Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202123 Sep 2021Morning ShiftMathematicsApplication of DerivativesActual

The maximum area of the rectangle that can be inscribed in a circle of radius r is

Options

  1. A2 r^2 sq. units
  2. Br ^2 4 sq. units
  3. Cr ^2 units
  4. Dr^3 sq units

Correct answer

A. 2 r^2 sq. units

Step-by-step solution

Refer figure aligned & B =( r , r ) & Ab 2 r and BC =2 r & Area ( ABCD )= AB BC & f ( )=(2 r )(2 r )=2 r ^2 2 & f ^ ( )=4 r ^2 2 and when f ^ ( )=0 , we write & 2 =0 2 = 2 = 4 & f ^ ( )=-8 r ^2 2 and f ^ ( )_ [ = 4 ] =-8 r ^2 < 0 aligned Thus, area of required rectangle is maximum when = 4 aligned & AB =2 r 4 =2 r ( 1 2 )= 2 r and & BC =2 r 4 =2 r ( 1 2 )= 2 r aligned Maximum Area ( ABCD )==( 2 r )( 2 r )=2 r ^2

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least 2025The difference between the absolute maximum and absolute minimum values of the function f(x)=2 x^3-15 x^2+36 x-30 on [-1,4] is 2025If f(x)=x e^ x(1-x) , x R , then f(x) is 2025The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025If the tangent of the curve 4 y^3=3 a x^2+x^3 drawn at the point (a, a) forms a triangle of area 25 24 sq.units with the coordinate axes then a = 2025If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025If the Lagrange's mean value theorem is applied to the function f(x)=e^x defined on the interval [1,2] and the value of c (1,2) is k , then e^ k-1 = 2025If the tangent to the curve x y+a x+b y=0 at (1,1) makes an angle Tan ⁻¹ 2 with X -axis, then ab a + b = 2025 Full Application of Derivatives list All MHT CET PYQs