JEE 2022 — Mathematics PYQ
JEE | Mathematics | 2022The number of solutions of the equation in the interval is ________.
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The number of solutions of the equation in the interval is ________.
1. Quadratic in Sine
Using the quadratic formula for :
Since , we must take .
2. Finding the Number of Solutions
The interval is . Note that , , and .
In , there are 2 solutions (where is positive).
In , there are 0 solutions (where is negative).
In , there are 2 solutions (positive cycle).
is , and is slightly more. We check if another solution exists before : The next positive cycle starts at , and the solutions are at roughly and . would be > 10.
Total solutions = 2 (from first cycle) + 2 (from second cycle) = 4.