at the rate of $\frac{1}{\sqrt{\pi}}$ sq. units/sec, then the rate (in units/sec) at which the perimeter of the circle changes, when perimeter is $\sqrt{\pi}$ units, is
MCQ+1 / -02020
10Application Of Derivatives
\(\text { Match the functions of List I with the items of List II. }\)
List I
List II
A.
3
x
4
−
2
x
3
−
6
x
2
+
6
x
+
1
3
x
4
−
2
x
3
...
List I
List II
A.
3
x
4
−
2
x
3
−
6
x
2
+
6
x
+
1
3
x
4
−
2
x
3
...
MCQ+1 / -02020
11Application Of Derivatives
A tank in the shape of a rectangular parallelopiped has volume 27 cubic meters. This tank is filled with water such that the rate of change of level of the water is thrice the rate of change water quantity falling in the tank, then the heig...
MCQ+1 / -02020
12Application Of Derivatives
If $\frac{k}{\alpha^3}$ is the length of the sub normal at any point $P(\alpha, y)$ on the curve $x^2-a^2=\frac{x^2 y^2}{a^2}$, then $k=$
MCQ+1 / -02020