JEE 2022 — Mathematics PYQ

Q: How do I solve JEE 2022 Mathematics questions?

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Question

JEE 2022 — Mathematics PYQ

JEE | Mathematics | 2022

The number of solutions of the equation $2 θ - cos^{2} θ + 2 = 0$ in $R$ is equal to:

Choose the correct answer:

Explanation

Solution

Explanation: Given equation:

2\theta - \cos^2 \theta + \sqrt{2} = 0

\implies \cos^2 \theta = 2\theta + \sqrt{2}

Let's draw the graph of the two functions separately to find the points of intersection:

Curve 1: $y = \cos^2 \theta$
Curve 2: $y = 2\theta + \sqrt{2}$

By observing the graphs:

The function $y = \cos^2 \theta$ oscillates between $0$ and $1$ .
The function $y = 2\theta + \sqrt{2}$ is a straight line with a positive slope.
Both graphs intersect at exactly one point.

$\therefore$ The number of solutions for the given equation is 1.

Choose the correct answer:

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