The five month moving averages for the following data | Month ($r^{th}$) | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | |---|---|---|---|---|---|---|---|---|---| | Actual Demand | 105 | 106 | 110 | 110 | 114 | 121 | 130 | 128 | 137 | is:

The five month moving averages for the… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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The five month moving averages for the following data

Month ( $r^{th}$ )	43	44	45	46	47	48	49	50	51
Actual Demand	105	106	110	110	114	121	130	128	137

is:

Official previous-year question

Held on 27 May 2025 · Verified 13 Jul 2026.

Options

A
109, 112.2, 117, 120.6, 126
B
109, 112, 117, 123, 128
C
109, 112, 119, 126, 135
D
109, 112.2, 117, 120, 131

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Solution

The angle between two lines is the angle between their direction vectors.

For the first line, the direction vector is $\vec{v}_1 = 2\hat{i} + 1\hat{j} + 2\hat{k}$ , and for the second line, it is $\vec{v}_2 = 6\hat{i} - 3\hat{j} + 2\hat{k}$ .

The cosine of the angle $\theta$ is given by the formula $\cos \theta = \frac{|\vec{v}_1 \cdot \vec{v}_2|}{|\vec{v}_1| |\vec{v}_2|}$ .

Calculating the dot product gives $(2)(6) + (1)(-3) + (2)(2) = 12 - 3 + 4 = 13$ .

The magnitude of the first vector is $\sqrt{2^2 + 1^2 + 2^2} = \sqrt{9} = 3$ .

The magnitude of the second vector is $\sqrt{6^2 + (-3)^2 + 2^2} = \sqrt{36 + 9 + 4} = \sqrt{49} = 7$ .

Substituting these into the formula, we get $\cos \theta = \frac{13}{3 \times 7} = \frac{13}{21}$

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