A person invested ₹ 2,50,000 in a fund.… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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A person invested ₹ 2,50,000 in a fund. At the end of the year, the value of the fund is ₹ 3,00,000. If the market price is the same at the end of the year, then the nominal rate of return is

Official previous-year question

Held on 16 May 2025 · Verified 13 Jul 2026.

Options

A
10%
B
15%
C
20%
D
12%

Did you get this right?

Solution

Three points are given:
$(a₁, b₁)$ , $(a₂, b₂)$ , and $(a₁ + a₂, b₁ + b₂)$

These points are collinear, meaning they lie on the same straight line.

For three points to be collinear, the slope between any two pairs of points must be equal.

Finding the slope between $(a₁, b₁)$ and $(a₁ + a₂, b₁ + b₂)$ :

Slope $= \dfrac{(b₁ + b₂) - b₁}{(a₁ + a₂) - a₁}$

Slope $= \dfrac{b₂}{a₂}$

Finding the slope between $(a₂, b₂)$ and $(a₁ + a₂, b₁ + b₂)$ :

Slope $= \dfrac{(b₁ + b₂) - b₂}{(a₁ + a₂) - a₂}$

Slope $= \dfrac{b₁}{a₁}$

Since the points are collinear, the slopes must be equal:

$\dfrac{b₂}{a₂} = \dfrac{b₁}{a₁}$

Cross-multiplying:

$a₁b₂ = a₂b₁$

Therefore, the required condition is $a₁b₂ = a₂b₁$ .

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