Calculus

Application of Derivatives

Medium

common

The maximum area of a rectangle inscribed in a circle of radius $3\sqrt{2}$ cm, is:

$12\sqrt{3}$ Sq. units

36 Sq. units

$48\sqrt{2}$ Sq. units

$36\sqrt{2}$ Sq. units

✅ Correct Option: 2

The diagonal of the rectangle is the diameter $2r$ . With sides $a, b$ and $a^2+b^2 = 4r^2$ , area $ab$ is maximum when $a = b$ (a square), giving area $2r^2 = 2(3\sqrt{2})^2 = 36$ sq. units.

2026: 19 May Shift 1

If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, then the area of the triangle is maximum when angle between them is:

2026: 19 May Shift 1

The absolute maximum value of the function $f(x) = 2x^3 - 15x^2 + 36x + 7$ on the interval [1,5] is

2022: 6 Aug Shift 2

The maximum slope of the tangents to the curve $y(x) = -x^3 + 3x^2 + 9x - 30$ is

2025: 2 June Shift 1

If maximum value of $f(x) = 2x^3 + 3x^2 - 6ax + 10$ occurs at $x = -3$ , then the value of $\alpha$ is ____

2025: 21 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Maximum value of $f(x) = \sin^2 x - \cos^2 x$ , $\forall x \in (\pi, 2\pi)$ is	(I) 0
(B) Minimum value of $f(x) = \sin x \cos x$	(II) 1
(C) Point of Minima of $f(x) = x^x$ $(x > 0)$	(III) $-\frac{1}{2}$
(D) Maximum value of $f(x) = -x^{2026}$	(IV) $\frac{1}{e}$

Choose the correct answer from the options given below:

2026: 15 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Function)		LIST-II (Critical point)
A.	$y = x^2 + x + 1$	I.	$2/3$
B.	$y = 2x^3 - 6x^2 + 6x$	II.	$-1$
C.	$y = 2x^2 + 4x - 1$	III.	$-1/2$
D.	$y = x^3 - x^2$	IV.	$1$

Choose the correct answer from the options given below:

The maximum area of a rectangle inscribed in a circle of radius 323\sqrt{2}32​ cm, is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The maximum area of a rectangle inscribed in a circle of radius $3\sqrt{2}$ cm, is: