New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Derivatives question

2016 · Shift 0 · Q30

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Application of Derivatives
2016 · Shift 0 · Q30

Application of Derivatives question

2016 · Shift 0 · Q30

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

A wire of length

2

units is cut into two parts which are bent respectively to form a square of side

=x

units and a circle of radius

=r

units. If the sum of the areas of the square and the circle so formed is minimum, then:

A
$x=2r$
B
$2x=r$
C
$2x = \left( {\pi + 4} \right)r$
D
$\left( {4 - \pi } \right)x = \pi \,\, r$

More from Application of Derivatives

Let $f (x)$ be a polynomial of degree four having extreme values at $x = 1$ and $x = 2$ . If $x \to 0 lim [1 + \frac{f ( x )}{x ^{2}}] = 3$ , then f $(2)$ is equal to :2015 · MCQ
If $x = - 1$ and $x = 2$ are extreme points of $f (x) = α lo g ∣ x ∣ + β x^{2} + x$ then2014 · MCQ
The real number $k$ for which the equation, $2 x^{3} + 3 x + k = 0$ has two distinct real roots in $[0, 1]$ 2013 · MCQ
Let $a, b \in R$ be such that the function $f$ given by $f (x) = I n ∣ x ∣ + b x^{2} + a x, x e 0$ has extreme values at $x = - 1$ and $x = 2$ Statement-1 : $f$ has local maximum at $x = - 1$ and at $x = 2$ . Statement-2 : $a = \frac{1}{2}$ …2012 · MCQ
A line is drawn through the point $P$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle $O P Q,$ where $O$ is the origin. If the area of the triangle $O P Q$ is least, then the slope of the line $P Q$ is :2012 · MCQ
A spherical balloon is filled with $4500 π$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 π$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the…2012 · MCQ
For $x \in (0, \frac{5 π}{2}),$ define $f (x) = 0 \int x t sin t d t .$ Then $f$ has2011 · MCQ
Let $f : R \to R$ be defined by $f (x) = {k - 2 x, i f 2 x + 3, i f x \leq - 1 x > - 1$ If $f$ has a local minimum at $x = - 1$ , then a possible value of $k$ …2010 · MCQ