As per the graph given below: ![](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/afterboards-pyq/b6644b5e3411e161.webp) Match List-I with List-II | List-I | List-II | |---|---| | (Function/Area/point) | (Representation) | | (A) Consumers Surplus | (I) y=g(x) | | (B) Supply function | (II) v | | (C) Demand function | (III) s | | (D) Equilibrium point | (IV) y=f(x) | Choose the correct answer from the options given below:

As per the graph given below: Match… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

As per the graph given below:

Match List-I with List-II

List-I	List-II
(Function/Area/point)	(Representation)
(A) Consumers Surplus	(I) y=g(x)
(B) Supply function	(II) v
(C) Demand function	(III) s
(D) Equilibrium point	(IV) y=f(x)

Choose the correct answer from the options given below:

Official previous-year question

Held on 27 May 2025 · Verified 13 Jul 2026.

Options

A
(A) - (III), (B) - (IV), (C) - (I), (D) - (II)
B
(A) - (IV), (B) - (III), (C) - (II), (D) - (I)
C
(A) - (III), (B) - (I), (C) - (IV), (D) - (II)
D
(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

Did you get this right?

Solution

Given $\vec{a}$ is a unit vector, so $|\vec{a}| = 1$

Also given: $(\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = 15$

Expanding the dot product:

$(\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a})$

$= \vec{x} \cdot \vec{x} + \vec{x} \cdot \vec{a} - \vec{a} \cdot \vec{x} - \vec{a} \cdot \vec{a}$

Since the dot product is commutative, $\vec{x} \cdot \vec{a} = \vec{a} \cdot \vec{x}$ , the middle terms cancel:

$= \vec{x} \cdot \vec{x} - \vec{a} \cdot \vec{a}$

$= |\vec{x}|^2 - |\vec{a}|^2$

Since $|\vec{a}| = 1$ :

$|\vec{x}|^2 - 1 = 15$

$|\vec{x}|^2 = 16$

$|\vec{x}| = 4$

Therefore, $|\vec{x}| = 4$

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