A container contains 100 liters of milk.… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Arithmetic

2025mcqmedium

A container contains 100 liters of milk. From this container, 10 liters of milk is taken out and replaced by water. This process is repeated two more times.The amount of milk left in the container now is:

Official previous-year question

Held on 16 May 2025 · Verified 13 Jul 2026.

Options

A
85 liters
B
70 liters
C
67.1 liters
D
72.9 liters

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Solution

Given:

$|\vec{a}| = 1$ (unit vector)
$|\vec{b}| = 1$ (unit vector)
$|\vec{a} + \vec{b}| = 1$ (unit vector)

For the magnitude of a vector sum:

$|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + 2\vec{a} \cdot \vec{b}$

Since $|\vec{a} + \vec{b}| = 1$ , $|\vec{a}| = 1$ , and $|\vec{b}| = 1$ :

$1 = 1 + 1 + 2\vec{a} \cdot \vec{b}$

$1 = 2 + 2\vec{a} \cdot \vec{b}$

$2\vec{a} \cdot \vec{b} = -1$

$\vec{a} \cdot \vec{b} = -\frac{1}{2}$

For the magnitude of a vector difference:

$|\vec{a} - \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 - 2\vec{a} \cdot \vec{b}$

$|\vec{a} - \vec{b}|^2 = 1 + 1 - 2\left(-\frac{1}{2}\right)$

$|\vec{a} - \vec{b}|^2 = 2 + 1$

$|\vec{a} - \vec{b}|^2 = 3$

$|\vec{a} - \vec{b}| = \sqrt{3}$

Therefore, the magnitude of $\vec{a} - \vec{b}$ is $\sqrt{3}$ .

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