Mr. Mittal invested Rs. 20,000 in a… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

Mr. Mittal invested Rs. 20,000 in a mutual fund in the year 2019. The value of the mutual fund increased to Rs. 32,000 in the year 2024. The compound annual growth rate of his investment is:

[Given $(1.6)^{1/5} = 1.098$ ]

Official previous-year question

Held on 19 May 2025 · Verified 13 Jul 2026.

Options

A
8.5%
B
10%
C
9.8%
D
9.1%

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Solution

When a matrix is raised to a power, the determinant is also raised to that same power.

$|A^3| = |A|^3$

Given that $|A^3| = 64$ :

$|A|^3 = 64$

$|A| = \sqrt[3]{64}$

$|A| = 4$

For a 2×2 matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ , the determinant is $ad - bc$ .

For matrix $A = \begin{bmatrix} p & -3 \\ -4 & p \end{bmatrix}$ :

$|A| = (p)(p) - (-3)(-4)$

$|A| = p^2 - 12$

Since $|A| = 4$ :

$p^2 - 12 = 4$

$p^2 = 16$

$p = \pm 4$

Therefore, the value of $p$ is $\pm 4$ .

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