A startup company invested ₹ 5,00,000 in… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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A startup company invested ₹ 5,00,000 in shares for 4 years. The value of the investment was ₹ 5,50,000 at the end of first year, ₹ 5,25,000 at the end of third year, and on maturity, the final value stood ₹ 6,25,000. The CAGR on the investment will be :- [Given : $(1.25)^{\frac{1}{4}} = 1.06$ ]

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
10.7%
B
6%
C
5%
D
12.2%

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Solution

The edge of a cube is increasing at a rate of $7$ cm/s, so $\frac{da}{dt} = 7$ cm/s.

The edge length at this moment is $a = 3$ cm.

A cube has 6 faces, each face is a square with area $a^2$ .

Surface Area $A = 6a^2$

Differentiating both sides with respect to time $t$ :

$\frac{dA}{dt} = 6 \times 2a \times \frac{da}{dt}$

$\frac{dA}{dt} = 12a \times \frac{da}{dt}$

Substituting $a = 3$ cm and $\frac{da}{dt} = 7$ cm/s:

$\frac{dA}{dt} = 12 \times 3 \times 7$

$\frac{dA}{dt} = 36 \times 7$

$\frac{dA}{dt} = 252$ cm²/s

Therefore, the rate of change of surface area of the cube is $252$ cm²/s.

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