In which of the following, the time… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqeasy

In which of the following, the time series may show the gradual shifts to relatively higher or lower values over a long period of time?

Official previous-year question

Held on 13 May 2025 · Verified 13 Jul 2026.

Options

A
Cyclical component
B
Irregular component
C
Seasonal component
D
Trend component

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Solution

Since $\vec{a}$ is perpendicular to $\vec{b}$ , their dot product is zero:
$\vec{a} \cdot \vec{b} = 0$

Given:
$\vec{a} = (\sin \theta)\hat{i} + (\cos \theta)\hat{j}$
$\vec{b} = \hat{i} - \sqrt{3}\hat{j}$

Taking the dot product:
$(\sin \theta)(1) + (\cos \theta)(-\sqrt{3}) = 0$
$\sin \theta - \sqrt{3}\cos \theta = 0$
$\sin \theta = \sqrt{3}\cos \theta$
$\tan \theta = \sqrt{3}$

Since $\theta$ is an acute angle:
$\theta = \frac{\pi}{3}$

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