For predicting the straight line trend… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

For predicting the straight line trend in the sales of cars (in thousands) on the basis of 5 consecutive years' data, the company makes use of a 3-year moving averages method. If the sales of the cars for respective years are 15, 24, 18, 33 and 42 respectively, then which of the following averages will not be computed?

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

A
19
B
25
C
32
D
31

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Solution

When a point divides the line joining points with position vectors $\vec{p}$ and $\vec{q}$ externally in the ratio $m : n$ , its position vector is:

$\vec{r} = \dfrac{m \cdot \vec{q} - n \cdot \vec{p}}{m - n}$

Here, $m = 2$ , $n = 1$ , $\vec{p} = \vec{a} - 2\vec{b}$ , $\vec{q} = 2\vec{a} + \vec{b}$

$\vec{r} = \dfrac{2(2\vec{a} + \vec{b}) - 1(\vec{a} - 2\vec{b})}{2 - 1}$

$= \dfrac{4\vec{a} + 2\vec{b} - \vec{a} + 2\vec{b}}{1}$

$= (4\vec{a} - \vec{a}) + (2\vec{b} + 2\vec{b})$

$= 3\vec{a} + 4\vec{b}$

The position vector of the required point is $3\vec{a} + 4\vec{b}$ .

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