# Application of Derivatives · Mathematics · AP EAPCET

Start Practice## MCQ (Single Correct Answer)

AP EAPCET 2021 - 20th August Morning Shift

If $$y=4 x-6$$ is a tangent to the curve $$y^2=a x^4+b$$ at $$(3,6)$$, then the values of $$a$$ and $$b$$ are

AP EAPCET 2021 - 20th August Morning Shift

Find the positive value of $$a$$ for which the equality $$2 \alpha+\beta=8$$ holds, where $$\alpha$$ and $$\beta$$ are the points of maximum and minim...

AP EAPCET 2021 - 20th August Morning Shift

If the radius of a sphere is measured as 9 cm
with an error of 0.03 cm, then find the
approximate error in calculating its surface
area.

AP EAPCET 2021 - 20th August Morning Shift

The diameter and altitude of a right circular
cone, at a certain instant, were found to be
10 cm and 20 cm respectively. If its diameter
is increasing...

AP EAPCET 2021 - 19th August Evening Shift

Given, $$f(x)=x^3-4x$$, if x changes from 2 to 1.99, then the approximate change in the value of $$f(x)$$ is

AP EAPCET 2021 - 19th August Evening Shift

If the curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect at right angles, then $$a^2$$ is equal to

AP EAPCET 2021 - 19th August Evening Shift

Let $$x$$ and $$y$$ be the sides of two squares such that, $$y=x-x^2$$. The rate of change of area of the second square with respect to area of the fi...

AP EAPCET 2021 - 19th August Evening Shift

If $$f^{\prime \prime}(x)$$ is a positive function for all $$x \in R, f^{\prime}(3)=0$$ and $$g(x)=f\left(\tan ^2(x)-2 \tan (x)+4\right)$$ for $$0 ...

AP EAPCET 2021 - 19th August Morning Shift

The line which is parallel to X-axis and crosses the curve $$y=\sqrt x$$ at an angle of 45$$\Upsilon$$ is

AP EAPCET 2021 - 19th August Morning Shift

If the error committed in measuring the
radius of a circle is 0.05%, then the
corresponding error in calculating its area
would be

AP EAPCET 2021 - 19th August Morning Shift

The stationary points of the curve $$y=8 x^2-x^4-4$$ are

AP EAPCET 2021 - 19th August Morning Shift

The distance between the origin and the normal to the curve $$y=e^{2 x}+x^2$$ drawn at $$x=0$$ is units