Which of the following is correct about the compound annual growth rate(CAGR)? - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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Which of the following is correct about the compound annual growth rate(CAGR)?

Official previous-year question

Held on 21 May 2025 · Verified 13 Jul 2026.

Options

A
CAGR is calculated by only the final value of an investment.
B
CAGR is calculated by the final and beginning value of an investment.
C
CAGR describes the effect of simple interest.
D
CAGR is calculated by taking arthmetic mean of series of returns.

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Solution

The region is bounded by the parabola $x^2 = y$ (opening upward, vertex at origin) and the horizontal line $y = 4$ , in the first quadrant where $x \geq 0$ and $y \geq 0$ .

Setting $y = 4$ in $x^2 = y$ :

$x^2 = 4$

$x = 2$ (first quadrant)

The curves meet at $(2, 4)$ .

In the region from $x = 0$ to $x = 2$ :

Top curve: $y = 4$
Bottom curve: $y = x^2$

$A = \int_0^2 (4 - x^2)\, dx$

$A = \left[4x - \dfrac{x^3}{3}\right]_0^2$

$= \left(4(2) - \dfrac{(2)^3}{3}\right) - \left(0 - 0\right)$

$= 8 - \dfrac{8}{3}$

$= \dfrac{24 - 8}{3}$

$= \dfrac{16}{3}$

The area of the region $= \dfrac{16}{3}$ square units.

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